ML15247A067

Shine Medical Technologies, Inc. Application for Construction Permit Response to Request for Additional Information

ML15247A067
Person / Time
Site:	SHINE Medical Technologies
Issue date:	09/02/2015
From:	Bynum R SHINE Medical Technologies
To:	Document Control Desk, Office of Nuclear Reactor Regulation
References
SMT-2015-040
Download: ML15247A067 (19)

Text

Medical Technologies September 2, 2015 SMT-201 5-040 10 CFR 50.30 U.S. Nuclear Regulatory Commission ATTN: Document Control Desk Washington, DC 20555

References:

(1) SHINE Medical Technologies, Inc. letter to NRC, dated March 26, 2013, Part One of the SHINE Medical Technologies, Inc. Application for Construction Permit (ML130880226)

(2) SHINE Medical Technologies, Inc. letter to NRC, dated May 31, 2013, Part Two of the SHINE Medical Technologies, Inc. Application for Construction Permit (ML13172A324)

(3) NRC electronic mail to SHINE Medical Technologies, Inc., dated August 26, 2015, Draft Request for Additional Information Supporting SHINE Preliminary Safety Analysis Report (ML15239B051)

(4) NRC electronic mail to SHINE Medical Technologies, Inc., dated August 27, 2015, Draft Request for Additional Information Supporting SHINE Preliminary Safety Analysis Report SHINE Medical Technoloqies. Inc. Application for Construction Permit Response to Request for Additional Information Pursuant to 10 CFR 50.30, SHINE Medical Technologies, Inc. (SHINE) submitted an application for a construction permit to construct a medical isotope facility to be located in Janesville, WI (References 1 and 2). Via References (3) and (4), the NRC staff determined that additional information was required to enable the staff's continued review of the SHINE construction permit application. provides the SHINE response to the NRC staff's request for additional information.

If you have any questions, please contact Mr. Jim Costedio, Licensing Manager, at 608/210-1730.

Aq-ooi Iy( ~

2555 Industrial Drivel Monona, WI 53713 I P (608) 210-1060 .F (608) 210-2504 www.shinemed~corn

Document Control Desk Page 2 I declare under the penalty of perjury that the foregoing is true and correct.

Executed on September 2, 2015.

Very truly yours, Chief Operating Officer SHINE Medical Technologies, Inc.

Docket No. 50-608 Enclosure cc: Administrator, Region III, USNRC Project Manager, USNRC Environmental Project Manager, USNRC Supervisor, Radioactive Materials Program, Wisconsin Division of Public Health

ENCLOSURE 1 SHINE MEDICAL TECHNOLOGIES, INC.

SHINE MEDICAL TECHNOLOGIES, INC. APPLICATION FOR CONSTRUCTION PERMIT RESPONSE TO REQUEST FOR ADDITIONAL INFORMATION The NRC staff determined that additional information was required (References 1 and 2) to enable the continued review of the SHINE Medical Technologies, Inc. (SHINE) application for a construction permit to construct a medical isotope facility (References 3 and 4). The following information is provided by SHINE in response to the NRC staff's request.

CHAPTER 6 - ENGINEERED SAFETY FEATURES Section 6b.3 - Nuclear Criticality Control (Applies to RAIs 6b.3-31 through 33)

As requiredby 10 CFR 50.34(a), "Contents of applications;technical information," a preliminary safety analysis report should include "[a]preliminaryanalysis and evaluation of the design and performance of structures, systems, and components of the facility with the objective of assessing the risk to public health and safety resulting from operation of the facility..., and the adequacy of structures, systems, and components provided for the prevention of accidents and the mitigation of the consequences of accidents."Additionally, the preliminary design of the facility should provide reasonable assuranceto the NRC staff that the final design wili conform to its design bases with adequate margin for safety.

With respect to nuclear criticalitycontrol, the Interim Staff Guidance (ISG) Augmenting NUREG- 1537, Part2, Section 6b. 3, "NuclearCriticality Safety for the Processing Facility,"states, in part that '[c]riticality process safety controls should be provided for criticalitysafety, and a description of their safety function should be described. The applicantshould use enough safety controls to demonstrate that, under normal and abnormal credible conditions, all nuclearprocesses remain subcritical"and that "NCS

[nuclear criticalitysafety] limits on controlled parameters will be established to ensure that all nuclearprocesses are subcritical,including an adequate margin of subcritica/ity for safety."

RAI 6b.3-31 The ISG augmenting NUREG-1537, part 2, Section 6b.3, contains criteria for the use of mass, geometry, density, enrichment, reflection, moderation, concentration, interaction, neutron absorbers,and volume as controlledparameters. Additional information is needed in orderfor NRC staff to determine the adequacy of SHINE'S treatment of controlledparametersin order to ensure that all nuclearprocesses are subcritical, including an adequate margin of subcriticallty for safety. Specifically, SH-INE'S constructionpermit applicationdoes not contain the necessary commitments to following technical practices for the use of each controlled parameterin order demonstrate a sufficient design basis in its preliminary design.

