ML20055D971
| ML20055D971 | |
| Person / Time | |
|---|---|
| Issue date: | 07/05/1990 |
| From: | Aggarwal S NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES) |
| To: | John Thomas EQUIPMENT QUALIFICATION ADVISORY GROUP |
| References | |
| NUDOCS 9007100212 | |
| Download: ML20055D971 (81) | |
Text
-
JUL 0 A 1990 Mr. James E. Thomas, Program Manager EQAG Steering Committee
- Duke Power Company 422 South Church Street P.O. Box 33189 l
Charlotte, NC 28242:
SUBJECT:
UTILITY' REVIEW 0F NRC DRAFT REPORT NUREG/CR-XXXX, " DEGRADATION MODELING' WITH APPLICATION TO AGING AND MAINTENANCE EFFECTIVENESS EVALUATIONS" i
Dear Mr. Thr ias:
Enclosed for your review and comment is a' final draft of the subject report.
I would welcome any comments your. utility review group may have.
Comments will be most helpful if received by me by August 6, 1990.
Sincerely,
. Originalsigned by Satish K. Agganval Satish K. Aggarwal, Program Manager l-Electrical & Mechanical Engineering Branch Office of Nuclear Regulatory Research
Enclosure:
As stated cc: G.Sliter,EPRI(w/ encl)
J. H. Taylor, BNL (w/o enc 1)
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4 NUREG/CR-BNL-NUREG-DEGRADATION MODFLING WITH APPIJCATION TO AGING AND MAINTENANCE EFFECTIVENESS EVALUATIONS Prepared by PX Samanta, W.E. Veuly', F. lisu, and M. Subudhi Brookhaven National Imboratory
- Science Applications International Corporation Prepared for U.S. Nuclear Regulatory Commission
'L NUREG/CR-BNL-NUREG-l sj i
-l DEGRADATION MODELING WITII APPIlCATION TO AGING AND MAINTENANCE EFFECI'IVENESS EVALUATIONS-
.i Manuscript Completed:
Date Published:
Prepared by P.K. Samanta, W.E. Vescly*, F. Hsu, and M. Subudhi S. K. Aggarwal, NRC Program Manager 3
Brookhaven National Laboratory Upton, NY 11973
' Science Applications International Corporation Prepared for Didsion of Engineering Omce of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555 NRC FIN A3270 l
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=,
AHSTRACT 1
i This report describes a degradation modeling approach to analyze data on compo-nent degradation and failure to understand the processes in aging of components. As used here, degradation modeling is the analysis of information on component degrada-tion in. order to develop models of the process and its implications. This particular modeling focuses on the analysis of the times of component degradations, to model j
how the rate of degradation changes with the age of the conponent. The methodology _
presented also discusses the effectiveness of maintenance as applicable to aging evalu-ations.
The specific applications which are performed show quaititative models of com-ponent degradation rates and component failure rates from pl mt-specific data. The sta-tistical techniques which were developed and applied allow aging trends to be effec-tively identified in the degradation data, and in the failure data. Initial estimates of the effectiveness of maintenance in limiting degradations from becoming failures also were developed. These results are important first steps in degradation modeling, and show that degradation 'can be modeled to identify aging trends.
l i
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i lii
-f CONTENTS Page ABSTRACT.........................................
- iii AC KN OWLEDG MENTS...
vil i
EXECUTIVE S UMM ARY,
ix l
- 1. INTRO DU CTION...................................
I
- 2. CONCEPT AND OBJECTIVES OF DEGRADATION MODELING......
3
- 3. METHODOLOGY: DEGRADATION MODELING APPROACHES......
5 L
'3.l State Representation' of Degradation Modeling................
5 l
3.2 Transition Probabilities...............................
7 i
3.3 Degradation Frequency, Failure Frequency and Transition Probabilities....................................
7 3.4 Incorporation of Aging Effects in Degradation Modeling..........
8 3.5 Aging Effect on Degradation Rate.......................
9 i
3.6 Basic Steps in Degradation Modeling.....................
10
- 4. REGRESSION ANALYSIS USING COX'S MODEL TO ESTIMATE AGING RATES (DEGRADATION AND FAILURE RATES)..........
I1-i 4.1 Introd uc tion.................................... -
11 4.2 Cox's Model to Develop Aging Rates.....................
11 I
4.3 The Regression Approach............................
13 1
1
- 5. RESULTS AND INTERPRETATION OF AGE-RELATED DEGRADATION ~ AND FAILURE DATA.....................
19 5.1 Analysis Approach................................ 5.2. Aging Effect on Degradation..........................
20 5.3 Aging Effect on Failures.............................
21
' 5.4 Aging Evaluation Using Degradation and Aging-Failure Rate.......
23 5.5 Maintenance Effectiveness Evaluation.....................
25
- 6.
SUMMARY
AND INSIGHTS OF DEGRADATION MODELING AN ALY S I S,................................... -..
29
- 7. REFERE N CES.....................................
31' APPENDIX-A. MATHEMATICAL DEVELOPMENT OF' DEGRADATION MODELING APPRO ACHES.....................
A-1 APPENDIX B. AGING DEGRADATION AND FAILURE DATA BASE B-1 APPENDIX C. STATISTICAL TESTS FOR USE OF DATA FROM DIFFERENT RHR PUMPS IN DEGRADATION AND FAILURE RATE AN ALYSES....................
C-1 y
l 1
-),
'k
' APPENDIX-D. ESTIMATION OF AGING EFFUCT ON DEGRADATION AND FAILURES AND~ MAINTC3ANCE EFFECTIVENESS
. EVALUATION FOR RHR PUMPS................ -. :
D-1 APPENDIX E. ANALYSIS OF AGE-RELATED DEGRADATION
.I
'AND FAILURE DATA FROM SERVICE WATER -
(S W) P U M P...............................
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ACKNOWLEDGMENTS The'. authors wish to acknowledge Mr. S.= Aggarwal and Mr. J. Vora, of USNRC, for.
- their support during this project.
The report also benefited from reviews by the following individuals: D. Rasmuson of USNRC, and-J. Taylor, J. Boccio, and R. IIall of Brookhaven National Laboratory.
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EXECUTIVE
SUMMARY
This report describes new. work which is called degradation modeling. As used here degradation modeling is the analysis of information on component degradation in order to develop models of the degradation process and its implications. The particular degradation modeling focuses on the analysis of the times of component degradations, to model how the
- degradation rate changes with the age of the component. The times of degradation which are analyzed include times of degraded failures, and times of corrective maintenance. Failures of components also are analyzed to model how this rate changes with component's age. The models of the changes in degradation rate and failure rate with age are important results in a
.themselves, since they quantify the aging reliability behavior of the component.
However, the work goes beyond an analysis of times of degradation and failure. Thus, theoretical models are developed which relate the degradation rate of the component to its -
failure rate. With these relationships, information on component degradations can be used to predict the implications on the component failure rate. Specifically, with this methodology, aging trends in the component degradation rate can be used to predict future aging trends in the component failure rate.
The capability of making such a prediction is important for several reasons. Component aging failure rates are required to quantify the core-melt frequency effects and risk effects from aging and also to quantify the effectiveness of a given maintenance program in controlling aging impacts on the core-melt frequency and risk. However, failure data is often sparse. On the other hand, degradation data is more abundant because degradations occur at 4
a higher rate than failures. Thus, the methodology developed in this report allows component aging failure rates to be estimated from component degradation rates. This ability has the potential of greatly increasing the accuracy and availability of component aging failure rates,_
which can be used in risk evaluations of aging effects.
As importantly, the methodology allows maintenance indicators to be constructed which relate component degradations to reliability and risk impacts. When the degradation indica-tors become severe enough, implying significant impacts on the component failure rate and resulting risk, then maintenance needs to be performed to correct the degradations. Thus, the degradation indicators can provide a practical and effective means of monitoring condition.
Furthermore, by monitoring the effectiveness of maintenance, degradations can be corrected
{
before having significant implications for reliability and risk.
The specific applications which are performed develop quantitative models of compo-nent degradation rates and component failure rates from plant-specific data. As part of the data analysis, statistical techniques are developed which identify aging trends in failure and degradation data. The aging trends can be of any shape and can exist in any segment of the 4
data. The figure below illustrates the quantified degradation rate that is obts.ed for RHR pumps: a definite " bathtub" curve is identified, with a distinct, increasing aging trend I
occurring in later ages. The corresponding RHR pump failure rate has not yet shown the aging trend which is indicated in the degradation rate.
1' 1~
xx
i
.I Degradation Rate h( # per quarter)
I"l o l-S4.6 4
\\
33.12 20.09
-~
Estimated Deg.. Rate 3
1 12.1B 95% confidence bounds 7.39 4,43 Data Method 1 - Combining -, y' O.37
. Quasi Cubic spline fit -
1 1.66
, co 061
/
~~
0.37
/
~
~1
~~
o.22 f.
0.14
-2
~
0.08 0.06
- 0.03 0.02
-4 0
10 20 30 40 Age in Quarters (a month periods) j Age dependent degradation rate i
(Component: RHR pumps 3 plant data)
The statistical techniques which were developed allow aging trends-to be efficiently identified in the degradation and failure data. Initial estimates of maintenance effectiveness in. limiting degradations from becoming failures'also were developed. These results'are
. important first steps in showing that degradations can be modeled to identify aging effects.
The theoretical methodology which is developed is another advancement in that degradation characteristics are etplicitly related to failure-rate effects, and hence,' ultimately to risk-effects. The next step is to use the methodology and statistical techniques to develop and validate practical procedures for predicting aging failure rates from degradation data. This ability would provide,)owerful tools for analyzing aging effects in degradation data and for 1
predicting their implic1tions for reliability and risk.
X I
o
- 1. INTRODUCTION i
The assessment of risk associated with aging in nuclear power plants encompasses many facets, of which an important element is the understanding of the aging phenomena l
associated with components of safety systems. We study the aging phenomena at the
{
component or sub-component level so that we can develop an aging reliability model representing the aging process experienced by components in nuclear plants under existing test and maintenance practices. In this study, we present an approach to analyze component degradation and failure data to understand the aging process, and also to evaluate the effectiveness of maintenance in preventing age-related failures.
The study of aging at the component level can be broadly divided between two types of components - active components (e.g., pumps, valves, and circuit breakers), and passive components (e.g., structures and pipes), in this report, the primary focus is on active components, although the approaches that are presented can also be explored for application to passive components.
l Study of aging characteristics at the component level is an assessment of the deteriora-_
(
tion of component reliability with time, and an identification of the activities or processes that could mitigate such deterioration. Reliability analyses are typically, focused on deter-mining aging failure rate with time. Analyses of data on plant experience indicate that components experience various forms of degradation that are detected and corrected through testing and maintenance. This study presents an approach to using information on compo-nent degradation to understand aging reliability characteristics of components. Incorporation of component degradation characteristics in an aging reliability model (which has not been done) will improve our understanding of the aging process, and also help determine activities to mitigate such deterioration.
The degradation information evaluated in this study includes the times of 1) degraded failures, and 2) corrective maintenances. The data may also include the component's condition in terms of the parameter values recorded at times of corrective maintenances. The -
degradation modeling approaches presented can use this information to study the aging effects evident in degradations to relate reliability characteristics to the effectiveness of maintenance in mitigating aging effects. At present, we study degradation modeling using degradation times, and do not directly use component condition in terms of engineering conditions. The degradation modeling approach also is directly tied to the component reliability study, as such infonnation can be used to predict the component's failure rate and unavailability which can be used as input into risk and reliability models.
l t
This report develops the concept of using degradation information in an a 6, reliability study. An application of this concept is presented for a specific safety system components, namely Residual Heat Removal (RHR) system pumps and service water (SW) system pumps.- This analysis forms the basis for developing a component aging reliability model using degradation information. Such models will significantly improve studies of aging risk.
I
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The_ degradation mndeling in this study focuses on the following aspects:
- a. consideration of the degrawd state before an age-ralated failure in studying compo-nent aging,
. b. evaluation of maintenance effet tiveness parameter in preventing age related failure, i
- c. modeling of degradation and aling-failure rates using exponential rate models, j
- d. employing statistical approacher to use data across similar comporents and aeross plants in component aging stv3y,
- e. testing statistical trends to deline aging intervals showing (increasing / decreasing) trends in aging failure or deg adation times, and calculating the corresponding rates using regression analysis, ".nd
- f. interpretation of informwon on degradation and aging-failure rate in evaluations of aging and mthe!. nce effectiveness.
This report is organized as follows: the concept of degradation modeling, the methodol-ogy, the results of application, and their interpretations are presented in the main body of the report. The appendices provide the detailed methodology, data base development, and the statistical analyses that were conducted. Chapter 2 presents the basic concepts of degradation modeling; the methodology, with the mathematical formulations, is presented in Chapter 3.
The regression analysis approach to obtain degradation and aging-failure rates is presented in Chapter 4, which also discusses Cox's exponential rate model used'to define aging rates.
Chapter 5 presents the results obtained for the RHR pumps and their interpretation. A summary of the insights obtained from the applicatbn is presented in Chapter 6. Appendix A gives the details of the degradation modeling approach. The analysis of aging failure data (degradation times and failure times) is presented in Appendix B. Appendices C and D provide details of the statistical analyses for the RHR pumps.' Appendix E presents analyses of. degradation and failure data for SW pumps.
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2.-CONCEPT AND OBJECTIVES OF DEGRADATION MODELING Analyses of component reliability records show that besides data on component failure, significant information exists on component degraded conditions, including times at which such degraded conditions are observed, and also values of observed parameters indicating degradation. Many times, a component reliability record contains much more information on degradations than on failure. The concept of degradation modeling is to use degradation data to develop component reliability characteristics and to understand aging effects.
y The objectives of degradation modeling are:
- 1. To quantify and characterize the frequency of degradation,
- 2. To model and quantify the effects of aging on the frequency of component degrada-tion and degradation characteristics,
- 3. To model and quantify the frequency of component failure and aging effects on such r
frequency,
- 4. To establish the use of information on component degradation in aging evaluations l
such that-operational activities can be defined to mitigate such deteriorations,
- 5. To establish relations between component degradations and failures so that fre-quency of component failure can be estimated from the frequency of component i
degradation frequency and degradation characteristics, and
- 6. To develop a reliability model for component aging using information on degrada-tion and failure as an input to aging reliability and risk studies.
This study starts to develop degradation modeling approaches to accomplish the above
~
objectives. At this time, we primarily address the first four items and present results that l
provide insights on the last two items. The development of a degradation model for aging, evaluation ' studies requires investigation of all the above aspects.
L
. The concepts and steps of degradation modeling are as follows. Degradation data is l
collected, consisting of the times and characteristics of degradations The times of degrada-
'tions can include times of incipient failures, of degraded failures, and of corrective maintenances (based on many def' itions, certain incipient failures may not be applicable).
m The characteristics of degradations can include the values observed for various-operational l
parameters and material properties. The use of operational parameters and material proper-ties in defining degraded states has not been attempted at this time.
Such data are used to quantify the component degradation frequency.versus time and age. The times of component aging failure are also studied to quantify the aging failure frequency versus time. The degradation frequency and aging-failure frequency provide an L
evaluation of the aging process, and can also be used to evaluate the effectiveness of i;
maintenances in preventing age-related failures.
Data on degradation - and aging-failure can also be used to establish the relationships between the two. Based on such relationships, which are st ongly influenced by operational i
practices, such as maintenance, aging failure rates can be estimated from degradation rates.
