Exact Confidence Limits for the Acceleration Factor Under Constant-Stress Partially Accelerated Life Tests With Type-I Censoring

In modern lifetime assessment and reliability analysis, accelerated life test has frequently been used to yield information quickly so that the life distribution of products can be estimated. This paper considers the estimate of the acceleration factor for the exponentially distributed lifetimes under the constant-stress partially accelerated life test with Type-I censored data. In many applications with small sample sizes, the approximate confidence limits for the parameters based on large-sample asymptotic distributions or the bootstrap method are usually not accurate enough. This study defines two ordering relations on the sample space by the generalized maximum likelihood estimator of the acceleration factor, and proposes one new approach of constructing the exact lower and upper confidence limits for the acceleration factor. An efficient procedure of computing the exact lower and upper confidence limits for the acceleration factor is presented via the EM algorithm. The approximate confidence limits for the acceleration factor using the asymptotic and bootstrap methods are also derived in this study. The proposed exact approach is compared with the two approximate methods by carrying out extensive simulation studies, and it is shown that the exact method performs well and is robust in small sample settings. Finally, we present a real example of the accelerated life test to illustrate all methods studied in this paper.