Page 1 of 9

In order to provide reasonableassurance that SHINE's final design will conform to its design bases with adequate margin for safety, as requiredby 10 CFR 50.34, commit to following technicalpractices for the use of each controlledparameterdescribedin the ISG augmenting NUREG- 1537, Part2, Section 6b.3, "NuclearCriticality Safety for the ProcessingFacility," or state that rellance on particularparameterswill not be used. For those parametersthat are not controlled, commit to assuming the most reactive credible conditions. Additionally, describe any conservatism in the calculatedkeff resulting from the use of these technicalpractices.

SHINE Response SHINE will follow the technical practices for the use of each controlled parameter (i.e., mass, geometry, density, enrichment, reflection, moderation, concentration, interaction, neutron absorbers, and volume) described in Section 6b.3 of the Interim Staff Guidance (ISG) augmenting NUREG-1 537, Part 2 (Reference 5). These practices are listed on Pages 72 through 74 of the ISG augmenting NUREG-1 537, Part 2. For those parameters that are not controlled, SHINE will assume the most reactive credible conditions.

The conservatisms in the calculated keff values from the use of these technical practices for Atkins-NS-DAC-SHN-15-02, Revision 0, provided as Attachment 3 to Enclosure 1 of Reference (6), and Atkins-NS-DAC-SHN-15-04, Revision 0, provided as Attachment 2 to of Reference (6), are described below. These conservatisms result in a higher calculated keff value.

Atkins-NS-DAC-SHN-1 5-02. Revision 0

• Mass, Concentration: Solute saturation is assumed to be unlimited. Realistic saturation behavior is ignored in favor of showing the peak reactivity for the various materials regardless of concentration.

• Geometry: The vessel walls are assumed to be made of the fissile material being analyzed, effectively removing the need for measurements of vessel thickness with respect to nuclear criticality safety (NCS).

• Enrichment: Uranium is assumed to be enriched to 21 wt% 235U, an increase over the nominal value of 19.75%.

• Reflection: Concrete reflector walls are located six inches from the outside of the neutron absorber panel. This is a conservative estimate of the minimum anticipated distance.

• Reflection: Void and water flooded conditions are modeled in order to determine the most reactive conditions.

• Moderation: Uranyl sulfate is modeled assuming no excess acid as a conservative simplification. Excess acid would reduce moderation and increase neutron absorption.

• Neutron absorbers: The manufacturer specification for the minimum hydrogen density in the PPC-B is used. Minimum hydrogen density will result in the least amount of scattering in the absorber and thus the least amount of neutron absorption.

• Neutron absorbers: Only 75% of the calculated boron density is used for the PPC-B. This is a conservatism that reduces absorption.

Page 2 of 9

Atkins-NS-DAC-SHN-1 5-04. Revision 0

• Mass, Concentration: Solute saturation is assumed to be unlimited. Realistic saturation behavior is ignored in favor of showing the peak reactivity for the various materials regardless of concentration.

• Mass: Uranium oxide was modeled as UO 2 . This molecule has the least number of oxygen atoms per uranium atom which will result in the highest reactivity when compared to other oxide compounds (i.e., UOa or U30 8).

• Geometry: For the determination of the subcritical limit for mass and volume, the most reactive geometry (a sphere) was used.

• Enrichment: Uranium is assumed to be enriched to 21 wt% 235U, an increase over the nominal value of 19.75%.

• Reflection: For the mass and volume subcritical limits, the sphere was surrounded by 12 inches of close-f itting water reflection.

• Reflection: For the infinite uranyl sulfate solution concentration calculation, reflective boundary conditions were used on all sides to simulate an infinite amount of material.

• Moderation: Density of the uranium oxide and uranium metal were varied to determine the limiting conditions for NCS.

• Moderation: Uranyl sulfate is modeled assuming no excess acid as a conservative simplification. Excess acid will reduce moderation and increase neutron absorption.

RAI 6b.3-32 The NRC staff recalculatedSHINE's upper safety limit (USL) using the USLSTA TS code issued with the SCALE criticalitycode package. This recalculationproduceda lower USL than that determined in Table 8 of SHINE's Validation Report. This difference in USL calculations appears to be the result of SHINE's use of a smallersingle-sided lower tolerance limit factor, K*,

and pooled standarddeviation, St, than those determined by USLSTA TS. SHINE's tolerance limits factor is also smaller than the value listed in Table 2.1 of NUREG/CR-6698.

Additional information is needed in orderfor the NRC staff to determine the adequacy of SHINE's USL calculation to resolve the discrepancywith NRC staff calculations. This information is necessary to demonstrate reasonable assurancethat SHINE's final design will conform to its design bases with adequate margin for safety, as requiredby 10 CFR 50.34 Provide details of the USL calculations in Tables 6, 7, and 8 of SHINE's MNCP 6. 1 Validation Report, Rev. 2, including the formulas used and references justifying them.

