Publication Date: 6/1/74     Pages: 2     Date Entered: 2/22/84     Title: STATISTICAL EVALUATION OF MATERIAL UNACCOUNTED FOR     June 1974     U.S. ATOMIC ENERGY COMMISSION     REGULATORY GUIDE     DIRECTORATE OF REGULATORY STANDARDS     REGULATORY GUIDE 5.33     STATISTICAL EVALUATION OF MATERIAL UNACCOUNTED FOR A. INTRODUCTION     Paragraph 70.51(e) of 10 CFR Part 70 requires certain AEC     licensees authorized to possess special nuclear material to calculate     material unaccounted for (MUF) quantities and their associated     statistical limits of error (LEMUF) as part of their material control     and accounting procedures for use in assuring that special nuclear     material in their possession is accounted for. Paragraph 70.53(b)(1)     requires that a report be made to the Commission if any single MUF     exceeds its associated LEMUF and certain specified quantities and that     the report include a statement of the probable reasons for the MUF and     actions taken or planned. This guide identifies methods acceptable to     the Regulatory staff for evaluating the statistical significance(1) of     observed MUF values. B. DISCUSSION     While there may be mechanisms of process control involving     identification of process anomalies that can provide an indication of     possible missing material, the only positive means for assuring that the     material is not missing is to measure all of the material and establish     a measured material balance. Records are maintained of the measured     quantities received into a plant and the measured quantities removed     from a plant. The difference between these quantities should be on     inventory in the plant. A measured physical inventory will either     confirm that this quantity is present or indicate that some material is     missing. Assuming that there is no inventory at the beginning of the     time interval, the balance can be expressed by the equation:     ----------     (1) As defined in Regulatory Guide 5.3, "Statistical Terminology     and Notation for Special Nuclear Materials Control and Accountability,"     February 2, 1973.     ----------     Receipts - Removals = Inventory     If there was material on hand at the beginning of the time     interval for which a balance is being taken, a beginning inventory     component would have to be added to the equation to give:     Beginning Inventory + Receipts - Removals = Ending Inventory (1) Because of uncertainties(1) in measurements or unknown removals     such as losses or thefts, this equation seldom balances in practice,     indicating some observed material unaccounted for (MUF). Equation (1)     can be recast as:     (Beginning Inventory + Receipts) - (Removals + Ending Inventory) = MUF     (2) If equation (1) balances, the MUF of equation (2) is zero. When     equation (1) does not balance, the MUF of equation (2) represents some     finite quantity of SNM. The significance of this quantity could     represent only the uncertainties of the measurements, or it could     include an unknown loss or theft. The first step in determining the     significance of the MUF is to determine what value might be attributable     to uncertainties of the measurement system.     Each of the measured quantities in the material balance will have     some uncertainty associated with it. Combination of these individual     uncertainties by appropriate statistical methodology will result in     limits in terms of SNM quantities by which equation (1) could be     expected to be out of balance due only to the measurement system     uncertainties, i.e., the MUF in equation (2) that could be expected.     Since measurement uncertainties may be either positive or negative, a     confidence interval(1) is established within which the MUF could be     expected due only to measurement uncertainty. This confidence interval     is defined by the "limits of error of the material unaccounted for"     (LEMUF). It is the magnitude of this LEMUF value that determines, at a     95% confidence level, how well the total 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 that     MUF could have occurred by chance due to measurement variation. If the     MUF is greater than the LEMUF in either a positive or negative     direction, the indication is that the MUF could not have occurred by     chance due to measurement variation but that some other mechanism has     had an effect. This could be a loss or theft of material (positive MUF)     or an error in the system causing an unaccounted for gain (negative     MUF).     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 plant should tend toward zero. If this is not the case,     and MUF values tend to show a consistent difference from zero, factors     other than random measurement variations are indicated. Consistently     positive MUF values would indicate that there may be some biased     measurements, consistent measurement or recording mistakes, unknown or     unrecorded inventory, or some continual small losses or thefts of     material. Consistently negative MUF values would indicate that there     may be some biased measurements or consistent measurement or recording     mistakes.     MUF values that are not consistent with measurement system     variations, i.e., are in excess of such variations within stated     statistical probabilities, are considered statistically significant.     The purpose of this guide is to provide guidance in assessing the     significance of MUF values but not in the investigation of MUF values     that are found to be statistically significant. C. REGULATORY POSITION     The concepts, principles, and methods discussed and referenced     below are generally acceptable to the Regulatory staff for evaluating     the significance of MUF values resulting from measured material balances     as specified in paragraph 70.51(e) of 10 CFR Part 70. Individual MUF     values (short-term MUF) that are statistically significant (i.e., those     that exceed the LEMUF values specified in paragraph 70.51(e)(5) and that     exceed the minimum quantities specified in paragraph 70.51(e)(5)) are     required to be investigated and reported to the AEC. In addition,     combinations or sequences of MUF values (long-term MUF) which show     trends significantly different from zero should be investigated to     determine and correct the causes.     ----------     (1) As defined in Regulatory Guide 5.3, "Statistical Terminology     and Notation for Special Nuclear Materials Control and Accountability,"     February 2, 1973.     ----------     The evaluation of either short-term or long-term MUF should     consist of testing whether the MUF quantity observed over a single     material balance period or a cumulative period exceeds the LEMUF for     that period. Specifically, the test criterion should be whether MUF @@     LEMUF contains zero, i.e.,     O epsilon(MUF Plus or Minus LEMUF) (3) Thus, an appropriate decision rule is that if observed MUF is     greater than LEMUF, i.e.:     MUF > LEMUF (4)then MUF should be declared significant and investigated. This 95%     confidence interval test is equivalent to a two-sided hypothesis(1) test     with a null hypothesis that MUF is zero at a 5% level of significance.     Regulatory Guide 5.18, "Limit of Error Concepts and Principles of     Calculation in Nuclear Materials Control," describes acceptable methods     for calculation of limits of error.     An example of how single, isolated observed MUF values should be     evaluated is presented by John L. Jaech, Statistical Methods in Nuclear     Material Control, TID-26298, December 1973, Section 7.1, specifically     answers 7.A and 7.B of Section 7.1.3. However, the following     specifications should be applied: 1. The value of M(o) should be set to zero. 2. The limit of error is c(alpha)sigma. 3. Absolute signs should be placed around x, the observed MUF,     in order to indicate a two-sided test of significance. 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.     An example of how combinations and sequences of MUF values should     be evaluated is given in Section 7.2 of the above reference,     specifically answer 7.E of Section 7.2.2 with the following conditions     specified: 1. Any related M(o) should be zero. 2. Any test of significance should be two-sided. 3. Control charts in answer 7.F would be more appropriate as     the correlation between successive MUF values increases. 4. A 5% level of significance should be chosen. 5. The term denoted as a systematic-error variance in equation     (7.9) and throughout TID-26298 is clearly defined on an applications     basis in that reference. It should be noted in current practice that it     may be determined by a mean square error or the variance of the     estimated bias. Caution must be used in selecting which is appropriate     for the process in question.     29