3
,k t.,
i As is evident in component reliability data bases, there are more data on degradation than on aging failures: therefore, such relationships can provide an estimate of aging-failure rate where there is insufficient direct data. However, the relationship among degradations, failures, and maintenances is complex, and in this report,.we study a simple framework to l-define such a relationship.
5 Reliability models can also be constructed which relate the frequency of degradation to the frequency of component failure and to component reliability. The models use component operating characteristics, maintenance considerations, and engineering considerations. The age-dependent frequency ~of degradation is used as input into the models to predict the age-dependent frequency of failure. In such an approach, the key point is that failures do not necessarily have to be observed, rather only degradations, to predict the component's failure and reliability behavior, including the failure rate and unavailability of the components.
The degradation modeling approach studied in this report assumes that components pass through a degraded state before experiencing failures: this may be a simplified model, in reality, a component may experience multiple degraded states in its path to failure (Figure 1). The Markov modeling approach presented in this report can be-expanded to include multiple states, and so can provide a better explanation of the aging process and the influence of maintenances in that process. Further development of this approach will consider multiple states incorporating effects of tests and maintenance.
Degradation models have many potential applications. As. discussed, the times of corrective maintenances, that signify degraded states, can be used to predict future times of
- failures. The aging effect on degradation rates can be indicative of future growth in aging failures rates which may necessitate appropriate corrective actions, e.g., maintenance, overhauls, or replacements. Time-dependent degradation rates can be used to estimate time-dependent failures rates for use in aging intervals where failure data do not support the development of aging-failure rates. Component reliability models can be developed that incorporate information on degradation, and can be input to aging risk and reliability studies.-
Thus degradation models can be a valuable tool for aging evaluation applications, re-licens-ing applications, and reliability-centered maintenance' applications.
4
3; METHODOLOGY: DEGRADATION MODELING APPROACHES In-this section, we give a brief summary of the degradation modeling approaches.
Basically, we present the relationships to be used in applying degradation modeling to component degradation and failure data, the assumptions of degradation modeling, and basic
- formulations of the modeling approaches. Appendix A gives the detailed mathematics of.
specific degradation modeling.
I To understand degradation modeling, we study a repairable component, i.e., a compo-nent that is being repaired and maintained. The " active" components, as defined in the terminology of the NPAR program, are repairable components, and are the focus of this study.-
For one of the simplest models, we make the following assumptions:
- 1. Degradation always precedes failure.
- 2. When a component is repaired after a f ailure, the operational state of the component reflects more restoration than when on-line maintenance is performed.
- 3. When on-line maintenance is performed, the component is restored to a maintaiaed state which reflects less restoration than when repair is performed after a failure.
We call the state after repair of a failure the "o" state, the state after failure the "f" state and the one after maintenance is performed the "m" state.
We use Markov process approaches for degradation modeling; they have the advantage
- l that simple models can first be construcied and then expanded to yield more complex models. Statistical analysis is coupled to the models to estimate unknown parameters from i
degradation data. The' simplest model we present considers only one degraded state.
Expanded modeling will include multiple degraded states (Figure 1). For the simplest model using single degraded state definitions, approaches are developed that can be applied to current data, and to obtain significant insights, as demonstrated in Chapter 5 that defines the specific applications carried out and results obtained.
3.1. State Representation of Degradation Modeling The Markov approaches of degradation modeling can be described by the state diagram for a component (Figure 2). Based on our assumptions, the component can be in a degraded l
state (d-state) through three processes:
- a. the component reaches its first degraded state from a restored state (o-state),
- b. the component undergoes recurring degradation with no intermediate failure, (it is assumed that the component is in a maintained state (m-state) following a degrada-tion), and
- c. the component undergoes degradation following restoration resulting from a failure (f-state).
The component can fail only from a degraded state (d-state). However, it is assumed that maintenance is performed every time a degraded state is detected. Thus, a maintained state 5
+
-4 I
n i
(
Operating State Operating State s
Measure of j
Performance
~
Degraded State 1
?
Degraded State 2 Degraded State Degraded State n Failure State Falture State I
Single Degraded Multiple Degraded State Definition State Definition Figure 1. Altematives for degraded state definitions
.e 4
P-O P
00 DF 1
~
P,.o -
o-state: restored state d* states degraded state m-statei maintained state f-state: failed state
{ : tranaltion probability from state I to state J Figure 2. Markov state diagram for component degradation modelling (single degraded state) 6
p; a
j
'(m4 tate) is' reached following a degraded state (d-state). For Markov modeling consider-ations, these two states are equivalent in this analysis, 3.2 Transition Probabilities The transition probabilities among the various states are as follows:
Poo - =. probability that degradation occurs after the component is restored with no failure before a degradation l
'l
=.1 since we assume degradation always precedes failure Pou = probability that maintenance is carried out once a degraded state is identified
= 1 since maintenance will be performed to remedy the degraded state.
Puo = probability that degradation occurs after a maintenance before a failure occurs.
Por= Pup = probability that failure occurs after a maintenance (performed following detection of a degraded state) with no intermediate degradation.
Pro = probability that component is restored following failure
=1 Our interest lies in obtaining Pyo and Pop. Principally, Pop describes the effectiveness of maintenance and the probability of transferring to-a failed state once a degraded state is reached. Pun, similarly, expresses the probability of recurring degradation before failure.
)
3.3 Frequency of Degradation. Frequency of Failure, and Transition Probabilities Degradation frequency defines the frequency of degraded state,:1.e., the number of degraded states observed for a component per unit time. Similarly, the failure frequency represents the failure atates observed per unit time.
[
Let l
L W (t) = the degradation frequency at t o
l:
- Wp(t) = the failure frequency at t.
- Developing balance equations from the renewal theor' (Ref.1), one can obtaini he y
t steady state solution that relates -the degradation freq s.:ncy, failure frequency, and the transition probabilities. (Mathematical derivation is pret ited in Appendix A.) Wo and Wp represent the steady state degradation and failure frequencies.
~ Wo = Wp + WoPyo (3-1)
We = W Pop (3-2) o Expressed in terms of tranaition probabilities, 7
n s
2
'..),,
Pop = Wp / Wo (3-3)
Puo = 1 - W / Wo = 1 - Pop (3-4) p 1
The above expressions define how the steady state transition probabilities (Pop and Puo) can be obtained from the degradation frequency and failure frequency. Using component-reliability data bases like NPRDS or plant specific data bases, one can determine W and p
- Wo, and hence, Wp / Wo for various components. These ratios can also be determined for various failure modes of a component to determine the effectiveness of various mainte-q nances ' carried out for a type of component.
The interpretations of the steady-state solutions are as follows:
- 1. The larger the ratio of failure frequency and degradation frequency (W / W ) the p
o larger is the probability-that a failure will occur after degradation, Pop.
- 2. For a given degradation frequency, Wo, the larger the probability, Pop the larger is
)
the failure frequency Wp,
- 3. The ratio W / W is a measure of ineffectiveness of maintenance in that it is equal p
o to Pop. However, smaller values of Pop can result in larger values of W if Wois p
larger.
'4.' Another measure of maintenance effectiveness is the failure frequency Wp itself, which is equal to W P o op.
The approaches presented above define how information on degradation can be used to obtain the characteristics of degradation (frequency, the transition probabilities from.de-graded to failure state and from maintained to degraded state) and how component failure frequency relates to such characteristics.
3.4 Incorporation of. Aging Effects in Degradation Modeling To develop a model for component reliability using information on degradation in our study of aging effects, we need to develop the age-dependence of the degradation parame-ters._ Thus, for aging, at some threshold time- (age to) the failure frequency W and p
degradation frequency, W will begin to increase. On the other hand, degradation frequency o
- may show a significant aging effect (increase in degradation frequency with age) whereas the failure frequency may not (constant with age),. indicating a reduced probability of transition from the degraded to the failure state. This may signify that maintenance is L
effective enough to maintain a constant failure frequency l and that aging degradation is.
manifested through age-dependency of degradation frequency.
l The time dependent representation of W and Wo are presented in the appendix. From p
the relation one can obtain the frequency of failure in terms of the degradation frequency, i.
.t 6
W (x) =
W (x) fop (t - x) dx (3-5) p o
- l0 where f (t - x) is the probability density that the failure occurs at t with no intermediate op p
1.
8 1
i:
r observed degradation, given the component was maintained at x. The probability density 7
. function is assumed to depend only on the interval (t - x).
- A prediction of the aging effect on the frequency of component failure can be obtained from the aging effect in degradation frequency using the above equation. However, this
. requires information obtained from the steady state process and as such, introduces the 1
following assumptions:
- l. That aging begins at some threshold time, and that both W (t) ar.d W (t) increase i
r o
from that same time,
- 2. The transition probability density, for example, for(x), depends only on the interval, l
and the steady-state probability density, obtained from steady-state data,- can be 3
applied-for aging-dependent evaluation of W (t) and W (t).
p o
- 3. The same transition probabilities, Pop and P m, as developed from the steady-state 3
case, also apply.to the aging case.
The justification for using these assumptions and how the relationship expressed in Eqn. (3 5) can be obtained under these constraints are presented in the Appendix. The assumptions are both reasonable and necessary if we are to predict the aging effect on failure frequency, based on the observed frequency of degradation with a paucity of data on failure.
3.5 Aging Effects on Degradation Rate The effect of aging on component reliability may be manifested through either in-creased degradation or increased failures, or both. Generally, earlier studies have focussed on increased failures due to aging. Here, the focus has been on degradations, with an attempt l
to predict the corresponding characteristics of failure under appropriate constraints, The degradation rate, Asm, is defined as the rate of degradation occurring after m
maintenance given no previous degradation has occurred. Similarly, the failure rate, App, is p
the rate of a failure occurring after a degradation given no previous failure has occurred.
The age-dependent Asm can be obtained by observing the times of degradation. The time of degradations, t, t,... t from some threshhold time is used to estimate the parametric i
2 n
1 form of Asm(s). The process of estimation is briefly-discussed in the next chapter, a) Availability of Data on Failure
.When times of failure of the aged component are also present, along with the I;
information on degradation, the former can be used to develop the age-dependent App, which can then be compared to Asm. The different behavior of l p(t) and Asm(t) signify different o
effectiveness of maintenance in the component's aging process. If Asm(t) shows a significant
+
L aging effect as opposed to App (t), then the maintenance is effective in averting component L-failure. Conversely, maintenance is ineffective if the transition probability Psm in the aging -
. process is higher than the steady state value.
- b) Insufficient Data on Failure In the absence of data on failure, the degradation rate can be used to develop failure rate in the age-dependent scenario. However, this requires the assumption that both the failure rate and degradation rate have the same time dependence.
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(
+
I 1
. App (t) = korg(t)
(3-6)
Ano(t) = kung (tI (3-7) where g(t) is a general time-dependent or age-dependent function, possibly with a threshold
-l
. time to, i.e., -
j l
g(t) = I t < to j
= h(t) t > to.
-l Aor(t) can be obtained from Amo(t) using the ratio kop / (kop + kuo). Under this scenario,-
J
' the ratio kop / (kop + kuo).is a constant and is given by the transition probability Pop j
obtained for the steady-state solution. In this situation, any available failure data can be used -
to check the assumption used in obtaining lop (t) from ),up(t).
1 3.6 Basic Steps in Degradation Modeling
- 1. The data base on component reliability is evaluated to obtain the time of'degrada-l tions (when maintenance is performed) and times of aging failures, j
- 2. Degradation relationships are developed, based on the observed times at which
- i degraded states occur.
- 3. The degradation relationships give the rate of transition from one degradation state to another,
- 4. Using information on failure time, an aging failure rate is developed.
- 5. The aging failum rate, the degradation rate, and transition probabilities are used to evaluate the aging process and the effectiveness of maintenance in component aging.
]
- 6. The degradatio's rele.tionships are used to predict the time (age) of future failure of l
the component from the rate of. occurrence of degradations.
- 7. The predicted time (age) of future failure can be used to produce a component failure rate, which can be -used 'in probabilistic risk analysis (PRAs).
s In Chapter 5, we present analyses of degradation and failure data for RHR pumps following the steps defined. Degradation modeling is applied up to Step 5. Additional evaluations are necessary to. conduct. Steps 6 and 7.
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)
1
- 4. REGRESSION ANALYSIS USING COX'S MODEL TO ESTIMATE AGING RATES (DEGRADATION AND FAILURE RATES) 4.1 Introduction The degradation modeling approach presented in the previous chapter focuses on estimating two aging parameters-degradation rate and failure rate. The parameters are to be estimated from the degrndation and failure times observed in components as they age in this chapter, we discuss Cox's model (a form of exponential rate model) for developing aging rate parameters and the regression analysis used to estimate the model parameters.
4.2 Cox's Model to Develop Aging Rates As described in Cox's model (Ref. 2) the age-dependent failure rate or degradation rate A(t) for a component is given by:
A(t) = ae".
(41)
Cox's model is also termed the exponential rate model, because aging behavior is modeled as being exponential with age. In Eqn. (4-1), t is the time or age variable, and a and b are parameters characterizing the aging behavior if degradations are evaluated, then A(t) is the degradation rate instead of the failure rate. In the following discussions, we shall focus on failure rates; however, the discussions equally apply to degradation rates.
When A(t) is a failure rate, then A(t) can represent the rate at which first failures occur given no previous failure rate. A(t) can also represent the rate at which any failure occurs, first or otherwise. In this application, A(t) is also called the failure frequency or failure intensity. This later case, where A(t) represents the rate for any failure, is particularly applicable for repairable components.
Cox's model can accommodate constant failure rates, aging failure rates, and burn in failure rates. If b is zero, then there is no aging effect and the failure rate is constant:
A(t) = a for b = 0.
(4-2)
If b is positive, b > 0, then there is an aging effect, with the failure rate increasing as the age increases. If b is negative, b < 0, then there is a burn in or learning effect with the failure rate decreasing as the age increases. We shall be particularly concerned with aging effects or constant failure rates, i.e., b 2 0. However, if data indicates there is a burn in oi leaming effect, then this also will be identified by the analysis, if b is small such that bt 1, then the exponential that can be expanded by a first-order Taylor expansion and A(t) becomes:
11 1
'f I
(
1:
i f
I A(t) = a(1 + bt)
(43) t
= a + abt (44)
= a + ct (4 5)
I
- where,
[
c = ab.
(4 6)
Thus, Cox's model includes the linear aging failure. rate model, Eqn. (4-5), for parameter values b and ages t such that bt 1.
In addition to accommodating different failure rates and including the linear aging l
model, Cox's model has other features. If the parameter a is treated as a baseline failure are i
Ao, i.e.,
a = Ao,
(4 7) then, Cox's model can be written as:
b A(t) = A e '.
(4 8) n b
Thus, the factor e ' can be interpreted as a relative aging factor which modifies the f
baseline, constant failure rate Ao to account for aging behavior.
Cox's model allows standard statistical techniques to be applied to estimate.the h
parameters _a and b. Taking the natural logarithms of Eqn. (41) gives:
In A(t) = In a + bt.
-(4 9)'
Thus,in A(t) is a linear function of the time or age variable t with slope b and intercept f
in a. Consequently, linear regression analysis can be used to estimate the unknown parame.
. ters a and b from observed time or ages of failures. Because of its capabilities, the regression i
analysis approach for estimating the parameters of Cox's model is described in more detail in the next section.