SHINE Response In the SHINE validation report (Atkins-NS-DAC-SHN-15-03, Revision 2, provided as to Enclosure 1 of Reference (6)), the 140 benchmark experiments were evaluated to determine if trends exist between the calculated keff and the following independent parameters: the hydrogen to fissile ratio (HIX), the Average Neutron Energy Causing Fission (ANECF), the 235U enrichment, the moderator material, the reflector material, and the chemical form of the fissile material. SHINE determined that the calculated ke, did not trend with any of these independent variables.

Page 3 of 9

The ISG augmenting NUREG-1 537, Part 2 (Reference 5) lists ANSI/ANS-8.24, as endorsed by Regulatory Guide 3.71 (Reference 7), as an acceptable validation methodology.

ANSI/ANS-8.24-2007 (R2012) (Reference 8) references NUREG/CR-6698 (Reference 9) for details on calculating the upper safety limit (USL), such as statistical and nonstatistical methods and function fitting, computational margin determination, and justification for safety margin. The bias and bias uncertainty in the SHINE validation report were calculated using the equations listed in Section 2.4.1 of NUREGICR-6698, which are also listed in Section 3.4.2 of the SHINE validation report.

After determining the data to be normal and displaying no trends, the single-sided tolerance limit was selected as the appropriate statistical treatment for determining the USL. This method uses the bias uncertainty (pooled standard deviation) and applies a single-sided lower tolerance factor (K* or U) based on the number of data points. Values for K* with 10 to 50 data points are listed in Table 2.1 of NUREG/CR-6698. NUREG/CR-6698 states that the K* value for 50 data points, 2.065, may be used as a conservative number for more than 50 data points. SHINE chose to use this K* value for the intermediate enriched uranium (IEU) USL data set (54 points),

but chose to calculate the K* value for the other two data sets, when the number of data points significantly exceeded 50. The equations for calculating K* are listed below, and can also be found in Section 3.4.2 of the SHINE validation report. The equations are taken from Reference 9 of the SHINE validation report. Reference 9 of the SHINE validation report is the source of Table 2.1 of NUREG/CR-6698. The applicable pages of Reference 9 of the SHINE validation report are provided as Attachment 1.

K*-Zz-a+

ab Where:

2(n -1) 2 n

The ZpadZvalues are the critical values from the normal distribution that is exceeded with specified probability (P = 95% and y =95%), and are both 1.645. The resulting K*values for the larger data sets in the SHINE validation report are 1.952 for the low enriched uranium (LEU) and IEU USL data set (84 points) and 1.877 for the combined LEU, IEU, and highly enriched uranium USL data set (140 points).

The pooled standard deviation (Sp) in NUREG/CR-6698 has two components, and is calculated according to Equation 6b.3-32-1.

Sp= V-2 + *z Equation 6b.3-32-1 Page 4 of 9

For the single-sided tolerance limit method described in NUREG/CR-6698, these two components are the variance about the mean (s2) and the average total uncertainty (aY).

They are calculated according to Equations 6b.3-32-2 through 6b.3-32-6.

(~T) ~3~{keft.keff) 2 Equation 6b.3-32-2 71 G.

7%

Equation 6b.3-32-3 With the normalized keff value for the "ih' benchmark case, keffcac keff. -- ceffex~

Equation 6b.3-32-4 the uncertainty on the "ith keff value, O- /2 0- 2 Equation 6b.3-32-5 and the weighted mean keff

~Akeff.

keff a1 1 Equation 6b.3-32-6 Where:

n = number of critical experiments in the validation kefle~* effective multiplication factor for the benchmark keffcaic* effective multiplication factor for the calculation method 0

exp 1 = uncertainty in the benchmark 0

catc1 = uncertainty in the calculation method The pooled standard deviation is calculated differently in USLSTATS because a different statistical method is used. This method relies on there being a trend present in the data with a given independent variable. With no trend present in the data, the trend line determined by USLSTATS will have a poor fit. USLSTATS does not perform a "goodness of fit test" to determine how applicable this method is to the data set. The pooled standard deviation (Sp) for this method is a combination of the variance of the regression fit (S() n h ihnvrac of the data (Sw,).

Page 5 of 9

= +kx

+S2 Equation 6b.3-32-7 S2 1 [~k~ kef) (*"(Xi-')(keffi-ke")} I Equation 6b.3-32-8 S*= gY ef Equation 6b.3-32-9 Where:

xi = value for the independent variable associated with the "1 t"" keff value

)Z = the mean value of parameter s in the set of calculations k'eff = the keff value for .*, calculated using the fitted function In summary, USLSTATS calculates a different value for the pooled standard deviation because it uses a different statistical method, which relies on a trend being present in the data set.

SHINE has determined that there is no trend in the validation data set and has used the single-sided tolerance limit method as described in NUREG/CR-6698.

RAI 6b.3-33 While Table 9, 'Area of Applicability Summary," of the SHINE Validation Report, Rev. 2, includes cadmium, this materialis not mentioned as present in Table 2, "CriticalBenchmark Experiments Summary. "Additionally, the discussion of some of the benchmark experiment sets mentions cadmium, but it is not clearif it is present in any of the experiments chosen from those benchmark sets.

