Reliability estimation in a multicomponent stress-strength model for unit Burr III distribution under progressive censoring

We study the problem of estimating multicomponent stress-strength reliability under progressive Type II censoring when stress and strength variables follow unit Burr III distributions with a common shape parameter. Point and interval estimates of this parametric function are derived using both classical and Bayesian approaches. Different approximation methods are used to obtain Bayes estimates. In particular, uniformly minimum variance unbiased estimate of the reliability is discussed when the common shape parameter is known. Monte Carlo simulations are performed to compare proposed methods. Finally, we provide two numerical examples for illustration purposes.