The times (or ages) of failures can also be used to srtimate the agir43 raie parameter b independent _of the baseline parameter a. This approach can he useful if relative aging effectt only are to be estimated. The relative times of failure are described by the relative hilure distribution f(t), where:
e' b
f(t) =
(450) h.
e ' dt,
l b
- T i
i or l
l 12
- ' iD-
i y,u f(t) =
(4'II) e,.,, - e,.r, In the above formulas, T and T are the initial and final times, respectively, of the i
observation period: the relative distribution f(t) only involves the aging parameter b.
j Standard statistical techniques, such as maximum likelihood, can then be applied to f(t) to estimate the aging parameter b.
Finally, by constructing the appropriate likelihood functions describing the observed times of failures, standard statistical techniques cc.n estimate both parameters a and b.
Classical statistical techniques and Bayesian techniques, which incorporate prior infonna-tion, can be used.
i 4.3 The Regression Approach The regression approach for estimating the parameters a and b is described in more l
detail here. Since most standard statistical packages and PC codes contain regression analysis, the approach can be a powerful tool.
l Cox applies regression approach to estimate the parameters for the mean time between failures. We will show how regression can also be applied to data based estimates of the failure rate. Such estimates are described in Ref. 3, and are called cycle-based failure rates.
Our application also defines a framework for regression analysis using data based failure rate estimates as the observed, dependent variables.
Cox describes the regression approach only for independent observations, or independ-ent estimates; we have extended it to correlated estimates. This is important, since it allows cycle-based failure rates to be used which consist of overlapping times between failures.
Let t, t. i be the observed times (or ages) of failure. As discussed previously, even i
2 n
though failure rate modeling is discussed, Cox's model can model degradation occurrences versus time or age for any definition of degradation states. For degradation modeling, t,t.I are the observed times or ages at which the degradation occurs.
i 2 n
A data based estimate of the failure rate at an observed time (or age) of failure t is i
simply one over the time between failures. If we let ri e the empirical or data-based failure b
l rate estimate, then:
1 i = 2,...n.
(4 12) ri = t - t.i i
p l
l This is a standard empirical estimate of the failure rate (see for example, Ref. 4). More generally, an estimate rju f the failure rate at time t considering k times between failure is:
L o
i k
r!" = t - ta i = k_+ 1,...n (4-13) i In Ref. 3, the failure rate estimate rl" is termed the k-cycle-based failure rate since it encompasses k cycles (i.e, times between failure).
l 13
4 Now, in describing the segression approach, Cox focuses on the length L of k times between failure, where L = t, - t _t. The length of k times between failures are used, where i
k is generally 3 to 5, to smooth the failure behavior. Cox shows that the expected value of the log of L is a simple function of the parameters. Specifically, E(In L) = -In a - bt + c,
(414) where "E( )" denotes the expectation and "In" denotes the natural logarithm. The time t is a time at the midpoint of the k times between failure L. The constant c is a normalizing constant which is a function of k, the number of times between failure. Specifically, c = In k.
(4 15)
If we let:
d = In a.
(4-16) then Eqn. (414) becomes:
E(in L) = - d - bt + c.
(4 17)
Thus, if we let:
y = In L,
(4-18) we obtain a linear equation for the expected value of y E(y) = f - bt,
(4-19)
- where, f
f=c-d.
(4 20)
Cox also shows that if we partition the times of failitres into disjoint groups, each containing k failures, then the different times between k failures L, L,... are independent.
i 2
The variance of the times between k failures L is also independent of the failure rate.
i Specifically, V(In L) =
(421)
~
i 14 i
Again letting y = in L we have.
I V(y) =
(4 22) k3 Equations (4-19) and (4 22) show that a standard linear regression can estimate the parameters of Cox's model. The steps in applying the regression are as follows:
- 1. Divide the times of failure t, t,...t,, into disjoint groups, each containing k times i
2 between failure. Thus, the first group would be t, t,...tui (to obtain k times i
2 between failures). The second group would start at tai and would contain the next k
+ 1 time points. This gro.: ping would proceed until all observations are used or there are fewer than k + 1 observations to group. The last group of observations which is smaller than k+1 observations is truncated and not used. Thus, it is optimal if k is selected such that all observations are used, i.e., such that n+1 is a multiple of k.
- 2. Assign an associated time or age for each group of failures. The assigned time or age l
is a value at a midpoint of the k failures. Any centrally located value will generally be sufficient, such as the median of the times of failures.
- 3. Apply standard linear regression to the observations (yi, t) where t is the midpoint i
i time or age, and yi s the log of the k times between fallut; yi = in L.
{
i i
I The slope of the regression line will give -b [See Equation (4-19)]. Equations (4-15),
(416), and (4-20) can be used to determine the parameter a from the regression line intercept.
To show how we can apply the regression approach in terms of the empirical failure rate, we start with the basic :egression equation, Equation (414).
E(In L) = In a - bt + in k,
(4 23) i where we substitute c = In k into the equation [as given by Eqn (415)].
Transposing in k to the left hand side of the equation, we have:
I E(in L) - In k = -In a - bt,
(4 24) or, f
E in -(k,
= -In a - bt.
(4-25)
(
4 Multiplying both sides of the equation by -l we have:
L E in kh = In a + bt.
(4-26)
L, 15 l.
1 l
(
i Now k / L is the k-cycle failure rate estimate as defined by Eqn. (4-13), i.e.,
b=
(4-27)
L t - t.g i
i
= rju (4 28)
Hence, Eqn. (4-26) becomes E(in rj") = In a + bt.
(4 29)
Defining again d = In a (4 30) we thus have E(In r!") = d + bt.
(4-31)
From Eqn. (4 31) we thus see that under Cox's model the expected value of the k-cycle failure rate estimate is also a linear function of the time (or age) t.
To find the expression for the variance of rju we use the relationship between rj0 and L given by Eqn. (4 28), i.e.,
k rj" = {
(4-32)
Therefore, in rju = In k - In L,
(4-33) i Taking the variance of both sides, we have, using standard variance operator properties, V(In rj") = V(in L).
(4-34) where V( ) again denotes the variance of the variable in the parentheses. Substituting the '
expression for V(In L) given by Eqn (21) we have I
I V(In r!") =
(4-35) k3 l
16
Thus we have our re-defined regression equations, given by Eqn. (4-31) and (4 35),
now reformulated in terms of the empirical estimates of cycle based failure rate. (Note that i
Eqn. (4 35) which gives the variance is used for regression purposes to identify that all estimates rj", i.e., all observations, have equal variance and no weighting is needed in the regression analyses.)* The previous steps defined for the regression application can still be i
used where now yi = In rj" is the dependent variable (instead of in L). The midpoint time
]
or age t, is still the independent variable which is substituted for the variable t in Eqn. (31).
The regression slope gives the parameter b and the regression intercept given in a, from i
which a is determined, in the analysis presented for RHR pump, k = 1. We use standard 3
regression analyses (using STATGRAPH statistical package, Ref. 4) to obtain the parame-i ters a and b for the degradation or failure rate using the respective degradation or failure times.
h t
P v
Y
' Knowledge of the varianw allovs different size groupings k with the weight for each group equal to the square root of one over the varinace.
17
1
\\
- 5. RESULTS AND INTERPRETATION OF AGE.RELATED DEGRADATION i
AND FAILURE DATA I
In this section, we present an analyses of age related degradation and failure data for I
selected components, namely RliR pumps and SW pumps. The primary focus of the analysis Is to use the concept of degradation modeling, that provides us with an understanding of the aging process in the active components. Based on the data analyses, we discuss
- 1. behavior of degradation rate and aging failure rate with age of a standby safety l
system component and a continuously operating component (i.e., the RiiR pump and SW pump).
- 2. interpretation of aging process through degradation and failure rate behavior, i.e.,
how meaningful information can be obtained by studying these parameters, and
- 3. derivation of effectiveness of maintenance in preventing age related failures.
In addition to these items which focus on the interpretation of aging and evaluation of maintenance effectiveness, the analyses address the following aspects:
- 1. combining data from similar components in a plant and across plants,
- 2. data pooling across components, based on statistical tests of similar characteristics,
- 3. statistical trend testing to determine aging effect in failure and degradation data, and
- 4. regression analysis to obtain degradation rate and aging failure rate.
5.1 Analysis Approach The primary objective of the analyses was to obtain the aging failure rate and degradation rate based on component age-related failure and degradation data, respectively.
l These two parameters are used to obtain the effectiveness of maintenance in preventing L
age-related failures.
The process of data collection (Appendix B) provides specific degradation and failure times of several similar components. Focusing on the RHR pumps, data are obtained for a group of components from different plants. In this case, the data covered three different BWR units, each having four RHR pumps. The age of the plants differed, and the data did not cover the entire life of the component in all cases.
Individually, the data for each of the pumps were. insufficient to determine the parameters (degradation rate and aging failure rate). Accordingly, we studied a component type (the RHR pump) using data from the group of components (in this case,12 RHR pumps). Statistical tests were conducted to justify the use of data across components and across plants.
For SW pumps, data from seven BWR units out of twelve units were used in the analysis. Based on the statistical tests, the SW pump aging data in the remaining five units were not compatible with the data from the seven units used in the analysis. Each of these units has three or more SW pumps, thus providing a data base from about forty three pumps.
19
)
Similar to the analysis approach in RiiR pumps, statistical tests were conducted to justify the use of data across components and across plants.
Statistical tests for use of data across components and across plants J
The statistical tests were conducted with the following objectives:
- 1. to demonstrate that times between degradations (or between failures) across compo-nents within a plant are identically distributed, i.e., the components belong to the same population for analysis of degradation and failure rate characteristics, and
- 2. to demonstrate that components across the plants belong to the same population.
The tests were conducted separately for degradation and failure data hiann-Whitney U tests and Kruskal Wallis (K-U) tests were used, details of which are presented in the appendix. The results showed that components could be grouped together: for the RilR pumps, the statistical tests justifNi using data from 12 pumps across three different power plants. In the case of SW pumps, the test results justified use of data across seven units out of twelve units.
Data were combined in two ways. In hiethod 1, the data on time to degradation or time to failure were combined from different RiiR pumps, i.e., separate data from each compo-nent were used to develop the data base. In hiethod 2, data from different components were
" pooled", i.e., degradation and failure times obtained from each component were plotted on a single time line to obtain new degradation and failure times for the analysis. In our terminology, we describe Method I as " data combining" and hiethod 2 is called " data pooling".
Trend testing and identification of age-groups with degradation and failure time l
The data obtained by either of the methods (" data combining" or " data pooling") were tested for time trends before developing age-related degradation and failure rates.
l Statistical tests were used to define component age groups showing similar aging behavior. We observed that early life showed a decreasing trend, and later life showed either i
increasing or constant trends with time. Using regression analysis, data from age groups were appropriately partitioned that showed statistically significant time trends for developing l
aging rates.
5.2 Aging Effect on Degradation The analysis of degradation data for the RiiR pumps and SW pumps was conducted with the following objectives:
- 1. identification of age-groups where statistically significant time trends exist, and
- 2. determination of the time-trends, and degradation rates, using regression analysis.
The details of the statistical analyses are presented in the appendices, liere, we discuss the i-results and the characteristics of degradation rate.
20
Figure 3 shows the logarithm of the degradation rate that characterized the RHR pumps over ten years (presented as 40 quarters). This degradation time was obtained from plant specific data bases of 12 RHR pumps,4 from each of 3 units (Appendix B). Statistical tests (in Appendix C) showed that the degradation behavior across these components are similar, and accordingly, a generic degradation characteristic was studied. Data combining and data pooling were studied: both showed similar results. The results obtained by data combining are discussed.
The following observations can be made from the age-dependent degradhtion rate for the RHR pumps:
- 1. The degradation rate shows significant age-dependence; the early life of the compo-nent (i.e., first five years) shows a decreasing trend (significance level: 0.001) and the later five years show an increasing trend (significance level: 0.05), with the age of the component.
- 2. The increase in degradation rate, which is of interest in aging studies, is significant:
the degradation rate increased by almost an order of magnitude at the end of ten years.
- 3. The 95% confidence bounds for the duradation rate show that the uncertainty in the estimation is not large. The increased number of degradations observed in a component (compared to failure data) and the statistical approach taken for using data across similar components exhibiting similar degradation behavior contribute to lower range of uncertainty. This signifies that statistical methods can be used to estimate degradation rates.
Figure 4 shows the logarithm of the degradation rate that characterized the SW pumps over twelve years (presented as 50 quarters). The method of data combining was studied for SW pumps. The generic degradation characteristic was obtained by combining data across~
seven units consisting of 43 pumps. Appendix E presents detailed results.
The observations on the age dependent degradation rate for the SW pumps are as follows:
- 1. The degradation ratt. shows age-dependence: the early life of the component (i.e.,
first five years) shows a decreasing trend and the remaining seven years show an increasing trend with the age of the component.
- 2. The increase in the degradation rate as the component ages is not as significant as in the case of RHR pumps; nevertheless, the degradati.on rate is showing aging effect on the component. During the later seven year period the rate increased by about a factor of 3.
5.3 Aging Effect on Failures The aging failure data for the RHR pumps and SW pumps were also analyzed with the following objectives:
- 1. identification of age-groups where statistically significant time trends exist, and
- 2. determination of aging failure rates where time trends exist, and estimation of time-independent failure rate where time-trends cannot be established.
21 l
l.~
[
. 3:
b.
j
?.
l L..
j-Degradation Rate ho( # per Quarter)
Inh o 64.6 4
j-'
33, f 2 :
20.00
- Estimated Dog. Rate 3
f f.18 95% confidence bounds d
7.39
. g l_
4.48 Data Method 1 - Combining O.37 Quest Cubic spline fit -
1 0
0.61
./
y-
~
W
~~
p o 22 O. f 4
.y 0.08 0.06 3
0.03; 0.02i i
i._..
t
,4 0
10 20 30 40
^
Age in Quarters' (a monih periods Figure 3. Age dependent degradation rate n'
(Component: RHR pumps; 3 plant data) t 5
In>
- Degradation Rate (1,, per quarter) 64.6 4
20.09
- Estimated Deg. Ratel,. 3 i
95% confide ce bounds 7.39
.- g Data Method 1 - Combining 2.72 Queal Cubic spline fit - j 1.00 o
O.37 LN'
- -1 s
p f
-.g 0.14 1y 0.06
-3 0.02 t_
i i
._.. a. _ _ _.. 4 i
O 10 20 30 50 60 Age in Quarters (3 month periods) 4 Figure 4. Age dependent degradation rate (Component: SW pumps; 7 plant data) i 22 i
Again we discuss the results and the characteristics observed in the aging failure rate and give details of the analysis in the appendices. Appendices C and D present the detailed results for the RHR pumps and Appendix E describes SW pump study. Figure 5 gives the logarithm of the age-dependent failure for RHR pumps. The data base used covered the same components as for the degradation rate. The statistical tests justifying the use of data across twelve RHR pumps were the same, but the sparsity of data on aging failure required a slightly different analysis.
The aging-failure data for the RHR pumps show only a few failures during the later five years of the components (age 5-10) and, in general, the number of failures was small. The statistical trend testing, based on both data combining and pooling, showed a decreasing trend in the early life, but no trend in aging-failure could be established in the later five years. Because of the sparsity of the data, isotonic regression analysis was used to estimate failure rate for the first five years of RHR pumps where decreasing trend was observed. For the later five years, due to a lack of any trends, a constant, time-independent, failure rate was estimated.
The following observations can be made from the aging failure rate obtained for the RHR pumps:
- 1. The aging failure rate shows decreasing trend in the first five years, but a constant failure rate can only be estimated for later five years of the overall ten years. In other words, there was no trend of increasing failure with age for the ten-year operating period of the RIIR pumps.