Additional information is needed on SHINE's analysis of benchmark experiments in orderfor the NRC staff to assess the adequacy of SHINE's preliminary design.

Clarify whether the area of applicability(AOA) in the SHINE Validation Report, Rev. 2, includes cadmium as a neutron absorber.

SHINE Response SHINE does not plan to use cadmium as a neutron absorber. Cadmium will be removed from Table 9 of the validation report during detailed design. An Issues Management Report (IMR) has been issued to track removing cadmium from Table 9 of the validation report during detailed design.

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RAI 6b.3-34 As required by 10 CFR 50.34(a), "Contents of applications; technical information," a preliminary safety analysis report should include '[a] preliminaryanalysis and evaluation of the design and pedformance of structures, systems, and components of the facility with the objective of assessing the risk to public health and safety resulting from operation of the facility..., and the adequacy of structures, systems, and components provided for the prevention of accidents and the mitigation of the consequences of accidents."Additionally, the preliminary design of the facility should provide reasonable assurance to the NRC staff that the final design will conform to its design bases with adequate margin for safety.

With respect to nuclearcriticality control, the Interim Staff Guidance (ISG) Augmenting NUREG- 1537, Part2, Section 6b. 3, "NuclearCriticalitySafety for the ProcessingFacility,"

states, in part that "[c]riticalityprocess safety controls should be provided for criticalitysafety, and a description of their safety function should be described. The applicant should use enough safety controls to demonstrate that, under normal and abnormal credible conditions, all nuclear processes remain subcritical"and that "NCS [nuclearcriticality safety] limits on controlled parameters will be established to ensure that all nuclearprocesses are subcritical,including an adequate margin of subcriticalityfor safety."

The ISG Augmenting NUREG-1537, Part2, Section 6b.3, states, in part, that thereviewer should determine "whether the margin of subcriticalityfor safety is sufficient to provide reasonableassurance of subcriticality."

In response to RAI 6b.3-4, SHINE states it intends to utilize a subcriticalmargin of 0.05 with additionalconsiderationsfor uncertainty in the validation and modeling. In addition, SHINE states in multiple places in the PSAR that processes will be maintainedto a keff < 0.95 (assuming a subcriticalmargin of 0.05).

The NRC staff's review of SHINE's responses to RAIs 6b.3-1 and 6b.3-26 found that there was insufficient benchmarking of the code against experiments utilizing the materials and enrichments expected in SHINE's processes. For this reason, the proposed subcriticalmargin of 0.05 is not sufficient to adequatelyaddress the uncertainty associatedwith the neutron interactionsof these process materials. The subcriticalmargin of 0.05, which SHINE quoted from NUREG- 1520, was intended for facilities with enrichment less than five percent utilizing well establishedprocesses and for which there is significantexperience and data. In contrast, the SHINE facility will be a first-of-a-kind facility using materials not normally utilized and of an enrichment up to 20 percent.

Provide additionalinformation describinghow SHINE has or will sufficiently benchmark against experiments utilizing the materials and enrichments expected to be used in SHINE facility processes for its proposed margin of subcriticality, or propose a new margin of subcriticalitythat appropriatelytakes into account materialsand enrichment.

SHINE Response The SHINE validation report, Atkins-NS-DAC-SHN-15-03, Revision 2, provided as Attachment 4 to Enclosure 1 of Reference (6), sufficiently benchmarks against experiments using materials and enrichments expected to be used in the SHINE facility processes. This report provides a proposed margin of subcriticality that appropriately takes into account materials and enrichment.

It should be noted that one set of experiments (IEU-SOL-THERM-001) from the International Page 7 of 9

Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook was initially considered for use by SHINE in the validation process, but was ultimately determined to not be suitable for inclusion, as described below.

Benchmarks in the ICSBEP Handbook provide information on experimental data, uncertainty, and modeling information. In accordance with Regulatory Guide 3.71 (Reference 7), "the rejection of outliers should be based only on the inconsistency of the data with known physical behavior."

The IEU-SOL-THERM-001 set of experiments were performed at the Russian Research Center "Kurchatov Institute" in 1980-1 981 to investigate nuclear safety issues for a special-purpose compact reactor and graphite reflector. During the review of the benchmark description, SHINE noted that sample calculation results from the Russian Federation indicated keff values that were significantly below (1.5% to 2.7%) the experimental keff values.

SHINE investigated this benchmark, and a comparison of the four IEU-SOL-THERM-001 benchmark cases with the modeling data has identified an inconsistency of the data with known physical behavior. Specifically, in the development of the Monte-Carlo N-Particle Transport Code (MCNP) models of IEU-SOL-THERM-001, SHINE noted that the calculated uranyl sulfate volume from the modeling information in the benchmark is approximately 3% less than the critical uranyl sulfate volumes specified in the benchmark description. Therefore, the data in the benchmark is physically inconsistent.

