Optimal designs of constant-stress accelerated life-tests for one-shot devices with model misspecification analysis

The design of constant-stress accelerated life-test (CSALT) is important in reliability estimation. In reliability studies, practitioners usually rely on underlying distribution to design CSALTs. However, model misspecification analysis of optimal designs has not been examined extensively. This paper considers one-shot device testing data by assuming gamma, Weibull, lognormal and Birnbaum-Saunders (BS) lifetime distributions, which are popular lifetime distributions in reliability studies. We then investigate the effect of model misspecification between these lifetime distributions in the design of optimal CSALTs, in which the asymptotic variance of the estimate of reliability of the device at a specific mission time is minimized subject to a prefixed budget and a termination time of the life-test. The inspection frequency, number of inspections at each stress level, and allocation of the test devices are determined in optimal design for one-shot device testing. Finally, a numerical example involving a grease-based magnetorheological fluids (G-MRF) data set is used to illustrate the developed methods. Results suggest the assumption of lifetime distribution as Weibull or lognormal to be more robust to model misspecification, while the assumption of gamma lifetime distribution seems to be the most non-robust (or most sensitive) one.