Estimating the Modified Weibull Parameters in Presence of Constant-Stress Partially Accelerated Life Testing

Abstract

Accelerated life testing is very important in life testing experiments because it saves time and cost. In this paper, assuming that the lifetime of items under use condition follows the modified Weilbull distribution, partially accelerated life tests based on progressive Type-II censored samples are considered. The likelihood equations are to be solved numerically to obtain the maximum likelihood estimates. Based on normal approximation to the asymptotic distribution of maximum likelihood estimates, the approximate confidence intervals for the parameters are derived. Two bootstrap confidence intervals called bootstrap-p and bootstrap-t are also discussed. It is difficult to get explicit form for Bayes estimates, so we use Markov chain Monte Carlo method to solve this problem, which gives us flexibility to construct the credible intervals for parameters. Finally, a simulation study is performed to compare between MLEs and Bayes estimates.

Keywords

• Modified Weilbull distribution
• Constant-partially accelerated life testing
• Progressive Type-II censoring
• Asymptotic confidence intervals
• Bootstrap
• Bayesian estimation