In addition, the ICSBEP Chairman agrees that there is an error in the sample calculations, which possibly indicates a more significant error in the benchmark model description. Per the ICSBEP Chairman, the current error would preclude it from being deemed an acceptable benchmark evaluation in the ICSBEP Handbook.

The ICSBEP is currently undergoing an investigation into the errors identified in IEU-SOL-THERM-001 with the intent of formally presenting the error and means to mitigate the problem, if possible. The ICSBEP Chairman stated that he does not recommend using IEU-SOL-THERM-001 to support validation efforts until the discrepancy has been corrected.

SHINE has determined that an error in the ICSBEP Handbook exists for the IEU-SOL-THERM-001 benchmark. This determination is based on inconsistency of the data with known physical behavior and the data should therefore be excluded in accordance with Regulatory Guide 3.71.

SHINE has sufficient benchmark cases covering the range of enrichments and materials in the SHINE facility, and has determined there are no trends in the bias with investigated parameters.

The calculated USL will protect public health and safety. SHINE will consider any new or revised data pertinent to the criticality safety validation during final design. An IMR has been issued to track this action.

Page 8 of 9

References (1) NRC electronic mail to SHINE Medical Technologies, Inc., dated August 26, 2015, Draft Request for Additional Information Supporting SHINE Preliminary Safety Analysis Report (ML15239B051)

(2) NRC electronic mail to SHINE Medical Technologies, Inc., dated August 27, 2015, Draft Request for Additional Information Supporting SHINE Preliminary Safety Analysis Report (3) SHINE Medical Technologies, Inc. letter to NRC, dated March 26, 2013, Part One of the SHINE Medical Technologies, Inc. Application for Construction Permit (ML130880226)

(4) SHINE Medical Technologies, Inc. letter to NRC, dated May 31, 2013, Part Two of the SHINE Medical Technologies, Inc. Application for Construction Permit (ML13172A324)

(5) U.S. Nuclear Regulatory Commission, "FINAL Interim Staff Guidance Augmenting NUREG-1 537, Part 2, "Guidelines for Preparing and Reviewing Applications for the Licensing of Non-Power Reactors: Standard Review Plan and Acceptance Criteria," for Licensing Radioisotope Production Facilities and Aqueous Homogeneous Reactors,"

October 17, 2012 (ML12156A075)

(6) SHINE Medical Technologies, Inc. letter to NRC, dated July 23, 2015, SHINE Medical Technologies, Inc. Application for Construction Permit, Response to Request for Additional Information 6b.3-30 (ML15222A231)

(7) U.S. Nuclear Regulatory Commission, "Nuclear Criticality Safety Standards for Fuels and Materials Facilities," Regulatory Guide 3.71, Revision 2, December 2010 (ML103210345)

(8) American National Standards Institute/American Nuclear Society, "Validation of Neutron Transport Methods for Nuclear Criticality Safety Calculations,"

ANSI/ANS-8.24-2007 (R2012), La Grange Park, IL (9) U.S. Nuclear Regulatory Commission, "Guide for Validation of Nuclear Criticality Safety Calculational Methodology," NUREG/CR-6698, January 2001 (ML050250061)

Page 9 of 9

ENCLOSURE 1 ATTACHMENT 1 SHINE MEDICAL TECHNOLOGIES, INC.

SHINE MEDICAL TECHNOLOGIES, INC. APPLICATION FOR CONSTRUCTION PERMIT RESPONSE TO REQUEST FOR ADDITIONAL INFORMATION APPLICABLE PAGES FROM NATIONAL BUREAU OF STANDARDS HANDBOOK 91 7 pages follow

UNITED STATES DEPARTMENT OF COMMERCE

• Luther H. Hodges, Secretary NATIONAL BUREAU OF STANDARDS

• A. V. Astin, Director Experimental Statistics Mary Gibbons Natrella National Bureau of Standards Reprint of the Experimental Statistics Portion of the AMC Handbook By permission of the Army Materiel Command National Bureau of Standards Handbook 91 Issued August 1, 1963 For sat by the Superintendent of Docutments, U.S. Government Prlntint* Office, Weuhingtont 25, D.C.

Price $4.25

CHARACTERIZING MEASURED PERFORMANCE ORP0-0 I' ii Procedure Example Problem: If we are to make a simple series of Problem:How large a sample would be required measurements, how many measurements are re- to estimate the standard deviation within 20%

quired to estimate the standard deviation with- of its true value, with confidence coefficient in P percent of its true value, with prescribed equal to 0.95?

confidence?

(1) Specify P, the allowable percentage devia- (1) Let P =20%

tion of the estimated standard deviation from its true value.

(2) Choose 7y, the confidence coefficient. (2) Let -y = .95 (3) In Figure 2-2, find P on the horizontal (3) For "y = .95, P = 20%, the required de-scale, and use the curve for the appropriate grees of freedom equals 46.

7. Read on the vertical scale the required degrees of freedom.

(4) For a simple series of measurements, the (4) n = 46 +- 1 required number is equal to one plus the =47 degrees of freedom.

