Sequential Testing for Comparison of the Mean Time Between Failures for Two Systems

Abstract

This study deals with simultaneous testing of two systems, one "basic" (subscript b), and the other "new" (n), both with an exponential distribution describing the times between failures. We test whether the mean TBF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> /MTBF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> ratio equals a given value, versus whether it is smaller than the given value. These tests yield a binomial pattern. A recursive algorithm calculates the probability of a given combination of failure numbers in the systems, permitting rapid, accurate determination of the test characteristics. The influence of truncation of Wald's Sequential Probability Ratio Test (SPRT) on its characteristics is analysed, and relationships are derived for calculating the coordinates of truncation apex (TA). A test planning methodology is presented for the most common cases