Text

Technical Basis for Granting Test Frequency Relief
	ML20245H515
Person / Time
Issue date:	06/09/1988
From:	Plumlee G; NRC OFFICE FOR ANALYSIS & EVALUATION OF OPERATIONAL DATA (AEOD)
To:	;
Shared Package
ML20245D469	List: ML20245D465; ML20245H515;
References
	TASK-AE, TASK-T808 AEOD-T808, NUDOCS 8905030420
	Download: ML20245H515 (19)
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1 j

4 AE0D TECHNICAL REVIEW REPORT I

i Uh:TS:

Multiple TR REPORT NO.: AE00/T808

'DO M ET N05:

Multiple DATE:

L * '. E NSEC :

Multiple EVALUATOR / CONTACT: G.L. Plumlee

SUBJECT:

A TECHNICAL BASIS FOR GRANTING TEST FREQUENCY RELIEF I

SLV.ARY i

The purpose of tr.is report is to provide a technical basis for granting In-Service Testing (IST) test frequency relief as requested by NRR (ref.1 ).

Eastd on contractor assistance (FIN D6151) and AE00 direction, a method was presented in EG&G's report EGG-NTA-8067 (ref. ? ) that can be used to form a technica ' bases for granting testing frequency reliefs and will in general irprove

.ie IST program.

To develop this method, Automatic Depressurization System (AD3) valves for which relief is frequently requested (ref. 3 ) were chosen for rample calculations.

The data source was limited to the Nuclear Plent Reliability Data System (NPRDS) database, so the choice of the ADS v61ves was aho advantageous because these valves have an application code which simplifies locating the data in the database.

The use of NPRDS data was limited to Janua y 1,1984 and on, since pre-1984 data is considered to be inconsistent and ?.herefore, unreliable.

However, since NPRDS data is considered proprietary and because no NPRDS failure data validation was per ormed, this AE00 report will simply provide the methodology on which l

f a;;-opriate testing frequencies can be based.

The ADS valve function is 4

utilized in this report only in an effort tu present the NPRDS based me t nodology. No calcubtional results are provided.

First, the data was collected and summarized in a qualita tive manner.

This was done to spot any trends that might exist.

A failure mode summary was empiled from the NPRDS faiiure report's (4-Formsi Failure Description, Cause, arc Corrective Action Narratives.

The engineering data (2-Formsl in the NPRDS database were used to provide 3 valve population and operating history.

Secend, quantitative calculations were made using the data collected in the first step, in particular the failure rode summary, and the valve ope rating history. The Failure Mode summary was reorganized into four categories for the quantitative calculations which categorized the failures as Degraded Loss of High Pressure (HP) Functicn, Degraded Loss of ADS Function, icediate Loss of HP Function, and Immediate Loss of ADS Function.

These are the failure categories considered appropriate for the ADS valves, and would be modified as appropriate for other components.

o This document supports ongoing AE00 and NRC activities and does not represent the position or requirements of the responsible NRC program office.

a90so30[O880609 PDR og NExD 1

PDC

~

, Dependent on the component chosen, this vthodology requires certain initie.1 assumptions to be made.

For example, the ADS sample calculations assurned thet one failure per unit would not adversely affect the ADS system's ability te perform its ADS function.

The test frequency and probability ca'culations are a function of the number of ADS valves used at a unit.

As suting cniv one valve failure, therefore, results in much shorter test frequencies and higher failure probabilities for units that have mcre ADS valves, because a greater fraction of valves must be reliable at such units if all but one valve is needed.

If the frequencies are too short for these units the calculation could be modified to account for unit specific information.

For example, some units may be able to allow two or more valve failures without affecting the ADS function adversely.

Therefore, calculations were performed based on avoiding more then one immediate failure, more than one loss of ADS failure, etc., to provide a broader perspective.

j The results of this repet indicate that a technical basis for g"nting test frequency relief can be generated using the methodology presented b Mis re po rt.

Sound engineering judgement is needed when compiling the data c :d an awareness of the limitations imposed by both the failure database utilize! and the assumptior,s used in the calculations is needed at all times.

For furts.er 1

use of this method, computerization of the compilations and calculations would oreatly reduce the amount of time needed to evaluate a component and be more j

error free at the same time.

{

i DISCUSSION

)

The purpose of this report is te provide a technical basis for granting relief from te' ting frequencies.