2-5 STATISTICAL TOLERANCE LIMITS 2-5.1 GENERAL Sometimes we are more interested in the Thus for the data on thickness of mica approximate range of values in a lot or popu- washers (Data Sample 2-1), we could give lation than we are in its average value. Sta- two thickness values, stating with chosen tistical tolerance limits furnish limits be- confidence that a proportion P (at least) of tween, above, or below which we confidently the washers in the lot have thicknesses be-expect to find a prescribed proportion of in- tween these two limits. We call the confi-dividual items of the population. Thus, we dence coefficient y, and it refers to the pro-might like to he able to give two values A portion of the time that our method will and B. between which we can be fairly cer- result in correct statements. If a normal dis-tain that at least a proportion P of the popu- tribution can be assumed, use the procedures lation will lie, (two-sided limits), or a value of Paragraphs 2-5.2 and 2-5.8; otherwise use A above which at least a proportion P will the procedures of Paragraph 2-5.4.

lie, (one-sided limit).

2-5.2 TWO-SIDED TOLERANCE LIMITS FOR A NORMAL DISTRIBUTION When the mean m and standard deviation a-of a normally distributed quantity are known, symmetrical limits that inclurde a prescribed proportion P of the distribution are readily obtained by adding and subtracting z0 a- from the known mean m, where z,, is read from Table A-2 with ca = 4 (P+1). When m and a- are not known, we can use an interval of the form X +/- Ks. Since both X* and s will vary from sample to sample it is impossible to determine K so that the limits X +/- Ks will always include a specified proportion P of the underlying normal distribution. It is, however, possible to determine K so that in a long series of samples from the same or different normal distributions a definite proportion y of the intervals X +/-* Ks will include P or more of the underlying distribution (s).

2-13

ORDP 20-110 ANALYSIS OF MEASUREMENT DATA ORDP 20-110 ANALYSIS OF MEASUREMENT DATA Procedure Example Problem: We would like to state two limits Problem: We would like to state thickness limits between which we are 100 y, percent confident between which we are 95% confident that 90%

that 100 P percent of the values lie. of the values lie (Data Sample 2-1).

(1) Choose P, the proportion, and y, the confi- (1) Let P = .90 dence coefficient. = .95 (2) Compute from the sample: (2)

=-- .1260 inch s = 0.00359 inch (3) Look up K for chosen P and -yinTable A-6.

(3) K = 2.839 (4) Compute: (4)

Xu = X+Ks Xv=.1260 +t 2.839 (.00359)

= 0.136 inch XL =X- Ks XL = .1260 -- 2.839 (.00359)

=0.116 inch Conclude: With 100 *, % confidence we may pre- Conclude: With 95% confidence, we may say dict that a proportion P of the individuals of the that 90% of the washers have thicknesses be-.

population have values between XL and Xu. tween 0.116 and 0.136 inch.

2-5.3 ONE-SIDED TOLERANCE LIMITS FOR A NORMAL DISTRIBUTION Sometimes we are interested only in estimating a value above which, or below which, a proportion P (at least) will lie. In this case the one-sided upper tolerance limit will be Xc= X* + Ks; and XL -- - Ks will be the one-sided lower limit. The appropriate values for K are given in Table A-7 and are not the same as those of Paragraph 2-5.2.

Procedure Example Problem: To find a single value above which we Problem: To find a single value above which we may predict with confidence yz that a proportion may predict with 90% confidence that 99% of P of the population will lie. the population will lie. (Data Sample 2-1).

(1) Choose P the proportion and y, the confi- (1) Let P = .99 dence coefficient. =.90 (2) Compute: (2)

X .1260 inch s = 0.00359 inch (3) Look up K in Table A-7 for the appropriate (3) K (10, .90, .99) = 3.532 n, "y, and P.

(4) XL - X - Ks (4) XL = .1260 -- 3.532 (.00359)

= .1133 inch Thus we are 90% confident that 99% of the mica washers will have thicknesses above

.113 inch.

2-14

CHARACTERIZING MEASURED PERFORMANCE OD 20--110 ORDP 0i1 Note: Factors for some values of n, v, and P not covered in Table A-7 may be found in Sandia Corporation Monograph SCR-13'*. Alternatively, one may compute K using the fol-lowing formulas :

2 (n - 1) (where z can be found in Table A-2)

I b = z-n 2-5.4 TOLERANCE LIMITS WHICH ARE INDE- of n = 60, then we may have a confidence of PENDENT OF THE FORM OF THE at least v = .95 that I00P% = 75% of the DISTRIBUTION population will lie between the fifth largest (s =5) and the fifth smallest (r = 5) of the The methods given in Paragraphs 2-5.2 sample values. That is, if we were to take and 2-5.3 are based on the assumption that many random samples of 60, and take the the observations come from a normal distri- fifth largest and fifth smallest of each, we bution. If the distribution is not in fact should expect to find that at least 95 % of the normal, then the effect will be that the true resulting intervals would contain 75 % of the proportion P of the population between the population.

