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 V SHINE Medical Technologies
To:	Document Control Desk, Office of Nuclear Reactor Regulation
References
SMT-2015-040
Download: ML15247A067 (19)

Text

Medical Technologies September 2, 2015SMT-201 5-04010 CFR 50.30U.S. Nuclear Regulatory Commission ATTN: Document Control DeskWashington, DC 20555

References:

(1) SHINE Medical Technologies, Inc. letter to NRC, dated March 26, 2013,Part One of the SHINE Medical Technologies, Inc. Application forConstruction Permit (ML1 30880226)

(2) SHINE Medical Technologies, Inc. letter to NRC, dated May 31, 2013,Part Two of the SHINE Medical Technologies, Inc. Application forConstruction Permit (ML1 31 72A324)(3) NRC electronic mail to SHINE Medical Technologies, Inc., datedAugust 26, 2015, Draft Request for Additional Information Supporting SHINE Preliminary Safety Analysis Report (ML15239B051)

(4) NRC electronic mail to SHINE Medical Technologies, Inc., datedAugust 27, 2015, Draft Request for Additional Information Supporting SHINE Preliminary Safety Analysis ReportSHINE Medical Technoloqies.

Inc. Application for Construction PermitResponse 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 permitapplication.

Enclosure 1 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-ooiIy( ~2555 Industrial Drivel Monona, WI 53713 I P (608) 210-1060

.F (608) 210-2504 www.shinemed~corn Document Control DeskPage 2I declare under the penalty of perjury that the foregoing is true and correct.Executed on September 2, 2015.Very truly yours,Chief Operating OfficerSHINE Medical Technologies, Inc.Docket No. 50-608Enclosure cc: Administrator, Region III, USNRCProject Manager, USNRCEnvironmental Project Manager, USNRCSupervisor, Radioactive Materials

Program, Wisconsin Division of Public Health ENCLOSURE 1SHINE MEDICAL TECHNOLOGIES, INC.SHINE MEDICAL TECHNOLOGIES, INC. APPLICATION FOR CONSTRUCTION PERMITRESPONSE TO REQUEST FOR ADDITIONAL INFORMATION The NRC staff determined that additional information was required (References 1 and 2) toenable the continued review of the SHINE Medical Technologies, Inc. (SHINE) application for aconstruction 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 FEATURESSection 6b.3 -Nuclear Criticality Control(Applies to RAIs 6b.3-31 through 33)As required by 10 CFR 50.34(a),

"Contents of applications; technical information,"

apreliminary safety analysis report should include "[a] preliminary analysis and evaluation of the design and performance of structures,

systems, and components of the facilitywith the objective of assessing the risk to public health and safety resulting fromoperation of the facility...,

and the adequacy of structures,

systems, and components provided for the prevention of accidents and the mitigation of the consequences ofaccidents."

Additionally, the preliminary design of the facility should pro vide reasonable assurance to the NRC staff that the final design wili conform to its design bases withadequate margin for safety.With respect to nuclear criticality

control, the Interim Staff Guidance (ISG) Augmenting NUREG- 1537, Part 2, Section 6b. 3, "Nuclear Criticality Safety for the Processing

Facility, "states, in part that '[c]riticality process safety controls should be provided forcriticality safety, and a description of their safety function should be described.

Theapplicant should use enough safety controls to demonstrate that, under normal andabnormal credible conditions, all nuclear processes remain subcritical" and that "NCS[nuclear criticality safety] limits on controlled parameters will be established to ensurethat all nuclear processes are subcritical, including an adequate margin of subcritica/ity for safety."RAI 6b.3-31The ISG augmenting NUREG-1537, part 2, Section 6b.3, contains criteria for the use of mass,geometry,

density, enrichment, reflection, moderation, concentration, interaction, neutronabsorbers, and volume as controlled parameters.

Additional information is needed in order forNRC staff to determine the adequacy of SHINE'S treatment of controlled parameters in order toensure that all nuclear processes are subcritical, including an adequate margin of subcriticallty for safety. Specifically, SH-INE'S construction permit application does not contain the necessary commitments to following technical practices for the use of each controlled parameter in orderdemonstrate a sufficient design basis in its preliminary design.Page 1 of 9 In order to provide reasonable assurance that SHINE's final design will conform to its designbases with adequate margin for safety, as required by 10 CFR 50.34, commit to following technical practices for the use of each controlled parameter described in the ISG augmenting NUREG- 1537, Part 2, Section 6b.3, "Nuclear Criticality Safety for the Processing Facility,"

orstate that rellance on particular parameters will not be used. For those parameters that are notcontrolled, commit to assuming the most reactive credible conditions.

