E-Bayesian and hierarchical Bayesian estimations for parallel system model in the presence of masked data

In this paper, we consider the statistical analysis of parallel system with inverse Weibull distributed components. Due to cost and time constraints, the causes of system failures are masked and the type-II censored observations might occur in the collected data. Under the symmetric and asymmetric loss functions, the expected Bayesian (E-Bayesian) method and the hierarchical Bayesian method are proposed to estimate the parameters, as well as the reliability function. Numerical simulations using the Monte Carlo (MC) method are given to demonstrate the performances of the estimations under different masking levels and effective sample sizes. Finally, one data set is analyzed for illustrative purpose.