Estimating the Pareto parameters under progressive censoring data for constant-partially accelerated life tests

Abstract

Accelerated life testing is widely used in product life testing experiments since it provides significant reduction in time and cost of testing. In this paper, assuming that the lifetime of items under use condition follow the two-parameter Pareto distribution of the second kind, partially accelerated life tests based on progressively Type-II censored samples are considered. The likelihood equations of the model parameters and the acceleration factor are reduced to a single nonlinear equation to be solved numerically to obtain the maximum-likelihood estimates (MLEs). Based on normal approximation to the asymptotic distribution of MLEs, the approximate confidence intervals (ACIs) for the parameters are derived. Two bootstrap CIs are also proposed. The classical Bayes estimates cannot be obtained in explicit form, so we propose to apply Markov chain Monte Carlo method to tackle this problem, which allows us to construct the credible interval of the involved parameters. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, a Monte Carlo simulation study is carried out to investigate the precision of the Bayes estimates with MLEs and to compare the performance of different corresponding CIs considered.

Keywords:

• Pareto distribution
• constant-partially accelerated life tests
• progressive Type-II censoring
• maximum-likelihood estimation
• asymptotic confidence intervals
• bootstrap
• Bayesian estimation
• confidence intervals

Acknowledgements

The authors would like to express their thanks to the referees for their useful comments in revising the paper.

Funding

This research was supported by the Institute of Scientific Research and Revival of Islamic Heritage, Umm Al-Qura University, under the project (No. 43205014).