- 2. The aging failure rate shows a behavior similar to the degradation rate in the early five years, but differs after that. The aging failure rate was significantly lower than the degradation rate and the difference increased with increasing age. The degrada-tion rate was about a factor of 30 higher than the aging failure rate at the end of 10 years.
- 3. The 95% confidence bounds associated with aging failure rate show higher uncer-tainty compared to the degradation rate, due to the few observations of failures.
Figure i gives the logarithm of the failure rate for SW pumps. For the SW pumps, only a few failure data points were available for analysis. The sparsity of this data base is partly attributable (3 the data source which is considered incomplete for the early life of the components. Appendix B discusses the SW pump data evaluation and the associated limitations.
The available SW pump data were not adequate to detect any statistical trend with confidence. Accordingly, no aging effect of the SW pump failures is established: a constant failure for the study period (approximatcly 12 yrs.) is estimated.
5.4 Aging Evaluation Using Degradation and Aging-Failure Rate The analysis of the degradation rate and the aging-failure rate provides a comprehensive picture of the agint process in the components studied (RHR and SW pumps) and provides interesting insights on component aging.
23
^
tj w
n il 4-I
+
i y
V i
e I" A I
Failure Rate *X, (# per Quarter) t 4.
p ss.e'
-Estimated Failure Rate, in l' - 3 i-pp,pl
- 2 i
96% confidence bounds
-l 7 39l~
~ l I
Data Method 1 - Combining A
Quatl Cubic soline fit
' l-o' f.00
~
i 3
0.37' i
N
..g
~-
0.14
~~
'N
.l
..i..
O.05 3
l i
i i
i
- 0. 0 2,... _.
,4 0
.10 :
20 30 40
- 1 Age in Quarters (3 month periods)
.i
! i Extrapolated Rate n
Estimated Rate Figure 5. Age dependent failure rate (Component: RHR pumps; 3 plant data) i t
I"l
. Failure Rate ( ),, per Quarter) e 54.6 4_
20.06
-Estimated Failure Rate, in 1,.- 3 96% confidence bounds
.(
7,39
- 2 t
Data Methos 1 - Combining.
i 1
],
1.00 n
0.37 3
O.14
..g
[
'O.05 3
l~
0.02 4
0 10 20 30
-- 4 0 50 60' a
' Age in Quarters (3 month periods)
Figure 6. Age dependent failure rate (Component: SW pumps; 7 plant data)
- 24 i
e
[
U
- 1. The use of information on degradation and failure not only increases significamly the information base for adequate analysis, but provides interpretations of the aging i
process that cannot be obtained by analyses of failure data alone. For both of these pumps the study of the failure data would not have resulted in any understanding of
- aging,
- 2. The aging trend in the degradation during the later 5 to 10 year period shows a significant effect on component degradation as the RHR pump ages, but a simulta-neous lack of aging trend in the failure rate signifies that degradation has not been manifested in an increasing failure rate. Similarly, for the SW pumps, there is no aging effect on failures corresponding to the aging effect on degradations observed during the later seven years of operation. In the degradation modeling approach this finding signifies that maintenance is effective in preventing age related failures, and that aging is represented through an increase in the degradation rate.
- 3. The relation between degradation and aging-failure rate in the first five years of the RHR pumps remained the same, i.e., both curves were similar and the degradation rate was steadily and consistently higher than the aging-failure rate. In the case of SW pumps, the degradation rate was consistently higher than.the failure rate, but these rates show different behavior. However, failure data in the early life of SW pumps are considered incomplete.
- 4. The decreasing trend in the degradation rate for both pumps ends after the first five years, and the rates show differences with the corresponding failure rates, starting at this point.
- 5. Because there is more information on degradations, degradation rates are probably better indicators of aging than failure rates. Also, uncertainties in estimates of degradation rates are lower than those for aging-failure rates. Therefore, degradation rates can be effectively used to understand aging effects.
- 6. The relation between degradations and failures needs to be investigated further. The increase in degradation rate may be followed, after a time-lag, by an increased failure rate. The degradation rate, once it reaches a threshold value, may relate to failure. Investigation of these aspects through degradation modeling may suggest when maintenances or overhauls of components should be performed to prevent age related increase in failure rates.
5.5 Evaluation of Maintenance Effectiveness As discussed in Chapter 3, the degradation modeling al proach provides an estimate of i
the effectiveness of maintenance in preventing age-related failures. The transition probabil-ity from a maintenance state to failure state signifies the ineffectiveness of maintenance in the simplified model studied. The complement of maintenance ineffectiveness is mainte-nance effectiveness.
l-For the RHR pumps, the maintenance effectiveness is obtained (Figure 7) for each 10 l-quarters of age. Effectiveness varies between 0.6 to 0.7 for the first 30 quarters, but significantly increases 11 the last 10 quarters, it is possible that effect of degradation on failures is delayed and Cata beyond 40 quarters might provide better estimates of mainte-l 25
~
r Maint. Ef fectiveness 1
Estimated Maint. Ef fectiveness 0.9 Data Method 1 - Combining 0.8 0.7 0.6 0.5
- - --- ---~~----
-_L._.
0 10 20 30 40 Age in Quarters (3 month periods) l Figure 7. Maintenance effectiveness (Component: Rl!R pumps; 3 plant data)
I nance effectiveness in the last ten quarters. The maintenance effectiveness for the SW pump (Figure 8) shows slightly different behavior. It declines in the early life and then shows l
increase in the later life. As discussed, the relationship among degradations, failures, and l
maintenances is complex but extremely useful for studying aging in repairable components, i
A better understanding of this parameter will allow estimation of aging failure rate based on degradation rate estimates.
i f
l-I L
26 l
i-Maint. Ef fectiveness 1
l
- Estimated Maint. Ef fectiveness i
0.8 Data Method 1 - combining 0.6 0.4 0.2 L-i 0
0 10 20 30 40 50 60 Age in Quarters (3 month pericos)
Figure 8. Maintenance effectiveness (Component: SW pumps: 7 plant data) i b
27 w-
)
1
- 6.
SUMMARY
AND INSIGHTS OF DEGRADATION MODELING ANALYSIS The report presents the concept of the degradation modeling approach in an aging evaluation of the safety system components of nuclear power plants. The use of degradation modeling using information on componem degradation was studied, along with the statistical approach to data analyses needed in such modeling. Applications to RHR pumps across three nuclear units md SW pumps across seven nuclear units were carried out to demon-strate the approach liiid the use of the modeling concept. In summary, we addressed the following aspects to derive insights on the component aging process:
- 1. use of degradation information to develop a degradation modeling approach for use in aging studies,
- 2. statistical approach to the analysis of information on degradation failure, and
- 3. aging and maintenance effectiveness evaluation using degradation information.
As discussed in the report, the degradation modeling approach can have broader applications in aging reliability studies. The simple models presented provide interesting insights that are summarized below; further developments and evaluations are necessary to develop this tool for understanding and modeling component aging.
- 1. Benefit of using degradation information and degradation modeling Aging is manifested through degradation of components. As presented in this report, analysis of degradations provides an understanding of aging that cannot be obtained by studying age-related failures only. The other important aspect is that significantly more information is available on degradations compared to failures, that is, how current practices at plants are exhibited on component reliability and component reliability data bases.
Degradation data enhance the data base for aging reliability and thus, the lack of data problem is reduced in this modeling approach.
- 2. Statistical approach to analysis of aging data This report presents a statistical approach to analyzing aging data (degradation and failure data). Statistical tests are presented to demonstrate the similarity of component behavior so that data can be taken from a group of components. Statistical trend tests are presented to demonstrate the existence or lack of agmg trends in the data before developing age-related rates using regression analyses. Using information on degradation and failure from 12 RHR pumps across three units, we demonstrated the statistical approach. A similar analysis is also presented for SW pumps. The uncertainty in the analysis also is controlled-by using the statistical approach.
- 3. Aging evaluation using degradation modeling approach In this report, RHR pump degradation and failure data were studied to understand the aging effect on the component. The result showed an aging effect on the rate of component degradation even though no aging effect on the aging failure rate could be established.
29 N
Similar results are also obtained for the SW pumps. The increase in the degradation rate may be ir icative of future increases in the aging failure rate. We showed that component aging can be explained and demonstrated in a relatively short time studying degradations, whereas a much longer time is needed to demonstrate the aging effect through study of failure data.
- 4. Relations between degradations and failures In degradation modeling, components are assumed to degrade in their path to age-re-lated failures. This assumption is justified based on understanding of aging, but relations between degradations and failures are not yet known. Plant maintenances and operating practices clearly play a role. A large number of possibilities that define the relationship between degradations and failures exist, and deriving such relations will help define the required maintenance practices and help develop component reliability models for aging studies.
- 5. Evaluation of Maintenance Effectiveness An important aspect of evaluating the aging process is to understand and characterize the role of maintenance being performed on the component. A simple model was studied, based on degradation modeling approach, to obtain a parameter for maintenance effective-ness using age-dependent degradation and failure rates.
This parameter can define why component aging failure rates are being controlled it can also define when maintenance is ineffective to control component aging. The relation-ship among degradations, failures, and maintenance effectiveness are thus elemental in explaining and modeling component aging rcliability. The degradation modeling can further be developed to better model the role of maintenance in component aging.
- 6. Model for component aging reliability The analysis presented demonstrates that information ren component degradation can be used to express aging effects on components, and that statistical approaches can properly interpret this data. A component aging reliability model should be developed that incorpo-rates this information and can take into accour.: the effectiveness of maintenance in mitigating aging.
l 30
c c4.,
t i
' REFERENCES
- l. D.R. Cox, Renewal Theory, Chapman and IIall,1962.
- 2. D.R. Cox, Regression Models and Life Tables, J.R. Stat. Soc., B, 34, 187 220.'
- 3. W.E. Vesely and A. Azarm, System Unavailability Indicators, BNL Technical Report, A-3295 9 30 87. Sept.1987.
.4. STATGR APHICS, Statistical Ort phic System by Statistical Graphics Corporation, STSC, l
c Inc.,1988.
- 5. NPRDS' Prograrn Description, Institute of Nuclear Power Operations, INPO-86 010,.
i
~ Atlanta, Ga.,1986.
t 0
.p r
~.: 4:
i J
P 31
_~
APPENDIX A. MATHEMATICAL DEVELOPMENT OF DEGRADATION MODELING APPROACHES A.1 Specific Degradation Models Assume a component is being repaired and maintained. Assume, furthermore, that the component experiences both degradations and failures. We wish to derive relationships between the rate of degradation and the rate of failure for the component in a given environment and under a given test and maintenance program.
Degradation Precedes-Failure Model For one of the simplest models, we make the following assumptions:
- 1. Degradation always precedes failure.
- 2. After a failure, a component is repaired to an operational state which reflects more restoration than when on line maintenance is performed.
- 3. When on line maintenance is performed, the component is restored to a maintained state which reflects less restoration than when repair is performed after a failure.
We will call the state after a repair of a failure the "o state." We will call the state after maintenance is performed the "m-state."
Equations for the Degradation and Failure Rates Let Wo(t) = the degradation frequency at t (A-1)-
Wr(t) = the failure frequency at t (A 2)
Then unoer the above assumptions and assuming the component was operational at t = 0 we have the following balance equations for Wo(t) and W (t):
p
.t
.t W (t) = foo(t, 0) +
W (l')foo(t', t) dt' +
W (t')fgo(t', t) dt' (A-3) o p
o
- 0
- 0
- and,
,.t W (t) =
Wo(l')for(t', t) dt' (A-4) r
~0 where A1 l
l
q e
i L
4 fon(t, 0) = probability density for a first degradation occurring at t given the compo-nent was restored to an operational state at t = 0 foo(t', t) = probability density that a first degradation occurs at t given the component I
was restored to an operational state at t' fuo(t', t) = probability density that a recurring degradation occurs at t with no interme-I diate failure given the component was maintained at t' for(t', t) = probability density that a failure occurs at t with no intermediate observed degradation given the component was degraded and maintained at t' We will call foo(t', t), fuo(t', t), for(t', t) transition probability densities.
Function Forms for the Transition Probabilities For general time dependent and age dependent modeling the transition probability densities are functions of both t' and t, or equivalently, are functions of t' and t - t'. For age dependent evaluations, for example, l' is the age of the component and t - t' is the interval involved. For steady state modeling which we first address, the transition probability densities are functions only of the interval ; - t'. We distinguish these cases below.
General Time Dependent aml Age Dependent Functional Forms foo(t', t) = foo(t', t - t')
(A-9) fuo(t', t) = fuo(t', t - t')
(A 10) fop (t', t) = for(t', t - t')
(A-11)
Steady State Functional Forms fop (t', t) = fon(t - t')
(A-12) fuo(t', t) = fup(t - t')
(A 13) for(t', t) = for(t - t')
(A-14)
Steady State Failure and Degradation Equations
.f
.t
.t l
Wo(t) = fon(t) +
W (x)fon(t - x) dx +
W (x)for(t - x) dx (A-15) p o
- 0
'O o
A-2
'l
)-)
t:
x=
.t.
Wr(t) =
W (x)for(t - x) dx (A-16) o
.s l
Asymptotic Solutions At: t -4 = the asymptotic, steady state solutions for Wo(t) and W (t) are:
r Wo = WrPon + Wopuo (A 17)
W = W pop (A 18) l p
o I
- where, i
t
,1 Poo = limit fon(t - x) dx =
foo(x) dx (A 19) h
-e = 'O
- 0
,t
,=
puo = limit fuo(t - x) dx =
fup(x) dx (A 20) 8 -' "
- 0
- 0
.t pop = limit for(t - x) dx =
for(x) dx (A-21) 8 -* "
- O
- 0 The terms poo, puo, por are corresponding transition probabilities:
Poo = probability that a degradation occurs after the component is restored (A-22) with no failure before a degradation
= 1 under our assumption (A 23) pun = probability that a degradation occurs after a maintenance before a (A-24) failure occurs pop = probability that a failure occurs after a degradation and maintenance
\\-25) with no intermediate degradation Solving the Steady State Solutions The steady state balance equations are again Wo=WrPoo + Wopuo (A 26)
W = W pop (A-27) p o
A-3
(
l Under our model pon = 1 as indicated and hence, Wo = Wp + W puo (A 28) o W = Wopop (A-29) p From the above two equations we have, Wo
. + Wr P"
(^~
}
Wo Wp
= 1 + PMo, Por + Puo,1 D
(A 31)
W Pop pop pop p
PMD o -1 (A-32) m Pop Wp Pun Wo - Wp (A-33)
=
I'or Wo Interpreting the Steady State Relation
. The steady state solution is again:
Wo 1
(A-34) -
=-
Wp pop or Wp Por = w (A-35) n Interpretations:
- 1. The larger the ratio W / W the larger is the probability that a failure will occur p
o after degradation pop.
- 2. For a given degradation frequency Wo, the larger the probability por, the larger is the failure frequency W.
p
- 3. The ratio W / Wo is a measure of maintenance ineffectiveness in that it is equal to p
Por. However, smaller values of pop can result in larger values of Wp if Wo is larger.
A-4
5"
- 4. Another measure of maintenance effectiveness is the failure frequency Wp itself which is equal to W por-o
- 5. The ratios W / Wo can be calculated for various components and failure modes.
r Statistical relationships involving Wr / Wp, component types, failure modes, and failure causes can be investigated.
- 6. The ratios Wr / W, or equivalently Por, can be used to predict Wp from knowledge o
of Wo under different scenarios, e.g. under aging scenarios.