In order to perform this task, a sample corpenent, Automatic Depressurization System (ADSi va?ves, was chosen to prosent the methodology. Since the valve operators are integral parts of ADS valves, f ailur:s of the operatcrs were also included.

Information about the number of valves in the industry and failures of the valves and valve operators was obtained from the NPRDS database.

NPRDS data prior to 1984 is ccrsidered less reliable so only data from January 1,1984 and on was used.

The database was also used to obtain a time history of the valves (i.e., hours in service) in calendar time.

Calendar time was used, because relief is gr:nted in units cf calendar time.

The data was summarized in both a qualitative and quantitative ranner.

The qualitative surrary was compiled from selected fields in the NPRDS database.

The fields were DiTECTION, SYMPTOM, CAUSE CATEGORY, CAUSE DESCRIPTION, C0 RECTIVE ACTIDNS, SEVERITY, and EFFECT.

The Failure Description, Cause, and Corrective Action Narratives were also reviewed to develop a FAILURE MDDE su rna ry.

Qualitative observations about the data could then be made.

I l

l l

1 2

i

The quantitative summary, however, was by far the sost time consuming of the two sumaries. The quantitative sumary used the FAILURE MODE sumary and calendar time history from the qualitative summary.

The FAILURE MODE was rec 6tegorized into four categories (i.e., Degraded High-Pressure Function, N; adea Automatic Depressuriza tion (ADS) Function, Immediate High Pressure

~ n iure, and Immediate ADS F6ilure).

The categories above are listed in order c' increasing severity. These were the failure categories considered appropriate for the ADS valves, and would be modified as appropriate for other components. While the pneumatic actuation system may be used to manually oper tne valve for the high-pressure function, the pneumatic system is the heart of the ADS function, so any problems in this system were classified under the ADS ca tegories.

The failure count was ccimbined with the time histcry to obtain statistical bounds on the failure rate and an allowable testing frequency.

Six variables wera calculated for each case (a case being one combination of Manufacturer, namber of ADS valves used in a unit, and the set of failures being examined).

These six v6riables are:

1.

Maximum Likelihood Estimate ()) - This is the observed failure ra te. The units for this variable are failures /hr.

2.

Upper Bound of failure Rate ( A*) - This failure rate, given in failures / hours, is statistically higher than the true but unknown constant failure rate, with 95% confidence.

3.

Statistical Testing Frequency (t ) - This time, given in months, is the maximum testing frequency which statistically implies that only one valve failure or less will occur before the end cf the test interval with 95% confidence.

4, 5, and 6.

Statistical Probabilities for a Giver. Testing frequency (F

F, and F prMa,biNty of tN)or more valves failing during the given test These numbers are upper bounds on the freauency with 951 cunfidence.

F,,, F and F 6re the probabilities for testing frequendtes N,12,18 fend 24 months, respectively.

In the following sections the qualitative review ard quantitative calculational methodology utilizing the ADS valves is presented.

The ADS valves were chosen because their testing is an issue in granting IST relief (ref. 3 ) and because the NPRDS database gives these valves and their valve operators an application code which makes finding the associated records r:uch ec s ie r.

For other components it may be necessary to review Technical Evaluation Reports (TER) in order to utilize the NPRDS to find the components of interest, e.g., by the component ID obtained from the TER review.

The sample calculations were done with mostly hand calculations which is very time consuming and error prone. If more than.just a few addi:ional components are going to be examined, then development of a dBase-III+ program and/or a SAS program would be very helpful in cutting down the time required to handle the data and would be much less error prone.

Computerized routines would also allow more parameter studies to be made and data verification / corrections could be made with ease.

3

DESCRIPTION OF THE CALCULATIONAL METHODS The data was used in two ways (i.e., a qualitative review and quar.titative calculations).

The raw data was obtaired from the NPRDS database. The information in the database is considered less reliable prior to 1984, so cr.ly data from Janusry 1,1984 and un was used. Based on the fact that the data was not validated and its proprietary nature, all qualitative review and quantitative calculation results have been deleted from this report in an effort just to present the methodology in the most accurate and expeditious manner in order to support ongoing IST review efforts.

t The following subsections detail the methods used te review the data.

Qualitative Review The qualitative method was performed first, because it consists mainly of data collection and counts, some of which are needed to make the quar.titative calculations. The choice of BWR ADS valves for the sample calculation was due in part to the fact that the NPRDS database assigns the ADS valves and ADS valve operators a unique application code which simplifies the search of the database for these valves.