Additionally, describe anyconservatism in the calculated keff resulting from the use of these technical practices.

SHINE ResponseSHINE will follow the technical practices for the use of each controlled parameter (i.e., mass,geometry,

density, enrichment, reflection, moderation, concentration, interaction, neutronabsorbers, 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 72through 74 of the ISG augmenting NUREG-1 537, Part 2. For those parameters that are notcontrolled, SHINE will assume the most reactive credible conditions.

The conservatisms in the calculated keff values from the use of these technical practices forAtkins-NS-DAC-SHN-15-02, Revision 0, provided as Attachment 3 to Enclosure 1 ofReference (6), and Atkins-NS-DAC-SHN-15-04, Revision 0, provided as Attachment 2 toEnclosure 1 of Reference (6), are described below. These conservatisms result in a highercalculated 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 nuclearcriticality safety (NCS).* Enrichment:

Uranium is assumed to be enriched to 21 wt% 235U, an increase over thenominal value of 19.75%.* Reflection:

Concrete reflector walls are located six inches from the outside of the neutronabsorber panel. This is a conservative estimate of the minimum anticipated distance.

• Reflection:

Void and water flooded conditions are modeled in order to determine the mostreactive 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 thePPC-B is used. Minimum hydrogen density will result in the least amount of scattering in theabsorber and thus the least amount of neutron absorption.

• Neutron absorbers:

Only 75% of the calculated boron density is used for the PPC-B. Thisis 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 UO2.This molecule has the least number of oxygenatoms per uranium atom which will result in the highest reactivity when compared to otheroxide compounds (i.e., UOa or U308).* Geometry:

For the determination of the subcritical limit for mass and volume, the mostreactive geometry (a sphere) was used.* Enrichment:

Uranium is assumed to be enriched to 21 wt% 235U, an increase over thenominal value of 19.75%.* Reflection:

For the mass and volume subcritical limits, the sphere was surrounded by12 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 thelimiting 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.3-32The NRC staff recalculated SHINE's upper safety limit (USL) using the USLSTA TS code issuedwith the SCALE criticality code package.

This recalculation produced a lower USL than thatdetermined in Table 8 of SHINE's Validation Report. This difference in USL calculations appears to be the result of SHINE's use of a smaller single-sided lower tolerance limit factor, K*,and pooled standard deviation, 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 order for the NRC staff to determine the adequacy ofSHINE's USL calculation to resolve the discrepancy with NRC staff calculations.

Thisinformation is necessary to demonstrate reasonable assurance that SHINE's final design willconform to its design bases with adequate margin for safety, as required by 10 CFR 50.34Provide 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 ResponseIn the SHINE validation report (Atkins-NS-DAC-SHN-15-03, Revision 2, provided asAttachment 4 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 CausingFission (ANECF),

the 235U enrichment, the moderator

material, the reflector

material, and thechemical form of the fissile material.

SHINE determined that the calculated ke, did not trendwith 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 endorsedby 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) fordetails on calculating the upper safety limit (USL), such as statistical and nonstatistical methodsand function

fitting, computational margin determination, and justification for safety margin. Thebias 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 SHINEvalidation report.After determining the data to be normal and displaying no trends, the single-sided tolerance limitwas selected as the appropriate statistical treatment for determining the USL. This methoduses 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 arelisted in Table 2.1 of NUREG/CR-6698.

NUREG/CR-6698 states that the K* value for 50 datapoints, 2.065, may be used as a conservative number for more than 50 data points. SHINEchose 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 pointssignificantly exceeded

50. The equations for calculating K* are listed below, and can also befound in Section 3.4.2 of the SHINE validation report. The equations are taken fromReference 9 of the SHINE validation report. Reference 9 of the SHINE validation report is thesource of Table 2.1 of NUREG/CR-6698.

