On Order Restricted Inference in Multi‐Step Stage Life Testing for a General Family of Distributions

ABSTRACT Recently, ‐step stage life testing (SLT) has been proposed by Laumen and Cramer (2021) as a natural extension of progressive censoring with fixed censoring times (PC‐FCT) as well as of simple step‐stress accelerated life testing (SSALT). In this context, a failure‐rate based multi‐step SLT model is explored where the stress‐specific time‐to‐failure‐ distributions of the experimental units conform to the flexible proportional hazard (PH) family of distributions. In a multiple SSALT experiment, with an elevation in the stress level, the load on the experimental units increases and hence the tendency of the units to fail increases. Naturally, it gives rise to an ordering among the mean times‐to‐failure of the stress‐specific failure time random variables. We propose to use the method of generalized isotonic regression in order to carry out the associated order restricted inference. The order restricted maximum likelihood estimates (MLEs) of the unknown model parameters are obtained employing the principle of order restricted maximization of the likelihood function. In addition, the interval estimates of the model parameters are computed based on the observed Fisher information matrix. An extensive simulation study is performed to see the effectiveness of the proposed method. Finally, two datasets are analyzed in detail to illustrate the proposed estimation methodology.