Non-parametric inference based on reliability life-test of non-identical coherent systems with application to warranty time

In this paper, we develop non-parametric statistical inferential methods for component lifetime as well as system lifetime distributions based on a life-test of non-identical coherent systems with known signatures. This is done through maximum likelihood estimation method based on EM-algorithm and the cumulative hazard approach of Nelson–Aalen estimation method. We then extend the method to a multiple-stress problem by assuming the components in each sample to follow proportional hazards model. This model can also be used to test the effect of the structure of system on the lifetimes. Next, we apply the derived results in an application concerning warranty time. A Monte Carlo simulation study is then carried out to evaluate the performance of the developed inferential methods. Finally, some examples are presented for illustrative purpose.