Regulatory Guide 5.33

Statistical Evaluation of Material Unaccounted for

ML003739948
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Issue date:	06/30/1974
From:	Office of Nuclear Regulatory Research
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RG-5.33
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June 1974 U.S. ATOMIC ENERGY COMMISSION

REGULAT6ORY

DIRECTORATE OF REGULATORY STANDARDS

GU IDE

REGULATORY GUIDE 5.33 STATISTICAL EVALUATION OF MATERIAL UNACCOUNTED FOR

A. INTRODUCTION

Receipts - Removals = Inventory Paragraph 70.51(e) of 10 CFR Part 70 requires If there was material on hand at the beginning of the certain AEC licensees authorized to possess special time interval for which a balance is being taken, a nuclear material to calculate material unaccounted for beginning inventory component would have to be added (MUF) quantities and their associated statistical limits of to the equation to give:

error (LEMUF) as part of their material control and accounting procedures for use in assuring that special Beginning Inventory + Receipts - Removals nuclear material in their possession is accounted for. = Ending Inventory (1)

Paragraph 70.53(bXl) requires that a report be made to the Commission if any single MUF exceeds its associated Because of uncertainties] in measurements or un LEMUF and certain specified quantities and that the known removals such as losses or thefts, this equation report include a statement of the probable reasons for seldom balances in practice, indicating some observed the MUF and actions taken or planned. This guide material unaccounted for (MUF). Equation (1) can be identifies methods acceptable to the Regulatory staff for recast as:

evaluating the statistical significance 1 of observed MUF

values. (Beginning Inventory + Receipts)

(Removals + Ending Inventory) = MUF (2)

B. DISCUSSION

If equation (1) balances, the MUF of equation (2) is While there may be mechanisms of process control zero. When equation (1) does not balance, the MUF of involving identification of process anomalies that can equation (2) represents some finite quantity of SNM.

provide an indication of possible missing material, the The significance of this quantity could represent only only positive means for assuring that the material is not the uncertainties of the measurements, or it could missing is to measure all of the material and establish a include an unknown loss or theft. The first step in measured material balance. Records are maintained of determining the significance of the MUF is to determine the measured quantities received into a plant and the what value might be attributable to uncertainties of the measured quantities removed from a plant. The differ measurement system.

ence between these quantities should be on inventory in the plant. A measured physical inventory will either Each of the measured quantities in the material confirm that this quantity is preuent or indicate that balance will have some uncertainty associated with it.

some material is missing. Assuming that there is no Combination of these individual uncertainties by appro inventory at the beginning of the time interval, the priate statistical methodology will result in limits in balance can be expressed by the equation: terms of SNM quantities by which equation (1) could be expected to be out of balance due only to the IAs defined in Regulatory Guide 5.3, "Statistical Terminology measurement system uncertainties,. i.e., the MUF in and Notation for Special Nuclear Materials Control and equation (2) that could be expected. Since measurement Accountability," February 2, 1973. uncertainties may be either positive or negative, a USAEC REGULATORY GUIDES Copie of published guides may be obtained by request indicating the divisions desired to the US. Atomic Energy Commission. Washington. D.C. 20645.

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0. General

confidence interval' is established within which the MUF could be expected due only to measurement The evaluation of either short-term or long-term MUF

should consist of testing whether the MUF quantity uncertainty. This confidence interval is defined by the observed over a single material balance period or a

"limits of error of the material unaccounted for"

cumulative period exceeds the LEMUF for that period.

(LEMUF). It is the magnitude of this LEMUF value that Specifically, the test criterion should be whether MUF +/-

determines, at a 95% confidence level, how well the total LEMUF contains zero, i.e.,

material balance can confirm that all SNM is present or detect whether some is missing. When the MUF quantity is equal to or smaller than the LEMUF, the indication is 0 e (MUF +/- LEMUF) (3)

that MUF could have occurred by chance due to measurement variation. If the MUF is greater than the Thus, an appropriate decision rule is that if observed LEMUF in either a positive or negative direction, the MUF is greater than LEMUF, i.e.:

indication is that the MUF could not have occurred by chance due to measurement variation but that some MUF > LEMUF (4)

other mechanism has had an effect. This could be a loss or theft of material (positive MUF) or an error in the then MUF should be declared significant and investi system causing an unaccounted for gain (negative MUF). gated. This 95% confidence interval test is equivalent to a two-sided hypothesisI

MUF is zero at a 5% level test with a null hypothesis that of significance.

If MUF is due solely to random variations in the measurement system, MUF values taken over time from a series of balances. around the same process or plapt Regulatory Guide 5.18, "Limit of Error Concepts and should tend toward zero. If this is not the case, and Principles of Calculation in Nuclear Materials Control,"

MUF values tend to show a consistent difference from describes acceptable methods for calculation of limits of zero, factors other than random measurement variations error.

are indicated. Consistently positive MUF values would indicate that there may be some biased measurements, An example of how single, isolated observed MUF

consistent measurement or recording mistakes, unknown values should be evaluated is presented by John L.

or unrecorded inventory, or some continual small losses Jaech, Statistical Methods in Nuclear Material Control, or thefts of material. Consistently negative MUF values TID-26298, December 1973, Section 7.1, specifically would indicate that there may be some biased measure answers 7.A and 7.B of Section 7.1.3. However, the ments or consistent measurement or recording mistakes. following specifications should be applied:

MUF values that are not consistent with measurement system variations, i.e., are in excess of such variations 1. The value of M. should be set to zero.

within stated statistical probabilities, are considered 2. The limit of error is ccfa.

statistically significant. The purpose of this guide is to 3. Absolute signs should be placed around x, the provide guidance in assessing the significance of MUF observed MUF, in order to indicate a two-sided test of values but not in the investigation of MUF values that significance.

are found to be statistically significant. 4. A significance level of 5% should be assigned.

5 If the method of Section 7.1.3, question 7.B, is used, a confidence coefficient of 95% should be chosen.

C. REGULATORY POSITION

The concepts, principles, and methods discussed and An example of how combinations and sequences of referenced below are generally acceptable to the Regula MUF values should be evaluated is given in Section 7.2 tory staff for evaluating the significance of MUF values of the above reference, specifically answer 7.E of resulting from measured material balances as specified in Section 7.2.2 with the following conditions specified:

paragraph 70.51(e) of 10 CFR Part 7

0. Individual MUF

values (short-term MUF) that are statistically significant 1. Any related Mo shouldbe zero.

(i.e., those that exceed the LEMUF values specified in 2. Any test of significance should be two-sided.

paragraph 70.51(eX5) and that exceed the minimum 3. Control charts in answer 7.F would be more quantities specified in paragraph 70.51(eX5)) are appropriate as the correlation between successive MUF

required to be investigated and reported to the AEC. In values increases.

addition, combinations or sequences of MUF values 4. A 5% level of significance should be chosen.

(long-term MUF) which show trends significantly differ 5. The term denoted as a systematic-error variance ent from zero should be investigated to determine and in equation (7.9) and throughout TID-26298 is clearly correct the causes. defined on an applications basis in that reference. It should be noted in current practice that it may be lAs defined in Regulatory Guide 5.3, "Statistical Terminology determined by a mean square error or the variance of the and Notation for Special Nuclear Materials Control and estimated bias. Caution must be used in selecting which Accountability," February 2, 1973. is appropriate for the process in question.

5.33-2