Incorporation of Aging Effects Assume aging occurs. At some threshold time (age to), the failure frequency W and p
degradation frequency begin to increase with age. Under what constrairts will the same probabilities pop and puo which applied to the steady state case also apply to the aging case?
To answer this question consider agali the general time dependent balance equations:
1
,.t Wo(t) = foo(0, t) +
W (X)foo(x, t - x) dx +
Wo(x)fuo(x, t - x) dx r
- 0
'O (A-36)
,t W (t) =
Wo(x)for(x, t - x) dx (A 37) p
- 0 Translating the origin to to gives:
,t t
4 Wo(t) = foo(to, t - to) +
Wp(x) fop (x, t - x) dx +
W (x)fup(x, t - x) dx p
- to
- to (A-38)
.t Wr(t) =
W (x)for(x, t - x) dx (A-39) o
" to Assume again the transition probabilities are only depe. ::nt upon the interval t - x, i.e.,
fop (to, t - to) = foo(t - to)
(A-40) fuo(x, t - x) = fup(t - x)
(A-41) fon(x, t - x) = fon(t - x)
(A-42)
Then pop and puo will be the same as for the steady state case and the relations for W (t) p and Wo(t) in the aging case are given by:
et et Wo(t) = fop (t - to) +
W (X)foo(t - x) dx +
W (x)fuo(t x) dx (A-43) r o
- to
- 'O
(.
i A5 l
l
m e
,i Wr(t) =
W (x)fodt - x) dx (A-44) o
- t, The last equation for W (t) is the particularly relevant equation for predicting the failure r
frequency from the observed degradation frequency. If W (x) was observed and for(t - x) o were known, then Wr(t) could be predicted from the above equation. Assuming the same i
for(t - x) as in steady state behavior allows for(t - x) to be estimated from steady state 6
data to apply to aging monitoring and prediction, we study models for the transition probability distributions.
Models for the Transition Probability Distributions The simplest models for fuo(x), fur (x), and fon(x) involve assuming a constant rate of transferring from one state to another. Let:
Ago = the rate of a degradation occurring after a maintenance when (given)
(A-45) no previous degradation has occurred Apr = the rate of a failure occurring after a degradation when (given) no (A 46) previous failure has occurred Aon = the rate of a degradation occurring after an operational restoration (A-47) when (given) no previous degradation has occurred.
Assume that Amo, App, and Aon are constant. Then fun (x), fup(x), and foo(x) are given by:
fun (x) = Ano exp(-Au ) = A" Au exp(-Au )-
(A-48) x x
Au for(x) = App exp(-Au ) = A"" A exp(-Au )
(A-49) x x
u u
(
and L
fop (x) = Aoo exp(-loo )
(A-50) x wherc
- Au = Apr + Ano (A-51) l-Estimation of the Transition Rates The probability pop is given by:
A6
,~
gF Por =
Apr exp(-Au ) dx = y"M x
A eXp("A x) dx (A 52)
M
- 0
- 0 or, oF Por = gM (A-53)
Therefore, the ratio Apr / Au can be estimated from the ratio Wp / Wo since Wp =
W por-o The degradation rate Ago lso needs to be estimated. In general, Aun is age dependent a
even if we assume the ratio Apr / Au is constant. One scenario under which the ratio is the same but the transition rates can be age dependent is where the transition rates have the same time dependence:
App = NoF8(t)
(A-54)
Auo = kung (t)
(A 55) where g(t) is a general time dependent or age-dependent function with possibly a threshold time to, i.e.
g(t) 1 t < to
=
h(t) t > to
=
In the above case the ratio of Apr / Au will not be time dependent or age dependent:
N DF DF Au kop + kuo To estimate Ano in the age-dependent scenario, assume we observe times of degrada-tions when the component is aging:
Times of degradations:
t, t,...t (A-57) i 2
n Also, we may observe times of failures when the component is aging.
Times of failures: u i....,u (A-58) m We will not use the times of failure to estimate the transition rates since we may not have times of failures. When we have them, we can use them to check and refine the model.
[
l A7
l I
[.
Likelihood Estimation Assume the times of degradation are measured with regard to the threshold time. Then the likelihood L for the times of degradation is:
(
.t S
L = Amo(t )Ago(t )...Auo(t ) exp Au(x) dx (A-59) i 2
o
( *0 s
- where, Au(x) = Awo(x) + Aor(x)
(A-60)
- and, I
t., = t,
Time of last degrdation only measured.
(A 61) m o
t,,, = t,no, An observation time from t to t is also recorded (A-62)-
o end where there are no further degradations.
The above likelihood thus is a standard function which can be usco to estimate parametric forms (e.g., Weibull or exponential) for Ago(s) [and A p(s) using the determined ratio i
p estimate kup / (kup + kun)). Thus we can predict the aging failure frequency using the balance equation for Wr(t) and the steady state ratio kop / (kor + kun).
f l
l A-8 l
li
l
.o APPENDIX H. DATA BASE FOR AGING DEGRADATION AND FAILURE i
B.1 Data Analysis Data on degradation and aging failure were obtained for the analysis from the maintenance history of the component. The maintenance history includes activities (such as preventive and corrective maintenances, and testing) performed on the component from the day of its installation. Two sources of data were solicited: plant specific maintenance records and component reliability data base in Nuclear Plant Reliability Data System (NPRDS).
Data were collected for specific types of components where the maintenance history for each component was studied. We developed degradation and failure data bases for two types of components (residual heat removal (RilR) pumps, and service water (SW) pumps supplying cooling water to the RilR system). RiiR pump data were obtained from plant maintenance records, whereas NPRDS (Ref. 5) was used for SW pump data Both of these sources have individual component identification that is essential for obtaining the type of data desired for degradation modeling. The RHR pump data were taken from three BWR units, each consisting of four identical pumps. The SW pump data covered 33 BWR units in the NPRDS database, from twelve units experiencing 10 or more failures in each of six or more SW pumps.
B.2 Data Classification Each record of maintenance or reported failure was classified into three categories, defined in Table B.I. Plant-specific data, taken from the maintenance log, contain all three kinds of data, whereas the NPRDS covered mostly D and F type information. For this study, the N type of information is not used in the model, and hence, were not collected in this data i
analysis. However, this information will be useful later in judging the current preventive maintenance practices which can improve the maintenance effectiveness in a component.
Although these categories are not directly correlated with the severity levels (incipient, i
degraded, catastrophic) defined in NPRDS, comparing with NPRDS categorization it can be I
i Table 11.1. Categorization of Component Failure or Maintenance Data Category Description l
N Activities such as routir.c checks, inspections and testing that indicated no l
sign of degradation in the component. No particular maintenance was performed.
D Activities indicating definite degradation in the component subassemblics.
l Maintenance was performed to ameliorate the d: graded condition of the l
components.
F Activities indicating degradation in the component such that it required immediate maintenance to be able to perform its design function.
B1
I g
s -4 g
noted that most incipient type failure data in NPRDS were categorized as type 'D' and some degraded data were judged type 'F' for this analysis. All of the catastrophic data were judged te be of 'F' category Therefore each record (identified in plant specific maintenance history or NPRDS) was judged for relevance to age-related degradations and failures, and then was placed into one of the three categories, i
Figure B.1 lists the maintenance records for one RHR pump taken from a plant maintenance work request (MWR) or work authorization (WA) log list, and demonstrates
- the categorization of each of the items according to the scheme defined in Table B.I. The 4
description of each of the records was used to classify the record in one of the three
- 1 categories, as shown in, the last column (N, D, or F). The data for the SW pumps were taken j
from the NPRDS and are shown in Figure B.2. Again, the last column of this figure indicates the classification of each record, We note that this categorization is at variance with the severity classification (catastrophic, degraded, and incipient) used in NPRDS. The reason is that NPRDS is not directed at aging evaluations, whereas this data analysis focussed on i-identifying age related degradations and failures.
1 DESCRil'rlON
=IDENT.
FAILURE WA #
EQUIP. #
(ACrlON TAKEN)
DATE CLASS.
P21906 IP202D ANNL PM.RilR PMP motor INSPECTION '
12/15/52
-N OIL SAMPLES TAKEN/NO LEAKS FOUNC S24999 IP202D INST VIB PICKUP MOUNT LOCATIONS FoR V! bro PACK 7/08/82 N
PICK UP oN kilR CANCEU ED-No WORK WILL DE PERFORMED UNDER Tills WA U24318 IP202B REBUILD MECH SEAL TilAT WAS' REMOVED FRoM PUMP
-3/16/82 D
REBUILT SEAL, NEW 'o" RINGS & SEAL FACES RE.
TURNED TO STORES P30491 IP202D ANNL PM.RitR PMP SEAL HT XR 3/1//83 D
CLEANED. INSPECTED REPLACED OASKETS. REASSEM.
BLED. TORQUED TO 30 FT/LBS CLEANED AND IN-SPECTED HELIFLOW COOLET AS PER IOM 155.
P31444 IP202B EQ QL.RHR PUMP MOTORS 9/08/R3 N
REMOVED olL SAMPLES FROM UPPER & LOWER BEAR.
INGS. OK IS IN THE CilEM LAD. OIL LEVELS WERE AT Tile PROPER LEVEL SCREENS ON MOTOR WERE CLEAN.
SPACE HEATERS OK.
P40859 IP202B ANNL PM-RHR PMP SEAL llT XR 4/18/t4 F
A NEW SEAL WATER COOLER WAS INSTALLED UNDER WA #C44042 PMR 84 3014 DURINO Tile UNIT 1/ UNIT 2 TIE IN OUTAGE. INSPECTION IS NOr NECESSARY AT Tills TIME.
N - No Degradation /Fallure D - Degradation F - Failure Figure B.I. Maintenacce log for an RilR purr.p at a BWR unit B-2
T' %
- .. " f,.
~~
I FAILURE FAILURE UTILITY IN. SERV
~
START END UNIT COMPONENT DATE FAILURE DATE DATE ID ID FAILURE NARRATIVES (COMP)
CLASS.
08/12/82 05/30/82 GPCEllit P41-C001 A PLANT SERVICE WATER PUMP FAILED TO MEET REQUIRE-12/31/75
.F MENTS OF ASME SECTION 11 IWmnn THE CODE S INTENT IS TO TRACK PUMP PERFORMANCS AND Tti /MSURE TiiE PUMP PERFORMS PROPERLY. TF %USE OF THE FA1URE WAS DUE
'a0 NORMAL WEAR AND NAIURAL END OF LIF3. THE PUMP WAS REBUILT AND SAT 17 ACTORILY TESTED AND RETURNED TO SERVICE.
04/02/84 04/25/84 GPCEIHI P41-C001 A DURING PLANT OPERATION. OPERATIONS PERI *)NNEL DETER-12/31/75 F
MINED TilAT TIIE PLANT SERVICE WATER PUMVS SHAFT SEAL WAF LEAKING EXCESSIVELY. REF MR I-84-1385 FAILURE WAS CAUSED BY WEAR AND ABRASIVE WATER. THE PUMP *S SilAFT SEAL WAS REPLACED WITH A NEW ONE. TiiE PUMP SEAL WAS TIIEN SATISFACTORILY TESTED 06/02/85 10/02/85 GPCElHI P41-C001 A WillLE OPERATING AT RATED FOWER. OPERATIONS PERSON-12/31/75 D
NEL DETERMIMED TilAT PLANT SERVICE WATER PUMP "A" WAS OPERATING AT A DECREASED FLOW AND PRESSURE.
'TIIERE WAS NO EFFECT ON THE PLANT. (REF MWO'S 18503078 A8504604,18503227 AND DCR 84-59) THE CAUSE WAS ATTRIB-9 UTED TO EROSION OF Tile PUMP LNTERNALS (NORMAL W
WEAR), CAUSING LEAKAGE PAST TiiE IMPELLER TO T11E SUC-TION SIDE OF THE PUMP. TlHS WAS A CARBON STEEL PUMP.
Tile INTERNALS. DISCHARGE CASE AND SUCTION BELL OF
. TiiE PUMP WERE REPLACED WITil STAINLESS STEEL PARTS PER DESIGN CHANGE. T11E PUMP WAS OPERATIONALLY CHECKED AND PERFDRMED AS EXPECTED.
35/11/87 06/18/87 GPCElHI P41.C001 A DURING A PLANT REFUELING OUTAGE. OPERATIONS PERSON-12/31n$
D NEL LOCATED A SMALL LEAK ON TriE A PLANT SERVICE
- WATER PUMP COUPLING. THIS DID NOT CAUSE ANY CHANGES IN PLANT PARAMETERS. REF: MWO I-87-03830. Tile CAUSE OF THE LEAK WAS FOUND TO BE A HOLE IN Tile COUPLING CO7 LING WATER LINE. THIS WAS ATTRIBIflT.D TO l
NORMAIJCYCLIC WEAR. THE COOLING COIL WAS REMOVED l
AND REPAIRED. AFTER TESTING IT WAS REPLACED AND THE PUMP WAS RETURNED TO SERVICE.
l l
D - Degradation F - Failure f
{
Figure B.2. NPRDS reported data on SW pumps l
l l
l 2-
,a-.-
For each component, a time-line plot was generated indicating the age of the component and times of degradations and failures based on maintenance data for the life of the component. Figure B.3 shows an example of such a plot. The in-service date for the component is considered the beginning of life for the component. Following replacement or overhaul, components were treated as new, i.e., as if the component was at the beginning of life.
The age of the component was calculated by the difference between the component i
in-service date.(or overhaul date) and the problem identification date for maintenance. The i
age was expressed in quarter years. All maintenance records (types N, D, and F) for each component were plotted in a time line fashion to recognize any patterns in the records (Figure B.3).
Data for Statistical Analysis I
Two types of-data, time to degradation (TTD) and time to failure (TTF), were developed for each component from the time-line plots. The TTD was used to obtain the l
degradation rate, while the 1TF was used to obtain the failure rate of the component.
-Both F-and D-type records were used to calculate TTD. In estimating the 1TF, only F-type records were used. Both these parameters (TTD and TTF) are obtained as a function u
of component age from the maintenance records categorized as D or F. Continuity in the I
maintenance records was important to.obtain this data.
Data Source Limitations i
It was difficult to obtain complete maintenance records of aged components. Specifical-l ly, recently built plants have computerized lists of their maintenance activities and, thus, provide all three record categories (i.e., N, D, and F types). But they cover only the early r:
years of a component's life. On the other hand, older plants did not have such a system at an I
l i
TIME TO TIME TO l
DEGRADATION FAILURE (TTD)
(TTF) s l
s i
O' 1
DN F
D F
AGE IN QUARTERS Figure B.3. Example of time line of plot of degradation (D) and failure (F) times
\\
B-4
J. : +
i.
early age, so that information relating to their early life was not readily available in a form needed for this analysis.- However, after the plant adopted a computerized system, the data were as complete as the new plants' The data obtained from NPRDS are not as complete as those obtained from plant spe-cific maintenance records. Since utilities are not required to report all maintenance activities to NRPDS, only some maintenance of the component are obtained. Furthermore, data over the entire operating life are not always available in the data base.
RHR Pump Aging Data Aging data on RHR pumps are obtained by analyzing plant maintenance records for three units. Since the units are of different age, data for RHR pumps in each covered different periods: 34 quarters for Unit 1,25 quarters for Unit 2, and 50 quarters for Unit 3' (Table B.2). This table contains the observed dates both for degradations and failures. Table B.3 presents the failure data where only the observed failure times are recorded. As these tables show, significantly larger information on component aging is obtained by focussing on degration data.
