Reliability estimation of multicomponent stress-strength model based on copula function under progressively hybrid censoring

In reliability analysis of the stress-strength models, the stress and strength variables are typically assumed as independent. However, such an assumption may be unrealistic in some applications. It is a meaningful issue to estimate the reliability of the stress-strength model for dependent stress and strength variables. In this paper, we estimate the reliability of multicomponent stress-strength model by assuming the dependent Weibull stress variables and exponential strength variables based on Gumbel copula under Type-I progressively hybrid censoring scheme. The estimators of the unknown parameters and reliability are obtained by using the maximum likelihood estimation method. Also, the asymptotic confidence intervals and Bootstrap percentile confidence intervals of the unknown parameters and reliability of stress-strength model are derived. Monte Carlo simulations are used to evaluate the performance of the maximum likelihood estimators, asymptotic confidence intervals and Bootstrap percentile confidence intervals. Finally, real data are analyzed to demonstrate the practicability of the stress-strength model in this article.