Analysis of Masked Data in a Series System Subjected to Sources of Shocks Under Type Ⅰ Progressive Hybrid Censoring

摘要

In this paper, we consider the statistical analysis of masked data based on the fatal shock model under type Ⅰ progressive hybrid censoring. It is assumed that the time of shock follows Weibull distribution. Maximum-likelihood estimators for the unknown parameters are obtained by solving a one-dimensional optimization problem. Approximate maximum-likelihood estimators have been proposed based on a Taylor series expansion, and they have explicit expressions. In addition, the Bayesian approach, combined with Gibbs sampling, are developed based on the assumption that the shape parameter has a log-concave function, and for the given shape parameter, the scale parameters have Gamma-Dirichlet priors. Finally, Monte Carlo simulations are performed to compare the performances of the proposed methods under different progressive censoring schemes and masking levels.