The applicable pages of Reference 9 of the SHINEvalidation report are provided as Attachment 1.K*-Z z-a+abWhere:2(n -1)2nThe ZpadZvalues are the critical values from the normal distribution that is exceeded withspecified probability (P = 95% and y =95%), and are both 1.645. The resulting K* values for thelarger 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 enricheduranium 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+ Equation 6b.3-32-1 Page 4 of 9 For the single-sided tolerance limit method described in NUREG/CR-6698, these twocomponents 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) 271 G.7%Equation 6b.3-32-2 Equation 6b.3-32-3 With the normalized keff value for the "ih' benchmark case,keffcackeff. -- ceffex~Equation 6b.3-32-4 the uncertainty on the "ith keff value,O- /2 0- 2Equation 6b.3-32-5 and the weighted mean keff~Akeff.keff a11Equation 6b.3-32-6 Where:n = number of critical experiments in the validationeffective multiplication factor for the benchmark effective multiplication factor for the calculation method0exp1 = uncertainty in the benchmark 0catc1 = uncertainty in the calculation methodThe 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 agiven independent variable.

With no trend present in the data, the trend line determined byUSLSTATS will have a poor fit. USLSTATS does not perform a "goodness of fit test" todetermine how applicable this method is to the data set. The pooled standard deviation (Sp) forthis method is a combination of the variance of the regression fit (S() n h ihnvracof the data (Sw,).Page 5 of 9

= +kx +S2 Equation 6b.3-32-7 S2 1 [~k~ kef)

I Equation 6b.3-32-8gY ef Equation 6b.3-32-9 Where:xi = value for the independent variable associated with the "1t"" keff value)Z = the mean value of parameter s in the set of calculations k'eff = the keff value for calculated using the fitted functionIn summary, USLSTATS calculates a different value for the pooled standard deviation becauseit 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 thesingle-sided tolerance limit method as described in NUREG/CR-6698.

RAI 6b.3-33While Table 9, 'Area of Applicability Summary,"

of the SHINE Validation Report, Rev. 2,includes

cadmium, this material is not mentioned as present in Table 2, "Critical Benchmark Experiments Summary.

"Additionally, the discussion of some of the benchmark experiment setsmentions

cadmium, but it is not clear if it is present in any of the experiments chosen from thosebenchmark sets.Additional information is needed on SHINE's analysis of benchmark experiments in order for theNRC staff to assess the adequacy of SHINE's preliminary design.Clarify whether the area of applicability (AOA) in the SHINE Validation Report, Rev. 2, includescadmium as a neutron absorber.

SHINE ResponseSHINE does not plan to use cadmium as a neutron absorber.

Cadmium will be removed fromTable 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 detaileddesign.Page 6 of 9 RAI 6b.3-34As required by 10 CFR 50.34(a),

"Contents of applications; technical in formation,"

a preliminary safety analysis report should include '[a] preliminary analysis and evaluation of the design andpedformance of structures,

systems, and components of the facility with the objective ofassessing the risk to public health and safety resulting from operation of the facility...,

and theadequacy of structures,

systems, and components provided for the prevention of accidents andthe mitigation of the consequences of accidents."

Additionally, the preliminary design of thefacility should provide reasonable assurance to the NRC staff that the final design will conformto its design bases with adequate margin for safety.With respect to nuclear criticality

control, the Interim Staff Guidance (ISG) Augmenting NUREG- 1537, Part 2, Section 6b. 3, "Nuclear Criticality Safety for the Processing Facility,"

states, in part that "[c]riticality process safety controls should be provided for criticality safety,and a description of their safety function should be described.

The applicant should use enoughsafety controls to demonstrate that, under normal and abnormal credible conditions, all nuclearprocesses remain subcritical" and that "NCS [nuclear criticality safety] limits on controlled parameters will be established to ensure that all nuclear processes are subcritical, including anadequate margin of subcriticality for safety."The ISG Augmenting NUREG-1537, Part 2, Section 6b.3, states, in part, that there viewershould determine "whether the margin of subcriticality for safety is sufficient to providereasonable assurance of subcriticality."

In response to RAI 6b.3-4, SHINE states it intends to utilize a subcritical margin of 0.05 withadditional considerations for uncertainty in the validation and modeling.

In addition, SHINEstates in multiple places in the PSAR that processes will be maintained to a keff < 0.95(assuming a subcritical margin of 0.05).The NRC staff's review of SHINE's responses to RAIs 6b.3-1 and 6b.3-26 found that there wasinsufficient benchmarking of the code against experiments utilizing the materials andenrichments expected in SHINE's processes.

For this reason, the proposed subcritical margin of0.05 is not sufficient to adequately address the uncertainty associated with the neutroninteractions of these process materials.