SW Pump Aging Data Aging data on SW pumps supplying water to the RHR system were obtained from the NPRDS data base. Tne data gathered fmm twelve plant units were tested statistically for their compatability. Only seven units are found to have compatible data, and accordingly data from these plants were used in the analysis. Since each unit has three or more SW pumps, data from a total of forty three SW pumps form the data base for this evaluation.
Table B.4 lir.ts the pump data, except those relating to the pump seals.
A large number of datafor the SW pump was related to degradation or failure of pump seals. Since these pumps use cooling water from an external source (e.g., sea, river, or pond), seal degradation / failures are in many cases attributed to intrusion of sands, sea weeds, and other external materials. These seal failures are not attributable to normal aging of the seals and hence, were excluded from this study.
In many cases, the data on a SW pump covered a brief period of the component operating, life. This sparse data for a pump can create difficulty in calculating the time to degradation (TD) and the time to failure (TTF). Since the available data period did not necessarily cover the beginning of life of the component, the first failure / degradation occurrence was used to obtain TTD or TTF. Thus two data' points are required to calculate one TTF data (see Figure B.3). This difficulty resulted in a small data set for SW pump l
failure analysis. Therefore, Table B.5 which lists the failure data contains only five data points while Table B.4 has identified a number of data points categorized as type 'F'.
I Because of these difficulties, the NPRDS data source is found to be less useful compared to the maintenance records from a plant. Furthermore, the NPRDS data base for a l
component appears incomplete in comparison 'o plant maintenance records. In conducting degradation modeling analysis, a complete data of all detected degradations and failures are required which necessitate use of plant data bases that contain information collected during all test and maintenance of the comporient, e
B-5
M igu
-p, 4 '.
s Table B.2. RIIR Pump Aging Data: Degradation and Failure Times
-(3 Nuclear Units: 4 Pumps Per Unit)
Time to i
Time of Detection.
Degradation Age -
1/ Tij Mo Dy Yr Pit Comp Syty
. (Tij)
(TI)
(Yl) 5 1
80 I
a D
1.33 1.33 0.750 1
15 81 1
a D
2.88 4.21 0.347 3
16 82 1
a D
4.73 8.94 0.211 10 28 82 1
a D
2.47 11.41 0.405 9
8 83 1
a D
3.50 14.91 0.286 2
17 84
.I a
D 1.82 16.73 0.549 7
I 84 1
a D
1.49 18.22 0.672 7
.26 85 1
a D
4.33 22.56 0.231 5.
12 80 1
b D
1,46 1,46 0.687 1
15 81 1
b D
2.76 4.21 0.363 3
16 82 1.
b D
4.73 8.94
.0.211 10 28 82 1
b D
2.47 11.41 0.405 3
17 83 1
b D
1.60 13.01 0.625 4
18 84 1
b F
4.40 17.41 0.227 7
26 85 1
b D
5.14 22.56 0.194 3
10 86 1
b D
2.54
~25.10 0.393 1
9 87 1
b F
3.38 28.48 0.296 5
10 88 1
b D
5.40 33.88 0.185 6
7 80
.1 '
c
.D 1.73 1.73 0.577 1
15 82 1
c F
6.53 8.27 0.153 i
3 16
.82 1
c D
0.68
' 8.94 1.475 10 28 82 1
c D
2.47 11.41 0.405 9
8 83 I
c D
3.50 14.91 0.286 6.
8 84 1
c D
3.06 17.97 0.327 8,
7 84 I
c D
0.66 18.62 1.525 7
26 85 1'
c D
3.93 22.56 0.254
.2 2
87 1
c D
6.18 28.73 0.162 4
25 80 1
d D
1.27 1.27 0.789 5
12 80
'l d
D 0.19
. l.46 '
5.294 3
'16 82 1
d D
7.49 8.94 0.134 10 28 82 1
d D
2.47 11.41 0.405-12 15 82 1
d D
0.52 11.93 1.915 3
17 83 1
d D
1.08 13.01 0.928 4
18 84 1-d F
4.40 17.41 0.227.
5-5 84 1
d D
0.19 17.60 '
5.294 6
29 84 1
d D
0.60.
18.20 1.667 C
7 26 85 1
d D
4.36 22.56 0.230.
7 28 86 1
d D
4.08 26.63 0.245 1
4 83 2-a D
0.03 0.03 30.000 8
25 83 2
a F
2.57 2.60 0.390 11 8
83 2
a D
0.81 3.41 1.233-2 2
84 2
a D
0.99 4.40 1.011 Tij -- Time intervals of observed events Ti - Age at which an event is observed Yi - Reciprocal of Tij B-6
o =, -
Table B.2. RilR Pump Aging Data: Degradation and Failure Times (3 Nuclear Units; 4 Pumps Per Unit)-Cont'd.
Time to Time of Detection Degradation Age 1/Tij Mo~
Dy Yr Pit Comp Svty (Tij)
(TI)
(Yi) 1 8
7 84 2
a F
2.06 6.46 0.486 5
8 85 2
a F
3.07 9.52 0.326 1
16 86 2
a D
2.81 12.33 0.356 4
19 88-2 a
F 9.14 21.48 0.109 1
4
-83 2
b D
0.03 0.03 30.000
.7 28 83-2 b
D 2.27 2.30 0.4/1
, 11 8
83 2
b D
1.11 3.41 0.900 6
19 84 2
b F
2.51 5.92 0.398 8
2 84 2
b F
0.48 6.40 2.093 1-30 86 2
b D
6.09 12.40 0.164 2
11 86 2
b D
0.12 12.61 8.182 3
24 87 2
b_
D 4.53 17.14 0.221 l
12 17 87 2
b D
2.92 20.07 0.342 2
4 88 2
b D
0.58 20.64 1.731 1
I 4
83 2
c D
0.03 0.03 30.000 2
-1 83 2
c D
0.30 0.33 3.333 3
4 83 2
c D
0.37 0.70 2.727 5
25 83 2
c D-0.90 1.60 1.111
'I 9
27 83 2
c D
1.36 2.96 0.738 2
16 84 2
c D
1.60 4.56 0.625,
l 5
16 84 2
c D
1.00 5.56 1.000-8 15 84 2
c F
0.99 6.54 1.011 3
7 85 2
c D
2.30 8.84 0.435 2
3 89 2
e F
15.84 24.69 0.063
-j 1
4 83 2
d D
0.03 0.03 30.000
.I 11 83 2
d D
0.08
- 0.11 12.857 4
12 83 2
d
'D 1.01 1.12 0.989 3
~5 84 2
d F
3.64 4.77
.0.274 8
2 84 2
d D
1.63 6.40 0.612 8
15 84 2
d F
0.14 6.54 6.923 9
20 84 2
d F
0.39 6.93 2.571 3
7 85 2
d D
1.91 8.84 0.523 12 17 87 2
d D
11.22 20.07 0.089 8
1 74 3
a D
1.00 1.00 1.000 12 5
74 3
a F
1.38 2.38 0.726 12 15 75 3
a D
4.17 6.54 0.240 9
20 76 3
a D
3.11 9.66 0.321 11 21 76 3
a D
0.68 10.33 1.475 4
12 26 76 3
a D
0.39 10.72 2.571 I.
16 79 3
a D
8.39 9.11 0.119 3
16 82 3
a D
12.03 31.94 0.078 6
3 82 3
a D
0.86 32.80 1.169 4
Tij - Time intervals of observed events Ti - Age at which an event is observed Yi -- Reciprocal of Tij B-7
,..a Table 11.2. 'RilR Pump Aging Data: Degradation and Failure Times
-(3 Nuclear Units; 4 Pumps Per Unit)-Cont'd.
Time to Time of Detection Degradation Age 1/ Tij Mo- ~ Dy Yr Pit Comp Syty
- (Tij)
(TI)
(Yi) 10 -
23 82 3
a D
1,56
.34.36 0.643 1
2 25 83 3
a D
1.41 35.77 0.709 3
3 85 3
a D
8.20 43.97 0.122 7-1 86 3
a 5.37 49.33 0.186 4
23 75' 3
b 3.97 3.97 0.252 12 18 78 3
b 14.78 -
18.74 0.068 3
10 82 3
b 13.13 31.88 0.076 4
4 82 3
b 0.27 32.14 3.750 5
1 82 3
b 0.30 32.44 3,333 6
8 82 3
b L
0.41 32.86 2.432 8
1-82 3
b D
0.59 33.44 1.698 10 23 82 3
b D
0.91 34.36 1.098 2
9 83 3
b D
1.23 35.59 0.811 3
1 85 3
b D
8.36 43.94 0.120 4
23 82 3
c D
32.36 32.36 0.031 10 23 83 3
c D
6.06 38.41 0.165 3
1 85 3
c D
5.53 43.94 0.181 9
14 74 3
d F
1,48 1,48 0.677 3
18 76 3
d D
6.16 7.63 0.162 11 4
76
'3 d
D 2.51 10.14 0.398
'5 1'
82 3
d D
22.30 32.44 0.(M5 10 23 82 3
d D
1,91 34.36 0.523 12 1
82 3
d D
0.42 34.78 2.368 1-1 83 3
d D
0.39 35.17 2.571 1
1 84 3
d D
4.06 39.22 0.247 3
l' 85 3
d D
4.72 43.94 0.212 Tij Time intervals of observed events Ti - Age at which an event is observed Yi - Reciprocal of Tij i.
5 b
I B-8
k. y o - _,
I o-Table B.3. RilR Pump Aging Failure Data (3 Nuclear Units: 4 Pumps Per Unit)
Pit Compt ITij.
FTi FYi 1
2 17.41 17.41 0.057 l'
2 11.07 28.48 0.090 1
3 8.27 8.27 0.121 1
4 17.41
-I7.41 0.057 2
1 2.6 2.6 0.385 =
2 1
3.86 6.46 0.259-2 1
3.07 9.52 0.326 2
1 11.96 21.48 0.084 2
2
'5.92 5.92 0,169 2
2 0.48 6.4 2.083 2
3 6.54 6.54 0.153 2
3 18.I5 24.69' O.055 2
4 4.77 4.77 0.210 2
4 1.77 6.54 0.565 t
2 4
0.39 6.93 2.564
-3 1-2.38 2.38 0.420 3
2 3.97 3.97 0.252' 3
4 1.48 1.48 0.676 FT(J - Time intervals between observed failures 171 - Age at which an event (failure) is observed FYi - Reciprocal of FTij s
I t
B-9
F" j
i=
4-
. Table B.4. SW Pump Aging Data: Degradation Times (7 Nuclear Units)
Time to
' Time of Detection Degradation -
Age 1/Tij Mo Dy-Yr Plt Comp Syty Dsep (Tij).
(TI)
(Yl) 3 7
74 4
-d-d purrp 0.18 0.18 5.625 3
7 74 4
a f
ramp 0.18 0.18 5.625 8
14 86 5
g f
drain 0.37 0.37 2.727 1
12 84 3
e f
pump 0.51 0.51 1.957 3~
'7
-10 74 4
c d
impel 1.54 1.54 0.647 7
10 74 4
a J
impel 1.37 1.54 0.732 7
10 74 4
d d
impel 1.37 1.54 0.732 12 4
86 5
g f
gasket 1.22 1.59 0.818 3.
8 80-7 d
d pump 2.09 2.09 0.479 3
15 86 7
b f
impel 2.42 2.42 0.413 7
17 86
.7 b
d pump 1.36 3.78 0.738 5
15 86 5
a d
impel 0.80 4.01 1.250 11-22 83 5
h d
cooler 5.79 5.79 0.173 5
11 81 7
a f
pump 6.84 6.84-0.146 10 22 85 2
b f_
supp 7.68 7.68 0.130 6
14 87 11-I d
brgs 7.82 7.82 0.128-2 25 76 4
g.
f brgs 8.16 8.16 0.123 12 13 85 3
e d
flange 1.08 8.24 0.928 3
3 86 3
e d
btgs 0.94 9.19 1.059 5
15 86 3
d f
brgs 9.99 9.99
. 0.100 5
23 86 3
e d
lube 10.08 10.08 0.099 3
,14 82 7
e d
pump 10.27 10.27 0.097 8_
8.
86.
2 d
d sep 10.91 10.91 0.092 5
12 82 7
d d
pump 8.82 10.91 0.113
-3 3
85 5
c d
pump
.11.02 11.02 0.091
- 10 28 86 2
e d
motor 2.17 11.80 0.462 6
3 85 5
d f
valve 0.41 12.02 2.432 4
17 86 5
b f
brgs 15.57
'15.57 0.064 7
24 78 4
h f.
brgs 17.92 17.92 0.056 '
12 18 86' 5
b d
pipe 2.68 18.24 0.373 6
11 87' 5
e d
pump 8.30 20.22 0.120 8
6 85 7
d d
brgs 13.10 24.01 0.076 10 16 80 4
e f
pump 12.80 26.94 0.078 5
31-86 7
.a f
pump 4.18 27.34 0.239
'6 22 86 7
e f
diffu 17.31 27.58 0.058 1
87 7
g d
brgs 5.56 29.73 0.180 5
12 87 7
e f
pump 3.61 31.19 0.277 Tij - Time intervals of observed events Ti - Age at which an event is observed Yi - Reciprocal of Tij impel - Impeller brgs - bearings supp - support (hangers, snubbers) sep - separator diff-- diffuser tube - lube oil p.m - pump-motor B-10
/
s_-
,>c,,.
Table B.4. SW Pump Aging Data; Degradation Times (7 Nuclear Units)-Cont'd.
Time to Time of Detection.
Degradation Age 1/Tij Mo Dy, Yr Pit Comp Svty Dsep (Tij)
(TI)
(Yl) 3 25 88 7
d d
brgs 10.71 34.72 0.093 6
2 85.
6 a.
f pump 4.72 38.23 0.212
-6 25 82 11 h
d p-m 0.04 43.48 22.500 4
4 88 2
a d
pump 10.17 44.79 0.098
.5 11 87 6
a d
cooler 7.88 46.11 0.127 8
27 85 4
e d
drain 11.99 46.68
- 0.083 8
28 87 6
c f
brgs 10.66 47.30 0.094 11 14 85 4
b d
pump 4.66 47.53 0.215 7
30 86 4
b d
pump 2.90 50.43 0.345 7
1 88 b
c d
pipe 3.42 50.72 0.292 1
18 87 4
b d
pump 1.92 52.36 0.520 6
10 87 4
b d
drain 1,58-53.93 0.634 6
17 85 11 d
d vent 12.69 55.56 0.079 10 5-85 11 f
d pump 14.06 56.76 0.071 Tij - Time intervals of observed events Ti - Age at-which an event is observed
. Yi - Reciprocal of Tij impel - impeller brgs - bearings supp - support ('. angers, snubbers) sep - separator
' diff - diffuser tube - lube oil
. p-m - pump moti r Table B.S. SW Pump Aging Failure Data Times (7 Plants) row Mo Dy Yr Plt Comp Syty Dsep FTij FTl FYi i
12 4
86 5
g f-gasket 1.222 1.59 0.819 2
6 3
85 5
d f
valve 12.020 12.02 0.083 3
5
.31 86 7
a f
pump 20.500 27.34, 0.048 4
5 12 87 7
e f
pump 20.920 31.19 0.047 5
6 2
85
.6 a
f pump 38.230 38.23 0.026 FTij - Time intervals between observed failures FTi - Age at which an event (failure) is observed FYi - Reciprocal of FTij B-11
APPENDIX C. STATISTICAL TESTS ANALYSES FOR DATA FROM DIFFERENT RHR PUMPS IN DEGRADATION AND FAILURE RATE This appendix summarizes the statistical tests performed on degradation and failure data of the RHR pumps. The specific statistical tests and their purposes are as follows:
- 1. Tests to identify the similarity of degradation and failure of RHR pumps within a nuclear unit
- a. Mann-Whitney (M-W) U Test
- b. Kruskal-Wallis (K-W) Signed Rank Test l
- 2. Test to identify the similarity of degradation and failure behavior across nuclear units
- a. Mann-Whitney (M-W) U Test
- b. Kruskal-Wallis (K-W) Signed Rank Test 3, Test to identify periods where there are significant time trends in degradations and failures
- a. Mann's Rank Test.