In future reviews of other components, TERs may have to be searched for component ids to identify the subset of desired components from a larger set which is known to contain the desired subset.

Eight fields from the NPRDS failure report (4-Forn) database were of interest. These fields are: 1) DETECTION, 2) SYMPTOM, 3) CAUSE CATEGORY, 4)

CAUSE DESCRIPTION, S) CORRECTIVE ACTION, 6) SEVERITY, 7) EFFECT ON PLANT, and

8) EFFECT ON SYSTEM.

All fields but the SEVERITY field were used as is. The SEVERITY field cas modified as found necessary from reading the Failure Description, Cause, and Corrective Action Narratives.

In general, the SEVERITY code was not changed, because the licensee should know best ti.e severity of the failu re. However, when the SEVERITY code didn't agree with the narratives of the event or when the ccde varied although the events appeared to be the same, then a decision was made as to whether or not the code should be changed.

The code was never decreased in severity, enly increased. Changes in the severity code were made because this ccde is critical to categorizing the failures for the quantitative calculations.

The Failure Description, Cause, and Corrective Action Narratives were also reviewed to compile a Failure Mode surmary.

The sumr.ary broke the failures into thirteen main categories, with two to five subcategories for some categories.

If more than one failure category applied, then each applicable failure mode received a count.

This was done to preserve as much of the information from the narratives as possible. This summary format is shown in Table 1.

For the quantitative calculations, the failure modes were evaluated further to distinguish whether the high pressure and/or ADS functions of the valves were affected.

4

f TABLE.~ 1.

FAILURE MODES

SUMMARY

(Example Format) j Failure Counts Val,ve Manufacturers

. Failure Mode il

2

3

4

5 Tota l (1) Setpoint Drift - (Electrical)

High Low Unknown /Other

'(2) Setpoint Drift -

(Mechanical / Binding / Damage)

High (Generic Target Rock l

Lybrinth Seal Friction)

High(Other)

Low Unknown /0ther (3) Spurious Signal Valve Opens

Valve Closes (4) Failure to Open (COUNTS ARE ENTERED IN COLUMNS BY Mechanical MANUFACTURER IN ORDER TO OBSERVE Electrical TRENDS.)

(5) Failure to Close Mechanical Electrical (6) Leakage Accumulator / Air Lines / Fittings Solenoid Yalve Pilot Valve Valve Actuator Relief Valve Body / Fittings (7) Pilot Valve Failure Won't Operate; Sticky /Cerrosion Limited Operation Seat Problems; Steam Cutting / Dirt Cracks / Worn 5

I s'

' TABLE [1..'

SUMMARY

OF FAILURE MODES (Example Fonnat Continued)

Failure Counts Valve Manufacturer *.

Failure Mode

1

2 73

4 b

Total

-(8) Solenoid Valve Failure-(Mechanical)

'(Electrical)

(9) 0-Ring Seal Failure (Damage)

(Age)'

10)

Main ~' Seat failures Steam Cutting / Cracking

' Dirt / Corrosion Loose / Misaligned (Including Leakage duetothis)

Leakage due to wear

~ (11)

the 957 upper confidence bound on the failure rate the bounding testing frequency t

V number of valves used at a unit for the ADS function

=

5=

upper 95 percentile of Chi squared distribution with 2n + 2 degrees of freedom, where n is the number of observed failures, and q

i i

T the total calendar hours that the components were in

=

service.

i l

9 i

Letting

t*

R

= e Equation (1) becomes (2) i Y + V (1-R) R 'I Y

R

.95

=

(3)

Equation (3) shows the dependency of the calculations on the number of ADS valves used at a unit.

For each value of "V", iterative values of R be tween Since,A,0 and I are plugged into equation (3) until the equality is satisfied.

can be calculated from data given above, Equation (2) can be solved for t which is the desired quantity in this calculation.

.n more detailed derivation of the equations is provided in Appendix A.

Probability Calculations For the probability calculations given a testing frequency,. the 95% bound is changed to fit the testing frequency.

For example, if the given test interval is 12 months and the calculated probability is.079, then with 95%

confidence there is no more than a 7.9% chance that more than one failure will occur in the 12 month period.

The equation used for failure probability calculation is one minus Equation (1), the success probability used for the testing frequency calculation:

F=1-[(e-A*t*)V 4y(3_,-A*t*)(,-A*t*)V-ly (4) where F is the probability of more than one valve failure during the test frequency.

