Optimal plan for ordered step-stress stage life testing

Abstract

ABSTRACT In a progressively censored life testing experiment, the censored units can be used for some other life testing experiments. In a step-stress stage life testing experiment, we run parallel experiments while placing the progressively censored units at the higher stress level along with the main experiment. In this work, multiple step-stress stage life testing experiments are performed under the assumption that the experimental units at different stress levels follow Weibull distributions with the same shape parameter, but different scale parameters. The main objectives of this paper are to provide an order-restricted classical inference of the model parameters and also to find out the optimal life testing scheme. We provide the order-restricted maximum likelihood estimators of the unknown parameters and the associated confidence intervals based on the observed Fisher information matrix. An extensive simulation study and a data analysis are provided for illustrative purposes. In search of the optimal life testing plan under this set ups, a meta-heuristic approach based on a variable neighbourhood search algorithm is employed using D-optimality criterion. Finally, we have indicated how the method can be extended when the shape parameter of the Weibull distributions are also different at different stress levels.