Publication Date: 4/1/74     Pages: 2     Date Entered: 2/22/84     Title: ASSESSMENT OF THE ASSUMPTION OF NORMALITY (EMPLOYING INDIVIDUAL OBSERVED VALUES)     April 1974     U.S. ATOMIC ENERGY COMMISSION     REGULATORY GUIDE     DIRECTORATE OF REGULATORY STANDARDS     REGULATORY GUIDE 5.22     ASSESSMENT OF THE ASSUMPTION OF     NORMALITY (EMPLOYING INDIVIDUAL OBSERVED VALUES)A. INTRODUCTION     Part 70 of Title 10 of the Code of Federal Regulations requires     certain AEC special nuclear material (SNM) licensees to establish and     maintain written material control and accounting procedures to enable     the licensee to account for the special nuclear material in his     possession. Part 70 also requires applicants for certain AEC licenses     for SNM to submit to the Commission as part of the application a full     description of such procedures, including statistical controls. The     effectiveness of such controls depends greatly upon the validity of the     statistical procedures applied. A key assumption often encountered in     applications is that the measured value is a random variable that can be     described by a normal or Gaussian distribution function. This guide     identifies methods acceptable to the Regulatory staff for assessing the     validity of such an assumption. B. DISCUSSION     The general role of statistical methodology in SNM accountability     is to serve as the basis for evaluations which objectively provide     assurance that material in the possession of licensees is accounted for     effectively and that losses are localized when they occur.     In maintaining material balances, it is usually impracticable to     assay (observe) every item in a material process batch or lot     (population). It would also be impossible, of course, to measure any     material an infinite number of times. Accountability systems must     therefore rely on observing a portion (sample) of the population being     measured, from which general conclusions can be inferred about the     population. Such statistically calculated inferences based on sample     measurement data are basically predictions of what would be found if the     sampled populations could be and were fully observed. The validity of     inferences made on the basis of an assumed frequency function is     dependent on the extent to which the assumed distribution describes the     actual measurement process.     One of the most frequent assumptions made in developing and     applying statistical procedures for treating measurement data is that     observations comprising a sample were drawn from a population which can     be described by a normal distribution. The examination of a typical set     of measurements which adequately represent the distribution will show     the individual measurement values clustering around the average, forming     a symmetrical bell-shaped pattern. Two parameters, the mean and the     variance, are sufficient to define a normal distribution of a particular     set of data under examination.     Most statistical interval estimates and tests commonly used in     practice are based on the assumption of normal distribution. Two     features tend to promote the usage of the normal distribution, sometimes     without sufficient investigation as to whether its assumption is     justified. One is its usual applicability and the other is the fact     that its mathematical operations are comparatively simple and well     known. The basic procedural assumption that a measured random variable     is normally distributed can often permit slight to moderate departures     from normality without significantly affecting conclusions, depending on     the statistical technique employed. However when decisions are based on     the outcome of a statistical test, there is always a risk that a wrong     conclusion has been reached, and any decision based on incomplete     information runs the risk of either rejecting a true hypothesis or     accepting a false one. The discernibility (power) of a statistical test     will depend significantly upon the quantity and quality of data tested.     A major departure from the normality assumption could result in     misleading conclusions. For example, the level of control could be     incorrectly determined and assessed if measurement errors are not     characterized properly in the calculation of limits of error. This     could seriously affect the facility's ability to control quantities of     material unaccounted for and to evaluate their significance. Therefore,     the testing of the assumption of normality merits consideration as a     control procedure.     Subcommittee N15-3 of the American National Standards Institute     (ANSI) Standards Committee N15, Methods of Nuclear Materials Control,     has developed a standard for assessing the assumption of normality     (employing individual observed values). This standard has been     designated ANSI N15.15-1973.(1)----------     (1) Copies may be obtained from the American National Standards     Institute, Inc., 1430 Broadway, New York, New York 10018.     ---------- C. REGULATORY POSITION     The statistical hypothesis testing techniques contained in the     approved standard, ANSI N15.15-1973, "Assessment of the Assumption of     Normality (Employing Individual Observed Values),"(1) are generally     acceptable to the Regulatory staff for use in written procedures for the     control of special nuclear material subject to the following. The     interpretation of the significance of results from the application of     the test of normality should consider the amount of data treated (sample     size), in particular whether there are enough data available to reach a     meaningful conclusion pertaining to the validity of the assumption for a     given process.     11