Order restricted inference of a multiple step-stress model

In this manuscript both the classical and Bayesian analyses of a multiple step-stress model have been considered. The lifetime distributions of the experimental units at each stress level follow two-parameter generalized exponential distribution and they are related through the cumulative exposure model assumptions. Recently Abdel-Hamid and Al-Hussaini (Computational Statistics and Data Analysis, 53:1328–1338, 2009) provided the classical inference of the model parameters of a simple step-stress model, under the same set of assumptions. In a typical step-stress experiment, it is expected that the lifetime of the experimental units will be shorter at the higher stress level. The main aim of this paper is to develop the order restricted inference of the model parameters of a multiple step-stress model based on both the classical and Bayesian approaches. An extensive simulation study has been performed and one data set has been analyzed for illustrative purposes.