M.Sc Thesis
M.Sc Student Dayan Yoram Planning of Sequential Test for Checking the Desirable Ratio (different from unity) of Two Constant Failure Rates Department of Quality Assurance and Reliability Dr. Yefim Haim Michlin

Abstract

This study deals with simultaneous testing of two systems, with a view to checking the suitability of one of them as a substitute for the other. The systems are run in a Comparison Sequential Probability Ratio Test (SPRT), the definitive parameter being their constant failure rates ratio (Φ). The study focuses on a desirable ratio value different from unity (Φ0≠1). The need for Φ0≠1 arises when one of the systems should be more reliable than the other one, or when groups of systems of unequal size are to be compared (These latter tests are called Parallel Tests, in which several items in each group are checked at a time, whereby the failure rates can be increased and the test terminated faster).

Of the compared systems, one is “basic” (subscript b), and the other “new” (subscript n) with failure rates λb, λn, respectively. After a failure in one of the systems it is restored immediately, and the null hypothesis checked whether the ratio is not smaller than a prescribed value (Φ0), versus the alternative that it is.

Where the aforementioned hypothesis has to be checked, it is convenient to resort to sequential testing, by which means both the necessary numbers of failures and the test durations can be significantly reduced on the average. On the other hand, sequential tests have a major disadvantage - it is not known in advance when they should be stopped. The number of failures for sufficient information for a decision is random and depends on the data provided by each failure. In order to overcome this inconvenience, this work resorted to truncation of the test after a specific number of failures. The truncation mode - and the corresponding so-called Truncation Apex (TA) - are chosen judiciously on an iterative basis, with the focus on optimality.

The design method developed in this work comprises a fast algorithm and formulas for searching for the test boundaries over a wide range of the test parameters (Φ0, α, β, d) and optimal truncation parameters.