The subcritical margin of 0.05, which SHINE quotedfrom NUREG- 1520, was intended for facilities with enrichment less than five percent utilizing well established processes and for which there is significant experience and data. In contrast, the SHINE facility will be a first-of-a-kind facility using materials not normally utilized and of anenrichment up to 20 percent.Provide additional information describing how SHINE has or will sufficiently benchmark againstexperiments utilizing the materials and enrichments expected to be used in SHINE facilityprocesses for its proposed margin of subcriticality, or propose a new margin of subcriticality thatappropriately takes into account materials and enrichment.

SHINE ResponseThe SHINE validation report, Atkins-NS-DAC-SHN-15-03, Revision 2, provided as Attachment 4to 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 aproposed 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 foruse by SHINE in the validation

process, but was ultimately determined to not be suitable forinclusion, 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), "therejection of outliers should be based only on the inconsistency of the data with known physicalbehavior."

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, SHINEnoted that sample calculation results from the Russian Federation indicated keff values that weresignificantly 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 knownphysical 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% lessthan the critical uranyl sulfate volumes specified in the benchmark description.

Therefore, thedata 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 theICSBEP 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 inIEU-SOL-THERM-001 with the intent of formally presenting the error and means to mitigatethe problem, if possible.

The ICSBEP Chairman stated that he does not recommend usingIEU-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 theIEU-SOL-THERM-001 benchmark.

This determination is based on inconsistency ofthe data with known physical behavior and the data should therefore be excludedin accordance with Regulatory Guide 3.71.SHINE has sufficient benchmark cases covering the range of enrichments and materials in theSHINE 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 orrevised data pertinent to the criticality safety validation during final design. An IMR has beenissued to track this action.Page 8 of 9 References (1) NRC electronic mail to SHINE Medical Technologies, Inc., dated August 26, 2015, DraftRequest for Additional Information Supporting SHINE Preliminary Safety AnalysisReport (ML1 5239B051)

(2) NRC electronic mail to SHINE Medical Technologies, Inc., dated August 27, 2015, DraftRequest for Additional Information Supporting SHINE Preliminary Safety Analysis Report(3) SHINE Medical Technologies, Inc. letter to NRC, dated March 26, 2013, Part One of theSHINE Medical Technologies, Inc. Application for Construction Permit (ML1 30880226)

(4) SHINE Medical Technologies, Inc. letter to NRC, dated May 31, 2013, Part Two of theSHINE 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 theLicensing of Non-Power Reactors:

Standard Review Plan and Acceptance Criteria,"

forLicensing Radioisotope Production Facilities and Aqueous Homogeneous Reactors,"

October 17, 2012 (ML12156A075)

(6) SHINE Medical Technologies, Inc. letter to NRC, dated July 23, 2015, SHINE MedicalTechnologies, Inc. Application for Construction Permit, Response to Request forAdditional Information 6b.3-30 (ML1 5222A231)

(7) U.S. Nuclear Regulatory Commission, "Nuclear Criticality Safety Standards for Fuelsand Materials Facilities,"

Regulatory Guide 3.71, Revision 2, December 2010(ML1 03210345)

(8) American National Standards Institute/American Nuclear Society, "Validation ofNeutron 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 SafetyCalculational Methodology,"

NUREG/CR-6698, January 2001 (ML050250061)

Page 9 of 9 ENCLOSURE 1ATTACHMENT 1SHINE MEDICAL TECHNOLOGIES, INC.SHINE MEDICAL TECHNOLOGIES, INC. APPLICATION FOR CONSTRUCTION PERMITRESPONSE TO REQUEST FOR ADDITIONAL INFORMATION APPLICABLE PAGES FROM NATIONAL BUREAU OF STANDARDS HANDBOOK 917 pages follow UNITED STATES DEPARTMENT OF COMMERCE

• Luther H. Hodges, Secretary NATIONAL BUREAU OF STANDARDS

• A. V. Astin, DirectorExperimental Statistics Mary Gibbons NatrellaNational Bureau of Standards Reprint of the Experimental Statistics Portionof the AMC HandbookBy permission of theArmy Materiel CommandNational Bureau of Standards Handbook 91Issued August 1, 1963For sat by the Superintendent of Docutments, U.S. Government Office, Weuhingtont 25, D.C.Price $4.25 CHARACTERIZING MEASURED PERFORMANCE ORP0-0I' iiProcedure Problem:

If we are to make a simple series ofmeasurements, how many measurements are re-quired to estimate the standard deviation with-in P percent of its true value, with prescribed confidence?