For the test frequency calculations, the bracketed part of equation (4) was set equal to 0.95 whiqh is (1-F).

This time we want to calculate F, and to calculate F, requires t to be assumed.

frequencies (t ) of 12,18, and 24 months were used.For these calculations testing Again A can be calculated, so F can be calculated.

RESULTS The results wili be presented in two parts which correspond to the two calculational r.ethods discussed above.

As mentioned earlier, the sample data was tabulated cown to the manufacturers level, and an overall irdustry calculation was made for all BWR plants in the NPRDS database.

Model variations were all lumped together for each manufacturer, since a breakdown to model number resulted in samples which were too small (i.e., the uncertainty in the calculations would become prohibitively large).

Table 3 provides a fonnat that could be used to list all plants and indicate which units had engineering data (2-Forms) available in the NPRDS database.

This is a useful data quality / validation tool. The results from all NPRDS data quality verification efforts should be fed back to AEOD for incorporation into the staff's ongoing NPRDS evaluation efforts.

10

1

)

TABLE 3.

LIST OF PLANTS WITH ENGINEERING DATA IN NPRDS DATABASE 1

BWR Plants (FID)

Unit No.a

),

1

[

3

'Conrnents 3

f

-(plant names)

(plantIDs) x x

x o

"x" indicates that data was available in the NPRDS database.

a.

Results of Qualitative Review The qualitative data is essentially a count of the entries made in the da tabase by the licensees.

Eight NPRDS fields were tabulated.

The fields DETECTION, SYMPTOM, CAUSE CATEGORY, CAUSE DESCRIPTION, CORRECTIVE are:

ACTION, SEVERITY, EFFECT ON PLANT, and EFFECT ON SYSTEM. The tabulations could be shown in a fonnat such as in Table 4.

This table lists the field name and the possible codes applicable to the field.

The number of counts for each manufacturer and totals for the industry would also be shown on the tables.

The Table 4 fonnat could be constructed for both the valves and valve operators, and could also be used to present a summation of all counts whether valve or valve operator (table titles would have to be revised).

Based on the above tabulations of NPRDS failure data, qualitative observations and conclusions can be discussed.

Results of the Quantitative Calculations The quantitative calculations use the failure mode counts combined with the calendar hours.

Calendar hours are used instead of service hours because the test interval relief requests are made in terms of calendar time. Six numbers were calculated for each combination of Manufacturer, ADSVglve Pcpulation at a Unit / Plant, and Failure Set.

These six calculations are:

1.

2 = n/T = the Maximum Likelihood Estirate where: n = cbserved number of failures T = calendar hours of service

2. [ =

95% upper confidence bound on failure rate 3.

t Calculated test frequency (mo.)

=

I 4.

F12, FNr,r.ind F 2

Upper bounds on probabilities that than $ne= valve will fail given testing intervals of 12,18, and 24 months, respectively.

See Appendix A for more detailed definitions of the calculated values.

a.

~

11 i

)

TABLE.4.. TABULATION OF ADS VALVE DATA (Example Format) 3 i

Valve Manufacturer i

(No. of Valve Failures)

1

2

3

4 iS' Total I) T) I) T) F)

(

)-

DETECTION

]

A - Operation Abnormality 1

8 - In-Service Inspection

.j i

C - Surveillance Testing D - Preventive Maintenance E - Special Inspection F - Audio / Visual Alarm H - Routine Observation J - Incidental Observation I. - Other i

SYMPTOM A - Physical Fault (C0UNTS WOULD BE TABULATED IN i

B - Out-of-Specification COLUMNSFORTRENDING.)

C - Demand Fault i

0

Abnormal Characteristic E

- Released Leakage F - Contained Leakage 3

CAUSE CATEGORY -

A - Engineering / Design

~

P

- Incorrect Procedure C

- Manufacturing Defect D - Installation Error i

E - Operating Error F - Maintenance / Testing

(

H - Wearcut J - Other Devices K - Unknown i

CAUSE DESCRIPTION l

Mechanical AB - Foreign / Incorrect Material i

AC - Particulate Contamination j

l

. AD - Normal / Abnormal Wear 1

12 I

l o_-______--_

J

i TABLE 4.

