Regulatory Guide 5.22

Assessment of the Assumption of Normality (Employing Individual Observed Values)

ML003739999
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Issue date:	04/30/1974
From:	Office of Nuclear Regulatory Research
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RG-5.22
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April 1974 U.S. ATOMIC ENERGY COMMISSION

REGULATORY

DIRECTORATE OF REGULATORY STANDARDS

GUIDE

REGULATORY GUIDE 5.22 ASSESSMENT OF THE ASSUMPTION OF

NORMALITY (EMPLOYING INDIVIDUAL OBSERVED VALUES)

A. INTRODUCTION

the basis of an assumed frequency function is dependent on the extent to which the assumed distribution Part 70 of Title 10 of the Code of Federal describes the actual measurement process.

Regulations requires certain AEC special nuclear material (SNM) licensees to establish and maintain One of the most frequent assumptions made in written material control and accounting procedures to developing and applying statistical procedures for enable the licensee to account for the special nuclear treating measurement data is that observations material in his possession. Part 70 also requires comprising a sample were drawn from a population applicants for certain AEC licenses for SNM to submit to which can be described by a normal distribution. The the Commission as part of the application a full examination of a typical set of measurements which description of such procedures, including statistical adequately represent the distribution will show the controls. The effectiveness of such controls depends individual measurement values clustering around the greatly upon the validity of the statistical procedures average, forming a symmetrical bell-shaped pattern. Two applied. A key assumption often encountered in parameters, the mean and the variance, are sufficient to applications is that the measured value is a random define a normal distribution of a particular set of data variable that can be described by a normal or Gaussian under examination.

distribution function. This guide identifies methods acceptable to the Regulatory staff for assessing the Most statistical interval estimates and tests validity of such an assumption. commonly used in practice are based on the assumption of normal distribution. Two features tend to promote

B. DISCUSSION

the usage of the normal distribution, sometimes without sufficient investigation as to whether its assumption is The general role of statistical methodology in SNM justified. One is its usual applicability and the other is accountability is to serve as the basis for evaluations the fact that its mathematical operations are which objectively provide assurance that material in the comparatively simple and well known. The basic possession of licensees is accounted for effectively and procedural assumption that a measured random variable that losses are localized when they occur. is normally distributed can often permit slight to moderate departures from normality without In maintaining material balances, it is usually significantly affecting conclusions, depending on the impracticable to assay (observe) every item in a material statistical technique employed. However when decisions process batch or lot (population). It would also be are based on the outcome of a statistical test, there is impossible, of course, to measure any material an always a risk that a wrong conclusion has been reached, infinite number of times. Accountability systems must and any decision based on incomplete information runs thereftre rely on observing a portion (sample) of the the risk of either rejecting a true hypothesis or accepting population being measured, from which general a false one. The discernibility (power) of a statistical test conclusions can be inferred about the population. Such will depend significantly upon the quantity and quality statistically calculated inferences based on sample of data tested. A major departure from the normality measurement data are basically predictions of what assumption could result in misleading conclusions. For would be found if the sampled populations could be and example, the level of control could be incorrectly were fully observed. The validity of inferences made on determined and assessed if measurement errors are not USAEC REGULATORY GUIDES Copies of published guides may be obtained by request indicating the divisions desired to the US. Atomic Energy Commission, Washington. D.C. 20645, Regulatory Guides are issued to descibe and make availabe to the public Attention: Director of Regulatory Standards. Comments end suggestions for methods acceptable to the AEC Regulatory staff of Implemening specific parts of improvements in these guides; ae encouraged and should be sent to the Sacretary the Commission's regulations, to delineate techniques used by the staff in of the Commission, US. Atomic Energy Commission, Washington, D.C. 20645, ealuating specific problems or postulated accidents, or to provide guidance to Attention: Chief, Public Proceedings Staff.

a 1lmnts.

Regulatory Gu~des are not substitutes for regulations and compliance with them is not required. Methods and solutions different from thoee set out in The guides ore issued in the following ten broad divisions:

the guides will be acceptable if they provide a basis for the findings requisite to Power Reactors 6. Products the issuance or continuance of a permit or license by the Commission. 2. RParch end Test Reactors

7. TransPortatoon

3. Fuels and Materials Facilities S. Occupational Health

4. Environmental and Siting 9. Antitrust Review Publtshad guides will be revined periodically, as aperon riate, to acc

o. odate

5. Materials and Plant Protection 10. General comments and to reflect now inforiation or experience.

characterived properly in the calculation of limits of error. This could seriously affect the facility's ability to C. RFGULATORY POSITION

control quantities of material unaccounted for and to cvaluate their significance. Therefore, the testing of the assumption of normality merits consideration as a The statistical hypothesis testing techniques c;ntrol procedure. contained in the approved standard, ANSI N15.15-1973,

"Assessment of the Assumption of Normality Subcommittee N15-3 of the American National (Employing Individual Observed Vnhues)," '1 are Standards Institute (ANSI) Standards Committee NIS, generally acceptable to the Regulatory staff for use in Methods of Nuclear Materials Control, has developed a written procedures for the control of special nuclear standard for assessing the assumption of normality material subject to the following. The interpretation of (employing individual observed values). This standard the significance of results from the application of the has been designated ANSI N15.15-1973.' test of normality should consider the amount of data treated (sample size), in particular whether there are

' Copies may be obtained from the American National enough data available to reach a meaningful conclusion Standards Institute, Inc., 1430 Broadway, New York, New York pertaining to the validity of the assumption for a given

10018. process.

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