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In this article, we consider estimating the parameters, reliability function  R ( t ) and failure rate function  H ( t ) of the two-parameter bathtub-shaped distribution introduced by Chen ( 2000 ) based on the progressive first-failure censored sample. The maximum likelihood estimators and Bayes estimators under squared error loss function are derived. We obtain the asymptotic confidence intervals for the parameters using the observed Fisher information matrix. The parametric bootstrap confidence intervals of reliability characteristics are also proposed. Lindley approximation procedure is adopted to establish Bayes estimates. Furthermore, we conduct Monte Carlo simulation to compare the behaviors of different methods. A real data set is analyzed to illustrate the proposed methods.

Reliability estimation for the bathtub-shaped distribution based on progressively first-failure censoring sampling