(1) Specify P, the allowable percentage devia-tion of the estimated standard deviation from its true value.(2) Choose 7y, the confidence coefficient.

(3) In Figure 2-2, find P on the horizontal scale, and use the curve for the appropriate

7. Read on the vertical scale the requireddegrees of freedom.(4) For a simple series of measurements, therequired number is equal to one plus thedegrees of freedom.ExampleProblem:

How large a sample would be requiredto estimate the standard deviation within 20%of its true value, with confidence coefficient equal to 0.95?(1) Let P =20%(2) Let -y = .95(3) For "y = .95, P = 20%, the required de-grees of freedom equals 46.(4)n = 46 +- 1=472-5 STATISTICAL TOLERANCE LIMITS2-5.1 GENERALSometimes we are more interested in theapproximate range of values in a lot or popu-lation than we are in its average value. Sta-tistical tolerance limits furnish limits be-tween, above, or below which we confidently expect to find a prescribed proportion of in-dividual items of the population.

Thus, wemight like to he able to give two values Aand B. between which we can be fairly cer-tain that at least a proportion P of the popu-lation will lie, (two-sided limits),

or a valueA above which at least a proportion P willlie, (one-sided limit).Thus for the data on thickness of micawashers (Data Sample 2-1), we could givetwo thickness values, stating with chosenconfidence that a proportion P (at least) ofthe washers in the lot have thicknesses be-tween these two limits. We call the confi-dence coefficient y, and it refers to the pro-portion of the time that our method willresult in correct statements.

If a normal dis-tribution can be assumed, use the procedures of Paragraphs 2-5.2 and 2-5.8; otherwise usethe procedures of Paragraph 2-5.4.2-5.2 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 readilyobtained by adding and subtracting z0 a- from the known mean m, where z,, is read fromTable A-2 with ca = 4 (P+1). When m and a- are not known, we can use an interval of theform X +/- Ks. Since both and s will vary from sample to sample it is impossible todetermine K so that the limits X +/- Ks will always include a specified proportion P of theunderlying normal distribution.

It is, however, possible to determine K so that in a longseries of samples from the same or different normal distributions a definite proportion y ofthe intervals X +/-* Ks will include P or more of the underlying distribution (s).2-13 ORDP 20-110ANALYSIS OF MEASUREMENT DATAORDP 20-110 ANALYSIS OF MEASUREMENT DATAProcedure Problem:

We would like to state two limitsbetween which we are 100 y, percent confident that 100 P percent of the values lie.(1) Choose P, the proportion, and y, the confi-dence coefficient.

(2) Compute from the sample:(3) Look up K for chosen P and -yin Table A-6.(4) Compute:Xu = X+KsXL =X- KsConclude:

With 100 % confidence we may pre-dict that a proportion P of the individuals of thepopulation have values between XL and Xu.ExampleProblem:

We would like to state thickness limitsbetween which we are 95% confident that 90%of the values lie (Data Sample 2-1).(1) Let P = .90= .95(2)--= .1260 inchs = 0.00359 inch(3) K = 2.839(4)Xv=.1260

+t 2.839 (.00359)= 0.136 inchXL = .1260 -- 2.839 (.00359)=0.116 inchConclude:

With 95% confidence, we may saythat 90% of the washers have thicknesses be-.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, aproportion P (at least) will lie. In this case the one-sided upper tolerance limit will beXc= + Ks; and XL -- -Ks will be the one-sided lower limit. The appropriate valuesfor K are given in Table A-7 and are not the same as those of Paragraph 2-5.2.Procedure Problem:

To find a single value above which wemay predict with confidence yz that a proportion P of the population will lie.ExampleProblem:

To find a single value above which wemay predict with 90% confidence that 99% ofthe population will lie. (Data Sample 2-1).(1) Choose P the proportion and y, the confi- (1) Let P = .99dence coefficient.