In the following, we briefly explain the tests performed and the results obtained. Only-representative results are presented; similar results are obtained in other cases as indicated in the text.
C.1 - Mann-Whitney U Tests for RHR Pumps Within Each Nuclear Unit l
r The Mann-Whitney U Test is conducted, based on the degradation data set, to see if the
. times between degradation T (or equivalently I / T )in each of the 4 pumps are identically y
y distributed within each of the 3 plants. The Mann-Whitney procedure is designed for tests of two independent samples; it.is a variation of the Wilcox rank-sum procedure, and the computational form of its statistic U uses the rank sum. The test combines and ranks the data from two samples; these ranks are then summed over all observations in each sample and the
. statistic U is calculated as follows to compare the average ranks:
i ni(ni + 1)
U ' = nin2 +
-T i
2 i
i n2(h2+ 1)
U = nin2 +
-T 2
2 2
where T = sum of ranks associated with X values (i = 1, 2), and i
i C-1
4 t
(+
n = sample size of X.
i i
In our degradation data sets most samples have more than 10 observations, therefore, a nor' al approximation of test statistic Z is used in'the test.
~
Z=
G,
- where,
[{ ni o = ([ ni) + 1 [{ n
-i 2
p, =
and i
2 I
The main assumptions of the Mann-Whitney Test are satisfied in our data, that is:
a, the samples are independent, and
- b. the populations are identical except for possible differences in location.
l However, in reality the_ Mann-Whitney Test enables us to identify any-differences'in the-i
. derlying distributions although it is particularly. sensitive to differences in location (in -
to as of medians or means). Therefore, it is a strong statistical test to identify whether -
mr ponents belong-to the same population.-
The Lan-Whitney Test for each pair in each of the three plants did not reject the null.
' hypothesis-of identical samples (based on comparison of average ranks and significance level of 0.05). Table C.1 presents the results for the pumps in one of the plants; similar results are obtained for all three plants. Null hypothesis of identical samples was not rejected in any of the cases. Accordingly, the degradation behavior of the four RHR pumps belonged h
li i
to t e same popu at on n each of the plants.
Tabic C.I. M-W Test Results for RIIR Pumps in Plant !
Average
- of Values Average
- of Values Test Comparison of Rank of of 1st Sam-Rank of of 2nd Total Statistic
!p Samples ist -Sample
- pie 2nd Sample Sample Obsery.
Z Value Compt 1 Compt 2 10.75 8'
8.5 10 18
-0.845 0.398 Compt 1 Compt 3 9.25 8
8.77 9
17
-0.145 0.885 Compt 1 Compt 4 8.44 8
11.14 11 19 0.992 0.321 Compt 2 Compt 3 9.65 10 10.39 9
19 0.245 0.806 Compt 2 Compt 4 8.6 10 13.18 11 21 1.656 0.098 Compt 3 Compt 4 9.16 9
11.59 11 20 0.874 0.382 C-2
C.2 Kruskal-Wallis:(K-W) Signed Rank Test K-W Signed Rank Test is similar to'Mann-Whitney Test and is applied as a multiple comparison test to. identify any abnormal component (s) in each of the plants. As with the M-W U Test, the K-W Test is a test of identical distribution and is particularly sensitive to location differences.~ The K-W Test is an extension of the M-W Test to cover situations involving multiple independent random samples. Thus, it provides an alternative distribution free test among all the components for each of the plants to identify any possible abnormal components.
i Table C 2 shows test tesults for Plant 1. Similar results are obtained for the other two plants. The K-W Test results, showing a significance level greater than 0.05, justify results i
from Mann-Whitney Tests in Section C.1, i.e., the hypothesis that RHR pumps in each of the plants belong to the same population cannot be rejected.
C.3 Mann-Whitney U Test for RHR Pump Degradation Data Across Plants The Mann-Wnitney U Test is used to identify the similarity of RHR pump degradation across plants. Here, the purpose _is to identify groups of plants where data can be combined to increase the sr.inple si7e.
The test was performed, based on data pooled (referred to as' Method 2 in Chapter 5.0) across 4 RHR pumps in each of the plants (Table C.3). Again, a null hypothesis of identical samples for each pair of plant's degradation data comparing medians based on average ranks of each plant is not rejected. This justified increasing the data base by using data across three plants.
e Table C.2. K-W Test for Plant 1: Kruskal-Wallis Analysis of 4 RHR Pump Degradation Data Pump Sample Size Average Rank 1
8 19.4375 i
2 10 15.7500 3
9 18.3333 4
11 23.9091 Test statistic = 2.97417 Significance level = 0.395625 Table C.3. M-W Test for Identifying Plant Groups
. Average
- of Values Average
- of Values Test Comparison of Rank of of ist Sam-Rank of of2nd Total Statistic p
Samples 1st Sample
~ ple 2nd Sample Sample Obsery.
Z Value Plant 1-Plant 2 23.3M 23 27.911 28 51 1.164 0.244 Plant 1 -Plant 3 25.304 23 27.31 29 52-0.498 0.619 Plant 2 Plant 3 30.125 28 27.241 29 57
-0.495 0.621 C-3 l
'\\\\;
v r,e +
1 q c C.4 Kruskal-Wallis Test to RHR Pump Degradation Data Across Plants Table C 4 presents'the Kruskal-Wallis Test to RHR pump data across_ plants (obtained i
by data pooling across four pumps in a plant). Again, the result obtained supported the conclusion obtained with the Mann-Whitney' Test.
C.5 Mann's Rank Test to Identify Age Groups with Significant Time Trends 1
Mann's Rank Correlation Test is-used to identify time trends over age in failure and degradation data. Age intervals showing significant trends are also identified..
Tests are conducted to both degradation and failure data by two methods discussed
_ before. Method 1 data combining, and Method 2, data pooling, show similar results (Table C5).-
A Type I error of 0.05 is used as a decision criterion for the significance level to define a trend with increasing age. For degradation data, a significant increasing time trend is found over the period of 19.5 to 38.6 (approximately 20 to 40) quarters, whereas a decreasing time trend is observed over the first 20 quarters. Similar results are obtained for both methods of using data from 12 RHR pumps. The significance levels and the Kendal's rank correlation coefficients are presented in Table C.5. For failure data, a decreasing trend is identified for the first twenty quarters, but there was no time trend in the remaining quarters.
Table C.4. K-W Test for Identifying Plant Groups Pump Sample Size Average Rank 1
23 363870 2
28 43.6786 3
29 39.6034 Test statistie = -2.83185 '
Significance level = 1 Table C.S. Mann's Trending Test Results Data Use Degradation Data Trending Failure Data Trending Methods -
Test Results Test Results b
Data Period Data Period Data Period '
Data Period (0,19.5) quarters (19.5, 38.6) quarters (0, 22) quarters (22, 40) quarters Data Combining (Method 1) p = -0.338 p =.2574 p = -0.256 Insufficient Data to Sig. Level = 0.001 Sig. Level = 0.049 Sig. Level = 0.22 Conduct Test l
Data Period Data Period Data Period Data Period (0, 21.6) quarters (21, 39) quarters (0, 20) quarters (20, 40) quarters j
Data Poolm, g h
(Method 2) p = -0.106 p = 0.285 p = -0.396 Insufficient Data to Sig. Level = 0.281 Sig. Level = 0.055 Sig. Level = 0.035 Conduct Test l
l-l l-C-4 1'
l l'
.- a
- APPENDIX D. ESTIMATION OF AGING EFFECT ON DEGRADATION AND FAILURES-AND MAINTENANCE EFFECTIVENESS EVALUATION FOR RHF. PUMPS
. This appendix summarizes the estimation pro;ess asing Cox's model (discussed in Chapter 4) to determine age-dependent degradation nd frdiure rate for the RHR pumps. The estimation of a maintenance ineffectiveness factor, bned on degradation rate, and failure rate is also discussed.
The steps for. estimating rates are similar for degradation and failure:
- 1. For the defined age groups showing significant aging trends perform regression analysis to estimate the aging parameters defined by the Cox model.
- 2. For the data not showing.any aging trend, obtain the time-independent rate.
- 3. Use spline fitting to obtain the aging effect for the entire period based on regression curves obtained for portions.
D.1 Regression Analysis to Obtain Aging Rates i
For the age groups showing significant trend with time, regression analyses are per-formed to obtain the aging rates. For degradation data, decreasing trend is defined for the 0-20 quarters, and increasing trend is defined for the remaining life, 20-40 quarters.
Analyses are performed for both methods of using data from 12 RHR pumps. Degrada-tion rate parameters a and b obtained are presented in Table D.I. Similar results for analyses of aging failure are presented in Table D.2. Since no trend could be established during 20 to 40 quarters of age, a constant failure rate is estimated.
- D2 Isotonic Regression Analysis Isotonic regression analysis is performed to estimate failure rate in.the interval 0-20
- quarters. This approach of obtaining the time trend in failure data i:: especially powerful for few data,'as is the case for the data on RHR pump failure. Re.calts of isotonic regression for both the methods of using data across RHR pumps are presented in Tables D.3 and D.4.
. D.3 Aging Rates Using Spline-Fitting Degradation and aging-failure rates obtained as through' regression analyses in different age intervals are used to obtain the aging effect over the entire age using spline-fitting.
Figures D.1 and D.2 show the aging effect in the degradation rate for ten years of RHR pump life data: Figure D.1 showc ths results based on combining data (Method 1 of using data from 12 pumps) and Figure D.2 on pooling data (Method 2). The results are comparable, i.e., the aging effects on degradation are similar, the degradation rates obtained are not very different, and the uncertainties in the results are of similar magnitude.
Figures D.3 and D.4 present the aging effect on failures based on these two methods:
'both these curves show a decreasing trend for first 20 quarters of life. The constant failure D-1
..s 7 - my
- 2-
- 4 Table D.I. Estimation Results for Degradation Rate Analyses Aging Rate b Constant in A ~
Model Data Use Age Uncertainty Uncertainty
~ Standard Methods Intervals Estimated Significance Range Estimated Significance
. Range Significance Error Parameter Level (5% error)
Parameter Level (5% error)
Level.
of Est.
0-20
--0.095 0.0006 '
O.541 0.025 0.0001 1.234 -
(9"*"*")
CU: -0.05086 CU: 1.0149 Method 1:
Data Combining
~
20-40 0.105 0.046
-4.161 0.012 0.0455'-
1.2875 (9"*"*"#
CU: 0.207 CU: -0.9975
[
CL: -0.0659 CL: -0.0247
-0.0285 0.1314 0.365_
0.06 0.131
'O.7453 I9"*"*")
CU: 0.00887 CU: 0.7549 -
Method 2:
Data Pooling
~-
20-40 0
0.095 0.0278'
-3.111 0.018 0.028 0.9638 tb (9"*"*")
CU: 0.1777 CU: -0.5882 CU = Upper (95%) range CL = Lower (5%) range
.,.ww A
y
.--p
-r.p.y w
g.a n
9y y-a w
(.
-. :~__
~
A Table D.2. Estimation Results for Failure Rate Analyses -
I Aging Rate b -
Constant in i Model Data Use Age Uncertaint, Uncertainty Standard Methods Intervals Estimated Significance Range Estimated Significance Range Significance Error Parameter Level (5% error)
Parameter Level (5% error)
Level of Est. <
O-20
- -0.249-0.584 0.0247 0.9309
-0.1338 0.025 (9"*"*")
Method I:
CU; -0.01995 CU: 0.7122 Data Combining 0.876 I
20-40 Not O.0146 Not Not (quarters)
Significant 3; ;g
-2.595*
0.95*
CU: -1.934*
Significant 0.2659*
0-20
-0.1513 0.027
-0.665 0.26 -
0.03 1.146 I9" "*"}
Method 2:
CU: -0.021 CU: 0.5821 Data 0.142t Q -3.798*
OM2
- 0. W Pooling 0.8418 20-40
. Not D
8.509E-3 Not Not
'Si "ifi'*"*
g (quarters)
E 0.1212*
. Significant
-3.497*
0.05*
CU: -3.197*
Significant J
- Based on direct estimation f Based on regression analyses e
e
.~n.
.~m
o
- Table D3. Isotonic Regression for Failure Rate Estimation (Data Combining-Method 1)
- Timc Interval T, 1.48 2.38
' 2.6 -
3.97 4.77 5.92 0.43 3.86
' _6.54 1.77 039 8.27 :.
3.07 17.41 11.96 18.15 11.07 (quarter).
Ta (1st Grouping) 3.2 2.9 5.67 14.68 14.61 T; (2nd Grouping) 1.45 238 2.6
' 3.97 4.77 3.05 5.67 '.
14.65 T[ (3rd Groupiag) 1.45 238 2.6 3.97 3.91 5.67 14.65 T[ (4th Grouping) 1.48 238 2.6 3.94
' 5.67 14.65 O.676 0.42 0J85 0.254 0.176 0.068 f
(in 1,)
(-039) (-0.868)(-0.955)
(-1377)
(-1.737)
(-2.69) -
No. of Faibres 17 O
(m)
E m-i
" *[I T, /
T e 0.497 Test Statistic V, =
(V )
=
Significance Ixvel a << 0.001== Reject H, (Constant Failure Rate)
(a)
Trend Decreasing Failure l
l l
I or L.4
_ _ - ~. -,,..
.L
,,.J.-..
c y.
,.~,4
-m
- Table D.4. Isotonic Regression for Failure Rate Estimation'(Data Pooling-Method 2)
Time Interval FT,
- 8.1 1.99 123 7.2 10.4 43 0.5 0.8 3.49 11.99 11 3 71 36.6 28.89 34.1 (quarter)
FT, (1st Grouping) 5.05 9.75 5.07 0.8 3.49 11.65 45.49 34.1 Ft; (2nd Grouping) 5.05 5.207' 3.49 -
11.65 39.79 Ff,' (3rd Grouping) 5.05 4348 11.65 39.79 Ft,~ (4th Grouping) 4.69 11.65 39.79 0.213 0.086 0.025 7
(in l')
(-l.546)
(-2.453)
(-3.688)
No. of Failures 15 9
(m)
M m-s[, T [
Test Statistic T
- 0.817 (V,)
6-1 Significance Level a
0.001 => Reject II,(Constant Failure Rate).
(a)
Trend Decreasing Failure l
l i
{
I.
l l
._-..A,.
Ny
,u Degradation Rate h( # per quarter)
'"h
- 54.6 -
4 33.12 -
po,op
- Estimated Deg. Rate 3
f t. f o 95% confidence bounds 7.39 2
4.48 Data Method 1 - Combining p,72 Quasi Cubic spline fit - j
..y
~
~~
,f O.14
-2 0.08 0.05
- -3 0.03 0.02
.1 1..-.-
.. a -
--.,..-.4 0
10 20 30 40-Age in Quarters (3 month periods)
Figure D.1 Age dependent degradation rate (Component: RHR pumps; 3 plant data)
. Degradation Rate (Inh, per quarter) 54.6 4
- Estimated Deg. Rate, Inh 95% confidence Dounda I'UE
~
Data Method 2 - Pooling.
