Reliability inference for multicomponent stress-strength model under generalized progressive hybrid censoring

This paper considers a reliability estimation of multicomponent stress-strength model under the assumption that both stress variable and strength variable follow the Weibull distribution (WD) with arbitrary shape parameter and scale parameter based on generalized progressive hybrid censoring (GPHC). First, the closed expression of reliability is derived. Then the point and interval estimates of the unknown parameters and system reliability are obtained by using the maximum likelihood estimates (MLE) and Bayes method. Meanwhile, the existence and uniqueness of MLE are proved. We propose to apply the modified approximate Bayesian computation with sequential Monte Carlo (MABC-SMC), Newton-Raphson and Metropolis- Hasting (MH) algorithms to carry out parameters estimates, respectively. The advantage of MABC-SMC algorithm is that it does not need to judge the convergence of the algorithm, which is very suitable for practitioners in engineering practice. The asymptotic normality of the MLE, Bayes and two non -parameter bootstrap methods are used to construct the corresponding interval estimates. Finally, simulation study and one real -life example have been presented for illustrative purposes.