=.90(2) Compute:

(2)(3) Look up K in Table A-7 for the appropriate (3)n, "y, and P.X .1260 inchs = 0.00359 inchK (10, .90, .99) = 3.532(4) XL -X -Ks (4) XL = .1260 -- 3.532 (.00359)= .1133 inchThus we are 90% confident that 99% of themica washers will have thicknesses above.113 inch.2-14 CHARACTERIZING MEASURED PERFORMANCE OD 0i1ORDP 20--110Note: Factors for some values of n, v, and P not covered in Table A-7 may be found inSandia Corporation Monograph Alternatively, one may compute K using the fol-lowing formulas

I2 (n -1)b = z-n(where z can be found in Table A-2)2-5.4 TOLERANCE LIMITS WHICH ARE INDE-PENDENT OF THE FORM OF THEDISTRIBUTION The methods given in Paragraphs 2-5.2and 2-5.3 are based on the assumption thatthe observations come from a normal distri-bution. If the distribution is not in factnormal, then the effect will be that the trueproportion P of the population between thetolerance limits will vary from the intendedP by an amount depending on the amount ofdeparture from normality.

If the departure from normality is more than slight we canuse a procedure which assumes only that thedistribution has no discontinuities.

The tol-erance limits so obtained will be substantially wider than those assuming normality.

2-5.4.1 Two-Sided Tolerance Limits(Distribution-Free)

Table A-30 gives values (r, s) such thatwe may assert with confidence at least y that100P% of a population lies between the rthsmallest and the sth largest of a random sam-ple of n from that population.

For example,from Table A-30 with y = .95, P -.75, andn = 60, we may say that if we have a sampleof n = 60, then we may have a confidence ofat least v = .95 that I00P% = 75% of thepopulation will lie between the fifth largest(s =5) and the fifth smallest (r = 5) of thesample values. That is, if we were to takemany random samples of 60, and take thefifth largest and fifth smallest of each, weshould expect to find that at least 95 % of theresulting intervals would contain 75 % of thepopulation.

Table A-32 may be useful for sample sizesof n -- 100. This table gives the confidence v with which we may assert that 100P% ofthe population lies between the largest andsmallest values of the sample.2-5.4.2 One-Slded Tolerance Litmits(Distribution

-FreelTable A-31 gives the largest value of msuch that we may assert with confidence atleast v that 100P% of a population lies be-low the int6 largest (or above the mtb small-est) of a random sample of n from that pop-ulation.

For example, from Table A-31 with7= .95, P = .90, and n = 90, we may saythat we are 95% confident that 90% of apopulation will lie below the fifth largestvalue of a sample of size n = 90.I.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 aNormal Distributio, Sandia Corporation Monograph SCR-13, April1958.2-15886-511 0 5a. -

1TABLE A-2. CUMULATIVE NORMAL DISTRIBUTION.-

VALUES OF zpzpValues of Zp corresponding to P for the normal curve.z is the standard normal variableP .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 0.23.60 0.25 0. 28 0,.31 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 0.81.80 0. 84 0. 88 0. 92 0.95 0. 99 1.04 1.08 1.13 1.18 1.23.90 1.28 1.34 1.41 1.48 1.55 1.64 1.75 1.88 2.05 2.33--I-lI'-mC.'Special Values02 ORDP 20-114TABLESTABLE A-7. FACTORS FOR ONE-SIDED TOLERANCE LIMITS FOR NORMAL DISTRIBUTIONS Factors K such that the probability is -y that at least a proportion P of the distribution will be tess than--Ks (or greater than X -iKs), where X and s are estimates of the mean and the standarddeviation computed from a sample size of n. --/41'= 0.75 7 =0.900.75 0.90 0.95 0.99 0.999 0.75 0.90 0.95 0.99 0.9993 1.464 2.501 3.152 4.396 5.805 2.602 4.258 5.310 7.340 9.6514 1.256 2.134 2.680 3.726 4.910 1.972 3.187 3.957 5.437 7.1285 1.152 1.961 2.463 3.421 4.507 1.698 2.742 3.400 4.666 6.1126 1.087 1.860 2.336 3.243 4.273 1.540 2.494 3.091 4.242 5.5567 1.043 1.791 2.250 3.126 4.118 1.435 2.333 2.894 3.972 5.2018 1.010 1.740 2.190 3..042 4.008 1.360 2.219 2.755 3.788 4.9559 0.984 1.702 2.141 2.977 3.924 1.302 2.133 2.649 3.641 4.77210 0.964 1.671 2.103 2.927 3.858 1.257 2.065 2.568 3.532 4.62911 0.947 1.646 2.073 2.885 3.804 1.219 2.012 2.503 3.444 4.51512 0.933 1.624 2.048 2.851 3.760 1.188 1.966 2.448 3.371 4.42013 0.919 1.606 2.026 2.822 3.722 1.162 1.928 2.403 3.310 4.34114 0.909 1.591 2.007 2.796 3.690 1.139 1.895 2.363 3.257 4.27415 0.899 1.577 1.991 2.776 3.661 1.119 1.866 2.329 3.212 4.21516 0.891 1.566 1.977 2.756 3.637 1.101 1.842 2.299 3.172 4.16417 0.883 1.554 1.964 2.739 3.615 1.085 1.820 2.272 3.136 4.11818 0.876 1.544 1.951 2.723 3.595 1.071 1.800 2.249 3.106 4.07819 0.870 1.536 1.942 2.710 3.577 1.058 1.781 2.228 3.078 4.04120 0.865 1.528 1.933 2.697 3.561 1.046 1.765 2.208 3.052 4.00921 0.859 1.520 1.923 2.686 3.545 1.035 1.750 2.190 3.028 3.97922 0.854 1.514 1.916 2.675 3.532 1.025 1.736 2.174 3.007 3.95223 0.849 1.508 1.907 2.665 3.520 1.016 1.724 2.159 2.987 3.92724 0.845 1.502 1.901 2.656 1.007 1.712 2.145 2.969 3.90425 0.842 1.496 1.895 2.647 3.497 0.999 1.702 2.132 2.952 3.88230 0.825 1.475 1.869 2.613 3.454 0.966 1.657 2.080 2.884 3.79435 0.812 1.458 1.849 2.588 3.421 0.942 1.623 2.041 2.833 3.73040 0.803 1.445 1.834 2.568 3.395 0.923 1.598 2.010 2.793 3.67945 0.795 1.435 1.821 2.552 3.375 0.908 1.577 1.986 2.762 3.63850 0.788 1.426 1.811 2.538 3.358 0.894 1.560 1.965 2.735 3.604Adapted 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.