TABULATION OF ADS VALVE DATA (Exemple Fomat Continued)

Valve Manufacturer (No. of Valve failures)

1

2

3

4

5 Total T) T) T) T) T)

(

)

CAUSE DESCRIPTION Mechanical (cont'd)

AE '- Lubrication Problem AF - Weld-Related AG - Abnormal Stress AV - Connection Defective / Loose Part A2 - Material Defect BB - Mechanical Damage / Binding BC - Out-of-Mechanical Adjustment BD - Aging / Cyclic Fatigue BE - Dirty BF - Blocked / Obstructed 86 - Corrosion Electrical / Electronic i

L AG - Abnomal Stress AR - Insulation Breakdown AS - Short/ Grounded AT - Open Circuit AU - Contacts Bumed/ Pitted, Corroded AV - Connection Defective / loose Part AW - Circuit Defective AX - Burned / Burned Out AY - Electrical Overload AZ - Material Defec' BE - Dirty

{

BG - Corrosion Adjustment / Human-Related AA - Foreign / Wrong Part AL - Set Point Drift l

AM - Previous Repair / Installation AN - Incorrect Procedure BC - Out-of-Mechanical Adjustment BH - Out-of-Calibration BJ - Incorrect Action 1

l 13

t i

TABLE 4.

TABULATION OF ADS YALVE DATA (Example _ Fomat Continued)

Valve Manufacturer

_(No. -of Yalve Failures) 41

2

3 34

5 Total l

T) F) T) T) T)

(

)

l' CORRECTIVE ACTION AA

. Recalibrates / Adjust AC - Temporary Measures AE - Modify / Substitute AG - Repair' Component /Part AH - Replace Parts AK - Replace Component SEVERITY i

J - Insnediate K - Degraded L - Incipient EFFECT On Plant A - Reduced Power Operation B - Unit Off-Line C - Reactor Trip D - Personnel Injury E - Off-Site Radiation F - Damage to Other Equipment G - No Significant Effect On System A - Loss of System Function B - Degraded System Operation C - Loss of Redundancy.

D - Loss of Subsystem / Channel E - No Significant Effect 14

1

'll '.

' Table 5'c~ould be used to summarize the: quantitative calculations. Table.S is

- an example format for an overall view of the : industry.

A similar format could be used to summarize the calculation results for each valve or component-manu facturer.

Figure I would show a comparison of the values of A and 1*.

In the left margin of Figure 1 is text indicating the failure set being compared.

There are five lines for each failure set which represent the five example valve manu fa cturers.

At the left end of each bgr a solid circle for each' manufacturer) is A and the right end is A. (The~ length of each har is proportional to the~ uncertainty in the calculations (i.e., a longer line indicates more uncertainty in the calculations). On the heavy line below each comparison are.two triangles A which are the end points of the industry line.

.In sunnary, the test frequency calculation assumes that there is a five percent chance of two or more failures during the calculated test frequency.

If a 'different test frequency (usually longer) than the calculated frequency (t ) is desired, then the values of F FI, and F indicate how much the probability of two or more failures cbkn,ge hith theNest frequency.

To use tables like Table 5, e.g., one needs to determine which failure modes are of concern and how much risk one is willing to accept.

CONCLUSIONS.

The data in general indicates that the method presented in this report can be used to form a technical basis for granting testing frequency reliefs and will in general help to improve the IST program.

The ADS valves were chosen as a trial case which shows the methodology used.

The sample testing frequency (t ) calculations were dependent on the number of ADS valves used in a unit.

This task assumed that the ADS function casn't endangered with one failure / unit.

This assumption was very restrictive for plants with 6, 7 or 8 ADS valves / unit.

Similar restrictive conditions could occur in other applications were multiple components are utilized to previde a single function.

Some possible solutions to this problem are:

1.

Accept a higher probability than five percent (i.e., F F

l

3) that two or more valves will fail curing the d$s,irN and F test Trequency.

2.

Determine how many ADS valves can fail at each unit without affecting the ADS adversely, and recalculate the allowable testing l

frequency for those units that can allow more than one failure.

-3.

Convert one or two additional relief valves into ADS valves, then l

more valves could fail before the ADS function was adversely affected.

15 i

1

F-1 w

j g

t TABLE 5. "

SUMMARY

OF INDUSTRY QUANTITATIVE CALCULATIONS (Example Fonnat)

Calculated Parametersa Failure D_e s c ri p tion -

V

+

F F

F 12 3g 24 r

All Failures, (n = _,

)a

=

a

-(TABULATE THE VARIOUS PARAMETER VALUES IN COLUMNS)

All ADS and Immediate High Pressure, In = _,

)a

=

l All Imediate (n = _,

)a

=

All ADS, (n = _,

)a

=

Imm diate ADS, (n = _,

)"

=

Imediate High Pressure, (n = _,

)a

=

a. n = Number of failures observed in the failure set population.