~
Quasi Cubic splino fit 2.72 T
~~
/
f.00 WT
--/.g~~
0 0.37 0.14
~ -2 0.05 o,og.
u.
...t.--....----...t.
4 0
10 20 30 40 Age in Quarters (3 month periods)
Figure D.2 Age dependent degradation rate (Component: RilR pumps; 3 plant data)
D-6
u--,,..-,,,,,,,,
u Failure Rate 1,(# per Quarter) 54.6-4
-Estimated Failure Rate, in ), _ 3 l
95% confidence bounda 7.39-
~
2 Data Method 1
- Combining
- II Quaal Cubic spline fit l 1.00 ~
O 0.3hO
..j 0.14-
-\\
~~
2 N.
0.0 3
0.02 L
4 0:
10 20 30 40=
Age in Quarters (3 month periods)
Estimated Rate Extrapolated Rate Figure D.3 Age dependent failure rate (Component: RilR pumps: 3 plant data) -
Failure Rate (In),, per quarter)
.54.6 4
- Estimated Failure Rate, in),
7.37 95% confidence bounds
- 2 Data Method 2 - pooling Quaal Cubic spline fit 1.00 0-0.37
~~
- 0. f 4 N
- -2 aos x
0.02
~~
. 5..
-4 0
10 20 30 40 Age in Quarters (a month periode)
Estimated Rate Extrapolated Rate Figure D.4 Age depent.ent failure rate (Component: RHR pumps; 3 plant data)
I D-7
Dy+,.
rate obtained for the remaining 20 quarters is slightly different; Method 1 (data combing) is slightly higher than Method 2 (data pooling). The uncertainty ranges are similar, but they are larger than those for degradation rates.
Figures D.5 and D.6 compare the aging rates obtained from linear regression analyses with those estimated by isotonic regression analyses. The failure rate obtained from linear regression analysis appears to be a good approximation of that obtained from isotonic regression.
' D.4-Evaluation of Maintenance ineffectiveness (or Effectiveness)
Maintenance ineffectiveness is def'med in Chapter 3 as the transition probability from a degraded state to a failure state, where maintenance is performed every time the component is detected to be in the degraded state. Mathematically, using steady state solution,
' maintenance ineffectiveness, pop, is expressed as:
WF Por = 9 (D-1) where _Wp is the average foiure frequency and Wo is the average degradation frequency.
The above expression is truly applicable to steady state solution, but is an approximate model in age-dependent situation. In our analyses, aging effect on degradations and failures show different effects (as discussed effects) and the age-dependent degradation and failure rates are used to obtain the average parameters.
We obtain maintenance ineffectiveness in every 10 quarters by using a piecewise approximation to Wp and Wo for equally separated age intervals of 10 quarters.
- Let,
.t, I
W(t.,t)_=
Ap(t) dt p
b tb - t,,,,
.t.
W (t., t ) =
Ao(t) dl o
b tg - t,
,t, i
- and, t, = 10(i - 1) quarters, i = 1, 2, 3, 4 13= 10i quarters, D-8
1 1
i l}
s.
k Fallute Rate (Inh,, por quarter)
Estimated Failure Rate, in A,
Data Method 1 - Combining 2
~
fellmated falture Rate Quasi Cub!c spline fit by linear Repression 0,
Estimated failure Rate j
by Isotonic Repression n
,s 2
~
-4 O
10 20 30 40 50 Age in Quarters (a month period.)
i Estimated Rate Extrapolated Rate
(
i Figure D.5 Age dependent failu'e rate
' (Component: RilR pumps; 3 plant data)
Failure Rate (In),, per quarter)
- Estimated Failure Rate, in ),
i Data Method 2 - Pooling I
E Estimated Failure Rate Dy Linear Regression
' \\
p 0
-/
6-Estimated Failure Rate i
by isotonic Regression N
'N
~
-4 0
10 20 30 40 50 Age in Quarters (a month ouarters)
Estimated Rate Extrapolated Rate i
Figure D.6 Age dependent failure rate (Component: RilR pumps; 3 plant data)
D-9
-- - -- ^^'---~^-----
.,w;, _
Therefore, W(t.,t)-
p 3
por(t., t ) =
3 Wo(t.,1 ).
3 The maintenance ineffectiveness factor obtained for each 10_ quarters are calculated from Ap(t) and Ao(t) obtained previously. Table D.5 shows the results on two methods of using data for 12 RHR pumps, t
i D-10
== '
. j
_;. - -- n_
~ ~
e N
Table D.S. Maintenance Ineffectiveness Calculation for RHR Pump Expected Degradation Frequency Maintenance Ineffectiveness
. # of Failures / Quarter)
(# of Degradations / Quarter)
(Transition Probability)
(
Age Method (quarters) -
.Wr -
W Por '= Wr / We o
0-10 2.651 12.538 0.2114 10-20 0.58 9.428 0.585 Data Pooling 30 032 I3 71 0.2334 30-40 032 12.87 0.0249 '
9 0-10 4.298 II.09 0387
~
10-20 1.127 4.289 0.2629 Data Combining 20-30 0.76 2312 03288 30-40 0.76 6.606 0.I15 3.
e O
e
APPENDIX E. ANALYSIS OF AGE RELATED DEGRADATION AND FAILURE DATA FROMl SERVICE WATER (SW) PUMPS This appendix presents results of age related degradation and failure data analyses for Service Water (SW) pumps using the degradation modeling approach. The methodology used for the SW pumps _ is similar tc that used for the RHR pumps (presented in appendices C and D).
Here, we summarize the results f ?.: **' Jeal tests, the estimation of aging rates and the evaluation of maintenance effectiveness for the SW pumps.
E.1 K-W Signed Rank Test for SW Pumps Within Each Nuclear Unit K-W signed rank test was conducted for the Service Water pump data to identify those pumps with similar distribution of degradation times within each nuclear unit. The test was applied as a multiple comparison test to identify any abnormal component (s) in each of the plants. K-W test is more efficient, compared to Mann Whitney (M-W) test, when applied to a larger sample. For each of the plant, four to eight SW pump data were analyzed and accordingly, K-W test was chosen.
Table E.1 shows test results for plant 1, similar results are obtained for the other 6 plants (Table E.2 through Table E.7). The results justify the hypothesis that the SW pumps L
in each of the plants belong to the same population can not be rejected. Accordingly, the SW pumps in each of the plants can be considered to belong to the same group and the degradation data for the pumps in each of the plants were combined for further analysis.
E.2 K-W Test to SW Pump Degradation Data Across Plants l
Table E.8 presents the K-W test of Service Water pump data (obtained by combining ~
across all the SW pumps data in each plant) across. plants. The results supported the conclusion that the component degradation (and failure) data from the' underlying 7 different l
nuclear units have similarities in their data distributions, thus can be combined together to investigate the common aging behavior of SW pumps. Method I, called data combining, of L
~ using data from multiple components across different nuclear units was used. Data pooling n
(Method 2) was not tried in this case, m
E.3 Mann's Rank Test to Identify Age Groups with Significant Time Trends l'
Mann's rank correlation test was used to identify time trends in degradation data. Age intervals showmg sigmficant trends are identified as well.
l t
Table E.9 summarizes the results to type I error of 0.05 is used on a decision criteria for l-the significance level to define a trend with increasing age.
For degradation data, a significant increasing time trend is found over the age period of approximately 23 to 55 quarters; whereas a decreasing time trend is obtained over the first 23 quarters. For the available failure data, no trend could be established.
Accordingly, a constant failure rate is estimated for the study period (60 quarters).
E-1
o-e Table E.1. K W Test for Plant 1: Kruskal-Wallis Analysis of 4 SW Pump Degradation Data
+.
Pump Sampic Size Average Rank w
a 1
3-0 b
I 2-0
~
c 1
10 d
1 40
. Test statistic = 3 Significance level = 0.3916 Table E.2. K-W Test for Plant 2: Kruskal-Wallis Analysis of 3 SW Pump Degradation Data Pump Sample Size Average Rank c
3 24 d
i 4-0 t
c.
1 5-0 e
Test statistic = 3.2 Significance level = 0.2018 i
i Table E.3. K-W Test for Plant 3: Kruskal-Wallis Analysis of 7 SW Pump Degradation Data Pump Sample Size Average Rank a
2 2.5
.b 4
7.5 e
2 8.5 d
2 2.5 e
i 11.00 g
i 10.0 h
1 13.00
)
- Test statistic = 9.779 Significance level = 0.13427 g
Table E.4.~ K-W Test for Plant 4: Kruskal-Wallis Analysis of 6 SW Pump Degradation Data Pump Sample Size Average Rank a
1 3.0 -
b 2
7.0 I
c 2
7.5 d
1 2.0 g
2 2.5 h
1 6.0 Test statistic = 6.26 Significance level = 0.281 E-2
-,h, Table E.5 K-W Test for Plant 5: Kruskal-Wallis Analysis of 2 SW Pump Degradation Data Pump Sample Size Average Rank a
2 2.5 c
2 2.5
'lest statistic = 0 Significance level = l Table E.6. K-W Test for Plant 6: Kruskal-Wallis Analysis of 5 SW Pump Degradation Data Pump Sample Size Average Rank a
2 6.0 b
2 2.0 c
3 8.33
-d 4
7.75 g
1 6.0 Test statistic = 4.42949 Sijnificance level = 0.3509 Table E.7. K-W Test for Plant 7: Kruskal-Wallis Analysis of 8 SW Pump Degradation Data Pump Sample Size Average Rank a
1 9.0 b
3 4.6 c
2 6.0 d
i 11.0 f
1 12.0 g
1 4.0 h
2 4.0 1
1 8.0 Test statistic = 6.7948 Significance level = 0.4505 P
Table E.8. K-W Test for Identifying Plant Group Pump Sample Size Average Rank 1
4 37.5 2
5 22.4 3
13 25.538 4
9 25.44 5
4 35.00 6
12 34.75 7
12 32.50 Test statistic = 4.763 Significance level = 0.5745 I
E-3
~
p e
Table E.9. Mann's Trending Test Results f
Data Un Degradation Data Trending Failure Data Trending i
Methods Test Results Test Results Data Period Data Period (0, 23) quances (23.55) quarters Insufficient Data to Per-Data CombininE p = -0.567 p = 0.5147 form Significant Test Sig. Level =0.0001 Sig. Level = 0.0039 n s gn cant
" (
Trending Significant decreasing Significant increasing ns n i
E.4 Estimation of Aging Effect on Degradation and Failuress As in the case with the RHR pumps, the same estimation process is used in this cc.se in determining age-dependent degradation and failure rates.
For the age-groups showing significant trend with time, regression analysis was performed to obtain the aging rates. For degradation data, decreasing trend was defined for the age period 0-23 quarters and increasing trend was defined for the remaining life 23 55 quartere.
Degrarlation rate parameters a and 6 are presented in Table E.10. For aging failure rate, since no trend could be established during the observed time period of ages, a constant failure rate is estimated in the age interval 0-40 quarters to be 0.089/ quarters (or -2,4783 in nature logrithm scale). It's 95% contidant internal is estimated as [-0.817,--4.1397] in the lug scale.
E.5 Aging Rates Using Spline Fitting FOure E.1 presents the spline fitting curve of the aging effect on degradations for SW p nips. The degradation rate curve shows a rapid decrease during the first 15 quarters followed by a significant increase for the remaining 40 quarters. The behavior of the degradation rate follows a " bathtub" curve as was observed also in the case of RliR puutps.
The failure rate curve, showing a constant rate, is presented in Figure E.2.
E.6 Maintenance Effectiveness Evaluation for SW pumps W (t., t )
r 3
The maintenance ineffectiveness factor Por(t., t ) =: Wo(t., t ) was calculated for each 3
3 10 quarters based on Ap's and An': obtained previously. Thc maintenance effectiveness is the complement of maintenance ineffectiveness. The results are presented in Table E.ll and shown in Figure E.3.
E-4
a=
e Table E.19 Estimation Results for DegWien Rare Analyses Aging Rate b Constant in s Wdel Dets Use Age
, pygy y
7 g
E Estineated Significinec Range Estineated
. W xance Range Signeficance Erewr Parmsneter Leves (5% error)
Parasneter Level (5% error)
Level of Est.
CL: --0.2207 CL:-0.4669 g
-0.1527
-0.0001 0.1693 0.589 0.0001 1.0406 I"*"*I CU: -0.0848 CU: -0.8065 g
Combining CL: 0.00438 CL:: -4.578 55 0.0365 0.0285
-3.2534 0.0001 0.029 0.6285 IF"'
CU: 0.0686 CU: -I.9287 9
v
=
m T
s.e+
g,,,,
,7 p
i Table E.11. Maimenance Ineff'ectiveness Calculation Results Age Maintenance Ineffectiveness pm
(# et Faileres / Quarter)
Expected Degradation Frequency
@
- Mi'" N )J Data Use (quarters)
W
(# of Degradations / Quarter) 1-Pw = I-(W/W )
r o
0-10 0.839 N
0.8618 10-20 0.839 13176 03633 Data 20-30 0.839 0.966 0.1315 Combining 30 4 0.839 1392 03973
?
e 40-45 1.26 331g 0.6208 I
h 6
E 7
.... ~ ~,, -,. _ _ _ _....,. _ _.
m_,.
,.m
.m,
e.
.c n
-c..
o c
- f.jo(d G m.
e +
'I i
k L
i
- t....
De
'"l '
St or gradation Rate ( A.. per quarter)
-4 l
l' 20.09
- Estimated Dep. Ratelo - 3 96% confidence bounds 3j
'7.39
~'
- =,
- 2 i
Data Method 3
- Combining i
. P. 7P Quasi Cubic spline fit -
1 f.00 N..
-4 r
0 m
I o3y
~
1 7
.p 0.14
,N
~
~
w s
-2
,t 0.05
~3'
?
~
0.02 w
.4 O
10 20 30 40-50 00 Age in Quarters (a monin cetiod )
s
. i l' Figure E.1 Age dependent degradation rate s
(Component: SW pumps; 7. plant data)
P h
.. t I"l Failure Rate ( ),
per quarter) e
.t 54.6 -
4 20.09
-Estimated Failure nato, in-),, 3-
>j 96% confidence bounds :
4 7,39,
' 2 Data Method 1 - Combining
. 6[
g7p w
= f.00 0
l 0.37
- 1 r
Di 0.14
+
-2
' l
-3, 0.05
- ~3
+
y,pg
,4-n n
n n
n 0
10-20 30
.40 60 60.
t Age in Quarters 13 month periods) i Figure E.2 Age dependent failure rate (Component: SW pumps; 7 plant data) s l'~
1 P
E7 i
3 14 i
i l:IL
I[m[;l mQjy ' -
?,.
cr; -
!(i '
[)
+
o_ of.,
y n'.
p}
yi;
(.
i 5
{;-c i
t-l t
y i
s p', o 1
. Maint. Ef fectiveness l
4- -
i V
J
- Estimated Melnt. Ef fectiveness
.l s
,g AV 0.8 Data Method 1
- Combining
(
p
-l ip3;b
- l
@l 0.6 l
h
-l e
E f,. 'I.$,:
i aka.,, /,
.w J
- 0.4 pl,
.ll 0.2 t.
e if
+p I
I l
l g
-- i
'O' 10 20 30 40 60 60 1
l Age in Quarters.(a month personst r.m Figure E.3 Maintenance effectiveness (Component: SW pumps: 7 plant data)
Y%
I
,g i
i t
9 J
)
f.
~ k !
Ii. '9 a
E-8 i
Y I
',5. n I
g