7-1 416'-VI TABLESTABLESORDP 20-114T ABL A7 (Continued).

FACTORS FOR ONE-SIDED TOLERANCE LIMITS FOR..

! RA,,,: DISTRIBUTIONS

',I _ , .-, .-.*" 70.95 'V = 0.990.75 0.90 0.95 0.99 0.999 0.75 0.90 0.95 0.99 0.9993.4567891011121314151617181920212223242530354045503.8042.6192.1491.8951.7321.6171.5321.4651.4111.3661.3291.2961.2681.2421.2201.2001.1831.1671.1521.1381.1261.1141.1031.0591.0250. 9990.9780. 9616.1584.1638.4073.0062.7552.5822.4542.3552.2752.2102.1552.1082.0682.0322.0011 *9741.9491.9261.*9051.8871.8691.8531.8381.7781.7321.6971.6691.6467.6555.1454.2023.7073.3993.1I883.0312.9112.8152.7362.6702.6142. 5662. 5232*4862.4532.4232.3962.3712.3502.3292.3092.2922.2202.1662.1262.0922.06510.5527.0425.7415.0624.6414.3534.1433.9813.8528.7473.6593.5853.5203.4633.4153.3703.3313.2953.2623.2333.2063.1813.1583.0642.9942. 9412.8972.86313 .8579.2157.5016.*6126*0615.6865.*4145.2035.0364.9004.7874.6904.6074.5344.4714.*4154.3644.3194.2764.2384.2044.1714.1434.0223.9343.8663.8113.7662.8492.4902.2522. 0851.9541.8541.7711.7021.6451. 5961.5531. 5141.4811.4501,4241.3971.3761.3551.3361.3191.2491*.1951.1541.1221.0964.4083.8563.4963.2423.0482.8972.7732.6772.5922.5212.4582.4052.3572.3152.2752.2412.2082.1792.1542.1292.0291.9571.9021.8571.8215.4094. 7304. 2873. 9713.7393. 5573.4103. 2903.1893.1023.0282.9622.9062.8552.8072.7682.7292.6932. 6632.6322. 5162.4312.3652.3132.2967.3346.4115.8115. 3895.0754.8284.6334.4724.3364.2244.1244.0383. 9613.8933.8323.7763.7273.6803. 6383.6013.4463.3343. 2503.1813.1249.5408.3487.5667.0146.6036.2846.0325.8265.6515.5075.3745.2685.1675.0785.0034.9324.8664.8064.7554.7064.5084.3644.2554.1684.096*!,:!T-1 5