Optimum Simple Step-Stress Plans for Accelerated Life Testing

TLDR

The life‑test model assumes an exponential life distribution with a mean that is a log‑linear function of stress and a cumulative exposure model for changing stress. This paper presents optimum plans for simple two‑stress step‑stress tests in which all units are run to failure. The authors design two‑step stress tests—time‑step and failure‑step—that minimize the asymptotic variance of the MLE of mean life at a design stress, with the time‑step test running a specified time at the first stress and the failure‑step test running until a specified proportion of units fail. The optimum time‑step and failure‑step tests achieve the same asymptotic variance as the corresponding optimum constant‑stress test, showing that step‑stress tests provide equivalent information to constant‑stress tests.

Abstract

This paper presents optimum plans for simple (two stresses) step-stress tests where all units are run to failure. Such plans minimize the asymptotic variance of the maximum likelihood estimator (MLE) of the mean life at a design stress. The life-test model consists of: 1) an exponential life distribution with 2) a mean that is a log-linear function of stress, and 3) a cumulative exposure model for the effect of changing stress. Two types of simple step-stress tests are considered: 1) a time-step test and 2) a failure-step test. A time-step test runs a specified time at the first stress, whereas, a failure-step test runs until a specified proportion of units fail at the first stress. New results include: 1) the optimum time at the first stress for time-step test and 2) the optimum proportion failing at the low stress for a failure-step test, and 3) the asymptotic variance of these optimum tests. Both the optimum time-step and failure-step tests have the same asymptotic variance as the corresponding optimum constant-stress test. Thus step-stress tests yield the same amount of information as constant-stress tests.