Sequential Test for Reliability Under Allowance for Target Uncertainty

Abstract

This paper deals with development of a sequential test for comparison of the mean times between failures (MTBF) of two items: a new one (subscript n) and another serving as a reference (subscript ref). In the test, the hypothesis is checked that MTBFn is not less than a given multiple of MTBFref. Prior of the test, information is available on a known quantity r of the time between failures (TBF) for the reference item, which is not involved in the test, and only the new item is tested. It is a common occurrence in industrial practice that a new, modernized item has to be checked versus a reference counterpart currently in use. We assume that the TBF of both items is distributed exponentially. The sequential probability ratio test (SPRT) is widely used for checking that an MTBFn is not less than a specified (target) value. The innovation here is that in the proposed sequential test the target is the MTBFref which is available not as an exact value but only as an estimate whose uncertainty depend on r . Accordingly, a search algorithm was developed for the decision boundaries in the proposed test, as well as for calculating the operating characteristic (OC), and the statistical parameters of the test duration and number of failures to stopping the test. Approximative relationships were obtained for the above, depending on the target OC. These straightforward relationships drastically simplify the planning process. Moreover, they will enable the reliability engineer to appreciate the need to take the above uncertainty into account, and the expediency of resorting to the test at an early stage of its planning. Its superior efficacy is demonstrated.