Inference for Partially Accelerated Life Test from a Bathtub-Shaped Lifetime Distribution with Progressive Censoring

Abstract

The analysis of the constant-stress partially accelerated life test was considered under progressive Type-II censoring when the lifetime of the products follows a two-parameter bathtub-shaped distribution. The maximum likelihood estimates of the unknown parameters were established, where the expectation–maximization iterative solution is proposed for the estimation. The approximate confidence intervals were also constructed based on asymptotic theory via the Fisher information matrix. For comparison purposes, the bootstrap (i.e., Studentized-t and percentile) confidence intervals of the unknown parameters were also obtained. Finally, simulation studies and a real-life data example are presented to examine the performance of the different results.

Keywords

• maximum likelihood estimator
• bathtub-shaped distribution
• bootstrap confidence intervals
• credible intervals
• Bayes estimates