טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKaplunov Vladimir
SubjectDevelopment of Planning Methodology for Comparison
Sequential Testing for Reliability at Unequal
Probabilities of I-and II-Type Errors
DepartmentDepartment of Quality Assurance and Reliability
Supervisor Dr. Yefim Haim Michlin
Full Thesis textFull thesis text - English Version


Abstract

The present work is devoted to planning of statistical comparison tests on the reliability of two systems: a newly-developed one and a reference one. The purpose of the tests is to show that the reliability parameters of the “new” system are not inferior to their counterparts of the “basic” one, irrespective of their actual value. It is shown in literature that complex systems consisting of large numbers of components are characterized by exponential distribution of the time between failures (TBF). In such a case, the ratio of the mean TBF is a sufficient evaluation criterion in comparing two systems. The comparison procedure for type I and type II censored tests is well developed in literature. An alternative comparison technique is sequential probability ratio testing. The SPRT is the optimal statistical test that yields a decision, on the average, in the shortest time compared to the most economical single sampling plan with the same levels of assurance. One shortcoming of the SPRT is that its duration is a random quantity, which may reach impractically high values. This is commonly remedied by test truncation. It was shown that “off-the-cuff” truncation impact the tests parameters. In the present work a search technique was developed for the optimal stopping boundaries of a heavily truncated test. It permits a rapid review of numerous versions of these boundaries and selection of the optimum on the basis of the directly calculated test parameters.  A case of unequal probabilities of I- and II-type errors (α and β) was treated in the work, which demonstrates the relationship between the truncation depth and the α and β levels. It was determined how the α/β ratio affects the decision boundaries. A user’s algorithm for planning of a reliability comparison test with preset characteristics was developed, as well as computer program for finding the optimal boundaries of a truncated SPRT was.