EM‐based likelihood inference for one‐shot device test data under log‐normal lifetimes and the optimal design of a CSALT plan

Abstract One‐shot devices result in an extreme case of interval censoring, wherein one can only know whether the failure time is either before or after the test time. The study of one‐shot device testing has been developed considerably recently, both in terms of estimation and optimal design under different lifetime distributions. However, one‐shot device testing analysis under lognormal lifetime distribution has not been studied yet. While the hazard function for exponential distribution is always a constant, and that of Weibull and gamma are either increasing or decreasing, the lognormal distribution has increasing ‐ decreasing behavior of hazard which is encountered often in practice as units usually experience early failure and then stabilize over time in terms of performance. In this paper, we develop the EM algorithm for the likelihood estimation based on one‐shot device test data under lognormal distribution and also the design of optimal CSALTs (constant stress accelerated life tests) under this set up with budget constraints. A simulation study is carried out to assess the performance of the methods of inference developed here and some real‐life data are analyzed for illustrative purpose.