Order-Restricted Inference for Exponentiated Rayleigh Distribution Under Multiple Step-Stress Accelerated Life Test

Both frequentist and Bayesian approaches are presented in this paper for a multiple step-stress accelerated life test. It is assumed that the lifetime distributions of experimental units under each stress level conform to a two-parameter exponentiated Rayleigh distribution. Additionally, the distributions corresponding to each stress level are related via the cumulative exposure model. In a step-stress experiment, with the applied stress level on the rise, the failure process of experimental units is accelerated, which gives rise to a reduction in their expected lifetime. This order restriction is explicitly incorporated into the statistical inference. Under the classical framework, via reparameterization, the order-restricted maximum likelihood estimates (MLEs) of unknown parameters are provided, and asymptotic confidence intervals are constructed based on the observed Fisher information matrix. In the Bayesian framework, we conduct the Bayesian analyses and obtain credible intervals using the importance sampling techniques. Extensive simulation studies are conducted, and a real dataset is analyzed for illustrative purposes.