Order restricted inference for a multiple step-stress model with long-term survivors for a general family of distributions

In this article, we propose a failure rate based step-stress accelerated life testing (SSALT) model assuming that the time-to-event distribution belongs to a fairly general family of distributions and the underlying population consists of long term survivors. With increase in stress levels, it is expected that the mean time to the event of interest gets shortened leading to an order restriction among the mean times-to-event. We propose here a method of obtaining order restricted maximum likelihood estimators (MLEs) based on expectation maximization (EM) algorithm coupled with the method of generalized isotonic regression technique. Additionally, we address the testing of hypothesis problem for the presence of long term survivors in the underlying population based on both asymptotic and non-asymptotic approaches. To illustrate the effectiveness of the proposed method, extensive simulation experiments are carried out and a real data set is analyzed.