טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGrunin Irit
SubjectExtension of the SPRT Set Tests in MIL-HDBK-781A
DepartmentDepartment of Quality Assurance and Reliability
Supervisor Dr. Yefim Haim Michlin


Abstract

MIL-HDBK-781A provides an assortment of test plans, methods and environmental profiles for equipment produced for military systems in order to ensure the required reliability levels and early detection of defects. The Sequential Probability Ratio Test (SPRT) described in MIL‑HDBK-781A and in IEC 61124, intended for checking the null hypothesis on the mean time between failures (MTBF) value under exponential distribution of the time between failures.

The drawback of the existing method described in the sources is the limitation on the number of tests and the specified values of the probability of errors of the first and second kind, which preclude its extension to cases where different probabilities of errors are necessary. An additional drawback is lack of an analytical connection between the parameter of limits of decision and the true error values obtained in the Sequential Test.

A check of the parameters presented in the sources revealed discrepancies between the formulae and the reported results: first of all, regarding the set limit points, and secondly, between the true values of the probability errors of the first and second kind presented in MIL‑HDBK-781A and in IEC 61124 and those obtained with the aid of simulations based on the limit points presented in them. An additional inconsistency was found between the expected test time (ETT) values calculated from the tabulated limit decision points and the ETT values in the sources' graphs.

The SPRT set of MIL-HDBK-781A was extended with the aid of the developed software for test simulation. The input for the statistical parameters' calculating was the probabilities of errors of the first and second kind and the discrimination ratio. The obtained results improve the accuracy of the accept/reject decisions, and enlarge the application range of the tests.

Special interest attaches to the distribution function of the final decision time and its components: rejection time and acceptance time of the null hypothesis. With the aid of the distribution and relative frequency functions the duration of the sequential test could be predicted. A review of major sources on the theory of sequential test analysis confirmed the originality of our graphs of the test time probability distributions, in whose construction both the discreteness and continuousness of the random variables were taken into consideration. The developed method for predicting the test duration makes for more efficient design and user convenience.