On estimation of modified Weibull parameters in presence of accelerated life test

ABSTRACT

This article deals with the problem of estimating parameters of the modified Weibull distribution (MWD) using a progressively type-II censored sample under the constant-stress partially accelerated life test model. The maximum likelihood, Bayes, and parametric bootstrap methods are obtained as point estimations for the distribution parameters and the acceleration factor. Furthermore, the approximate confidence intervals (ACIs), bootstrap confidence intervals, and credible intervals of the estimators have been obtained. The results of Bayes estimators are computed under the squared error loss (SEL) function using the Markov-chain Monte Carlo (MCMC) method. Gibbs sampling within the Metropolis–Hasting algorithm is applied to generate MCMC samples from the posterior density functions. Analysis of a simulated data set has been presented for illustrative purposes. Finally, a Monte Carlo simulation study is carried out to investigate the precision of the Bayes estimates with maximum likelihood estimates and two bootstrap estimates, also to compare the performance of different corresponding confidence intervals considered.

KEYWORDS:

• Modified Weibull distribution
• constant-stress partially accelerated life tests
• bootstrap confidence intervals
• MCMC approach

AMS SUBJECT CLASSIFICATION:

• 62NO5
• 62F10

Acknowledgments

The authors thank the editor, associate editor, and referees for valuable suggestions that led to the improvement of this article.