tolerance limits will vary from the intended Table A-32 may be useful for sample sizes P by an amount depending on the amount of of n -- 100. This table gives the confidence departure from normality. If the departure from normality is more than slight we can v with which we may assert that 100P% of the population lies between the largest and use a procedure which assumes only that the smallest values of the sample.

distribution has no discontinuities. The tol-erance limits so obtained will be substantially wider than those assuming normality. 2-5.4.2 One-Slded Tolerance Litmits (Distribution -Freel 2-5.4.1 Two-Sided Tolerance Limits Table A-31 gives the largest value of m (Distribution-Free) such that we may assert with confidence at least v that 100P% of a population lies be-Table A-30 gives values (r, s) such that low the int 6 largest (or above the mtb small-I. we may assert with confidence at least y that est) of a random sample of n from that pop-100P% of a population lies between the rt h ulation. For example, from Table A-31 with smallest and the sth largest of a random sam- 7= .95, P = .90, and n = 90, we may say ple of n from that population. For example, that we are 95% confident that 90% of a from Table A-30 with y = .95, P -. 75, and population will lie below the fifth largest n = 60, we may say that if we have a sample value of a sample of size n = 90.

REFERENCES

1. M. G. Kendall and W. R. Buckland, A Dictioiuxr' of Statistical Terms,

p. 79, Oliver and Boyd, London, 1957.

2. D. B. Owen, Table of Factors for One-.Sided Tolerance Limits for a Normal Distributio, Sandia Corporation Monograph SCR-13, April 1958.

2-15 886-511 0 5

a. -

1 TABLE A-2. CUMULATIVE NORMAL DISTRIBUTION.- VALUES OF zp zp Values of Zp corresponding to P for the normal curve.

z is the standard normal variable P .00 .01 .02 .03 .04 .05 .06 .07 .08 .09

.00 -- --2.33 -2.05 -1.88 -1.75 -1.64 --1.55 -1.48 -1.41 --1.34

.10 -1.28 -1.23 -1.18 -1.13 -1.08 -1.04 -0.99 -0.95 -0.92 -0.88

.20 -0.84 --0.81 -0.77 -0.74 -0.71 -0.67 -0.64 -0.61 -0.58 --0.55

.30 -0.52 -0.50 -0.47 -0.44 -0.41 -0.39 -0.36 -0.33 -0.31 -0.28

.40 -0.25 --0.23 --0.20 --0.18 -0.15 -0.13 -0.10 -0.08 -0.05 --0.03

.50 0.0O0 0. 03 0. 05 0.08 0. 10 0. 13 0. 15 0. 18 0.20 0.23 0.25 0. 28 0,.31 -l

-- I .60 0.33 0.36 0.39 0. 41 0.44 0.47 0. 50

.70 0. 52 0. 55 0. 58 0. 61 0. 64 0. 67 0. 71 0.74 0.77 0.81 I'-

m

.80 0. 84 0. 88 0. 92 0.95 0. 99 1.04 1.08 1.13 1.18 1.23 C.'

.90 1.28 1.34 1.41 1.48 1.55 1.64 1.75 1.88 2.05 2.33 Special Values 0

2

ORDP 20-114 TABLES 16'-

TABLE A-7. FACTORS FOR ONE-SIDED TOLERANCE LIMITS FOR NORMAL DISTRIBUTIONS Factors K such that the probability is -ythat at least a proportion P of the distribution will be tess than V

- - Ks (or greater than X - iKs), where X and s are estimates of the mean and the standard deviation computed from a sample size of n. --/4 1'= 0.75 7 =0.90 n* 0.75 0.90 0.95 0.99 0.999 0.75 0.90 0.95 0.99 0.999 3 1.464 2.501 3.152 4.396 5.805 2.602 4.258 5.310 7.340 9.651 4 1.256 2.134 2.680 3.726 4.910 1.972 3.187 3.957 5.437 7.128 5 1.152 1.961 2.463 3.421 4.507 1.698 2.742 3.400 4.666 6.112 6 1.087 1.860 2.336 3.243 4.273 1.540 2.494 3.091 4.242 5.556 7 1.043 1.791 2.250 3.126 4.118 1.435 2.333 2.894 3.972 5.201 8 1.010 1.740 2.190 3..042 4.008 1.360 2.219 2.755 3.788 4.955 9 0.984 1.702 2.141 2.977 3.924 1.302 2.133 2.649 3.641 4.772 10 0.964 1.671 2.103 2.927 3.858 1.257 2.065 2.568 3.532 4.629 11 0.947 1.646 2.073 2.885 3.804 1.219 2.012 2.503 3.444 4.515 12 0.933 1.624 2.048 2.851 3.760 1.188 1.966 2.448 3.371 4.420 13 0.919 1.606 2.026 2.822 3.722 1.162 1.928 2.403 3.310 4.341 14 0.909 1.591 2.007 2.796 3.690 1.139 1.895 2.363 3.257 4.274 15 0.899 1.577 1.991 2.776 3.661 1.119 1.866 2.329 3.212 4.215 16 0.891 1.566 1.977 2.756 3.637 1.101 1.842 2.299 3.172 4.164 17 0.883 1.554 1.964 2.739 3.615 1.085 1.820 2.272 3.136 4.118 18 0.876 1.544 1.951 2.723 3.595 1.071 1.800 2.249 3.106 4.078 19 0.870 1.536 1.942 2.710 3.577 1.058 1.781 2.228 3.078 4.041 20 0.865 1.528 1.933 2.697 3.561 1.046 1.765 2.208 3.052 4.009 21 0.859 1.520 1.923 2.686 3.545 1.035 1.750 2.190 3.028 3.979 22 0.854 1.514 1.916 2.675 3.532 1.025 1.736 2.174 3.007 3.952 23 0.849 1.508 1.907 2.665 3.520 1.016 1.724 2.159 2.987 3.927 24 0.845 1.502 1.901 2.656 3.509* 1.007 1.712 2.145 2.969 3.904 25 0.842 1.496 1.895 2.647 3.497 0.999 1.702 2.132 2.952 3.882 30 0.825 1.475 1.869 2.613 3.454 0.966 1.657 2.080 2.884 3.794 35 0.812 1.458 1.849 2.588 3.421 0.942 1.623 2.041 2.833 3.730 40 0.803 1.445 1.834 2.568 3.395 0.923 1.598 2.010 2.793 3.679 45 0.795 1.435 1.821 2.552 3.375 0.908 1.577 1.986 2.762 3.638 50 0.788 1.426 1.811 2.538 3.358 0.894 1.560 1.965 2.735 3.604 Adapted by perrmjeefn from Industrial Quality Control, Vol. XIV, No. 10, April 1958, from article entitled "TIablea for One-Sided Statistical Tolerance Limits" by G. J. Lieberinan.

