Three specific models are investigated: (1) diversion and k distinct falsifications (k + 1 degrees of freedom); (2) diversion and the accumulation of all the falsifications (2 degrees of freedom); (3) diversion only (1 degree of freedom). A test statistic has been derived for models (1) and (2) by the likelihood ratio procedure under the hypothesis of zero falsification and zero diversion versus a one-sided alternative of positive diversion, positive falsification, or both. An analogous test has been developed for model (3) for diversion only. A detailed discussion of this development is given by Shipley. J.P. Shipley, Notes for the Seminar on Data Generation and Evaluation for Safeguards, Los Alamos National Laboratory Seminar, Los Alamos, New Mexico, July 7-9, 1980 (to be published). Utilizing his notation, the test variables called Inspector's Sufficient Statistics - ISS/sub 0/, ISS/sub 1/, and ISS/sub 2/ - are used for testing the above three models (1), (2), and (3) respectively. Note that ISS/sub 2/ corresponds to the well-known MUF-D statistic, which is currently in vogue. These two tests, for purposes of this discussion, are equivalent. The objectives of this paper are to review the ISS procedures, develop optimal critical regions for ISS tests, and compare detection probability (power) curves for models (1), (2), and (3). Optimal critical regions depend upon values obtained from one-sided chi-squared tests with more than one degree of freedom. Details of such a procedure are not to be found in the literature, and this strange neglect was one of the motivating factors in this study.
