Partially constant stress accelerates life test model in analyses lifetime competing risks with a bathtub shape lifetime distribution in the presence of Type-I censoring

Abstract

In a highly reliable product when the experimental units expose to fatal risk factors and the unit is failure under the only one cause of failure, which called competing risk model the accelerate life tests (ALTs) is applied. In this article, we applied the partially constant stress ALTs model when the lifetime of units distributed as a competing risks bathtub shape or increasing failure rate function (Chen lifetime distribution) based on Type-I censoring scheme. Obtaining the data are used for constructing statistical inferences of model parameters. Material and Method: The system of differential likelihood equations is solved numerically to estimate the model parameters and the asymptotic distributions of maximum likelihood estimates are applied to construct asymptotic confidence intervals. The Bayesian point and credible interval with the help of the MCMC method of model parameters are adopted and compared with system results of differential likelihood equations. Results: Our results are measured and compare through numerical studies and finally, some comment is presented for illustration. Estimation results are more acceptable and Bayesian point and interval estimation are better than the approximate MLEs estimation. Conclusion: Estimation The results of estimation problem are more acceptable in each method and showing that under informative prior parameters Bayes method is better than the ML method.