7-1 4 I

TABLES TABLESORDP 20-114 z*,,, T ABL A7 (Continued). FACTORS FOR ONE-SIDED TOLERANCE LIMITS FOR

.. p./p*, r*-!,e*..  ! RA,,,: DISTRIBUTIONS

',I _ , . - ,. -.

• " 70.95 'V = 0.99 0.75 0.90 0.95 0.99 0.999 0.75 0.90 0.95 0.99 0.999 6.158 10.552

3. 3.804 7.655 13 .857 4 2.619 4.163 5.145 7.042 9.215 5 2.149 8.407 4.202 5.741 7.501 6 1.895 3.006 3.707 5.062 6.*612 2.849 4.408 5.409 7.334 9.540 7 1.732 2.755 3.399 4.641 6*061 2.490 3.856 4. 730 6.411 8.348 8 1.617 2.582 3.1I88 4.353 5.686 2.252 3.496 4. 287 5.811 7.566 9 1.532 2.454 3.031 4.143 5.*414 2. 085 3.242 3. 971 5. 389 7.014 10 1.465 2.355 2.911 3.981 5.203 1.954 3.048 3.739 5.075 6.603 11 1.411 2.275 2.815 3.852 5.036 1.854 2.897 3. 557 4.828 6.284 12 1.366 2.210 2.736 8.747 4.900 1.771 2.773 3.410 4.633 6.032 13 1.329 2.155 2.670 3.659 4.787 1.702 2.677 3. 290 4.472 5.826 14 1.296 2.108 2.614 3.585 4.690 1.645 2.592 3.189 4.336 5.651 15 1.268 2.068 2. 566 3.520 4.607 1. 596 2.521 3.102 4.224 5.507 16 1.242 2.032 2. 523 3.463 4.534 1.553 2.458 3.028 4.124 5.374 17 1.220 2.001 2*486 3.415 4.471 1. 514 2.405 2.962 4.038 5.268 18 1.200 1 *974 2.453 3.370 4.*415 1.481 2.357 2.906 3. 961 5.167 19 1.183 1.949 2.423 3.331 4.364 1.450 2.315 2.855 3.893 5.078 20 1.167 1.926 2.396 3.295 4.319 1,424 2.275 2.807 3.832 5.003 21 1.152 1.*905 2.371 3.262 4.276 1.397 2.241 2.768 3.776 4.932 22 1.138 1.887 2.350 3.233 4.238 1.376 2.208 2.729 3.727 4.866 23 1.126 1.869 2.329 3.206 4.204 1.355 2.179 2.693 3.680 4.806 24 1.114 1.853 2.309 3.181 4.171 1.336 2.154 2. 663 3. 638 4.755 25 1.103 1.838 2.292 3.158 4.143 1.319 2.129 2.632 3.601 4.706 30 1.059 1.778 2.220 3.064 4.022 1.249 2.029 2. 516 3.446 4.508 35 1.025 1.732 2.166 2.994 3.934 1*.195 1.957 2.431 3.334 4.364 40 0. 999 1.697 2.126 2. 941 3.866 1.154 1.902 2.365 3. 250 4.255 45 0.978 1.669 2.092 2.897 3.811 1.122 1.857 2.313 3.181 4.168 50 0. 961 1.646 2.065 2.863 3.766 1.096 1.821 2.296 3.124 4.096 T-1 5