T = Calendar hours that the component was in service.

V = Number of valves in ADS system.

A}, = Upper bound failure rate (failures /hr).= n/T = Maximum likelihood es t = Upper bound on test frequency (months) which will assure that the probability of two or more failures is less than or equal to five percent with 95% confidence.

F.= Upper bound probability with 95% confidence of two or more valve

'1 9

failures in test interval "t ". For these calculations "t " was set to 12,18 and 24 months.I I

16

l l

l 3Nl

! tr-$

1.ff.5 4 g.5 g g,g k

0 0

A i

9 E

0 l

l A

a l

0-4 i

g 2

3 i i

=

q 1

e m

.A A

T-Toryt Asch g

0-Oresser 4

6--

~

4 5

Ok-Oftters A

A tmemstry A A 1

w' e

a i =-5 i.=.s

3. a..

..a.,

f a ilure Aa ta Figure 1.

Comparison of A and A* for the Various Yalve Manufacturers and failure sets REFERENCES 1.

Memorandum for Edward J. Jordan (AE00) from Larry C. Shao (NRR), " Pump and Yalve Testing Frequency," July 8,1987.

2.

B.S. Anderson and C.D. Gentillon, "A Technical Basis for Granting Test Frequency Relief with Application to Automatic Degressurization System Valves," EGG-NTA-8057, Idaho National Engineering Laboratrry April 1988.

3.

Memorendum for G.L. Plumlee (AE00) from E.J. Sullivan (NRR), " Basis for Inservice Testing Frequencies," September 28, 1987.

17

. APPENDIX A DEPIVATION OF EQUATIONS The basic intent of the calculations is to bound the true but unknown failure rate of ADS valves based on information available in the NPRDS database.

Assumptions:

1.

Homogeneous failure rate which implies a Poisson distribution for the number of failures observed during a fixed time period (i.e.,

constant failure rate within each valve manufacturer's valves and across the industry for the industry calculation).

2.

One ADS valve failure occurring before the next test is allowable at each unit.

3.

Want to keep probability of two or more failums to five percent or less.

4.

Want to be 95 percent confident'in calculation.

Definition of terms:

M = Upper bound failure rate (failures /hr) = g 95

/2T 95= Upper 95 percentile of Chi squared distribution with 2n+2 degrees of freedom. (This is the way assumption 4 is entered into the equation.

T The total calendar hours that the components were in service

=

Number of observed failures in the NPRDS database n

=

The bounding test frequency t

=

F t

The probability of two or more failures occurring for a test

=

frequency of "t" months.

V The number of ADS valves used at a unit.

=

A-1

1 1

i Derivation:

The equation above for A* is a standard upper confidence bound for the From assumptien 1, the

]

failure rate, and is based on assumption 1.

probability of seeing no failures with a single valve is bounded by f

1 R = e- )L*t*

(3)

)

For the case of Y valves, the binomial distribution describes the number i

of failed valves between two consecutive tests.

l The probabilities for 0 failures and for 1 failure are bounded by, respectively, i

I P

Probability of no failures = R

=

(2) g P

3 Probability of one failure = V(1-R) R I

=

(3)

The sum of P and P represents the probability of acceptable events.

That is, zero or 8ne fai}ure won't affect. the ADS function (assumption 2.)

The probability of the unacceptable events; that is, two or more failures, would be one minus the sum of P and P equal to, at most, fivS pe edt.which according to assumption 3 must be The resulting equation is:

Y Y

1-R -V(1-R)R~I = 0.05 (4)

Simplifying, Y + V (1-R) R ~I =.95 Y

R (5)

Tht desired quantity is t ; which is easily calculated from R.

R is a probability, so it must lie between zero and one.

Using iterative values of R, the R that satisfies the, equality in Equation (5) can be found.

Then using Equation (1) the value of t can be calculated.

The left side of Equation (4), with R defined as in Equation (1), can be used to calcylate the probability of two or more failures when the test frequency (t ) is assumed.

A-2 1

_ _ _ _ _ _ _ _ _ _

ML20245H515

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the 957 upper confidence bound on the failure rate the bounding testing frequency t

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