Statistical Inference for Generalized Half-Normal Model Under Step-Stress Accelerated Life Test in the Presence of Hybrid Censoring

In this paper, we consider the problem of estimating the unknown parameters of a generalized half-normal (GHN) distribution when lifetime data are observed from accelerated life test (ALT) experiments in the presence of hybrid censoring. To relate the lifetime of products under different stress levels, we make use of a cumulative exposure model (CEM), and obtain maximum likelihood estimates using a numerical approach and stochastic expectation-maximization (SEM) algorithm. We further obtain the expected Fisher information matrix, and use it to compute associated confidence interval estimates for the unknown parameters of the distribution. The expected Fisher information matrix is also used to select the optimal time to conduct an experiment based on three considered optimality criteria. Next, we consider independent and conditional gamma priors and obtain the associated posterior distributions for the unknown parameters. We then make use of samples generated from the posterior distributions using importance sampling and the MH algorithm to compute the Bayesian estimates under the squared error loss function. Furthermore, the highest associated posterior density interval estimates are also computed. Finally, we conduct a simulation study to evaluate the efficiency of the suggested approaches in various situations and analyze a real data set for illustration purposes.