On estimating of the stress-strength model with more than two states under Gompertz distribution

Abstract

The Gompertz distribution, one of statistical distributions, is considered in survival analysis because it has an increasing hazard rate function. It has many applications in various fields such as medical and reliability. The problem of estimation of stress-strength model with more than two states is considered by other authors under exponential and Weibull distribution. The main aim of this paper is to consider the same problem under Gompertz distribution based on progressive type-II censoring data. Three estimation methods are considered to estimate the reliability parameter, maximum likelihood (MLE), uniformly minimum variance unbiased estimator (UMVE) and Bayes estimator. To compare and study the performance of three estimators, Monte Carlo simulation study is performed.