Using two Reliability Estimators in a Stress-Strength System

In this paper, we propose an estimate of reliability in a multicomponent stress-strength system. The reliability of such a system is obtained when strength and stress variables are given by Gompertz distribution with common scale parameter λ and different shape parameters α and . The system reliability is estimated using maximum likelihood estimation (MLE) and the best observational percentile estimation (BPE) methods in samples drawn from strength and stress distributions. Also, the asymptotic confidence interval for system reliability is obtained. The reliability estimators obtained from both methods are compared using mean squares error criteria and confidence interval length via Monte Carlo simulation. In the end, using two real data sets we illustrate the procedure. Before analyzing the data, we first show that the Gompertz distribution is fitted to this data sets using the Kolmogorov-Smirnov goodness-of-fit test statistic. In general, the simulation results show that due to the increase in sample size, the average mean, mean squares error and length of confidence interval in the maximum likelihood method is decreasing compared to the best percentile estimator method. This indicates that the maximum likelihood method is more efficient. Also, in this paper, it was shown that the one out of three component system reliability is more than the one out of two component system reliability for both methods of estimation.