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.
Highlights
There is a difficulity in getting information about the lifetime of products with high quality during testing under normal conditions, so ALTs are used in manufacturing industries to get failure data in short period of time
In step-stress PALT, items are tested at normal level, the stress will be changed at a certain time
The most common censoring schemes are Type-I censoring and Type-II censoring, but in these two types the withdrawing of units is not allowed until the end of the experiment, so a more general censoring scheme called PRO-II-C has been used in this paper to overcome this problem in which the removal of prespecified number of units is done when an individual unit fails, this continues until fixed number of units fail, at which stage the remainder of the surviving units are removed
Summary
There is a difficulity in getting information about the lifetime of products with high quality during testing under normal conditions, so ALTs are used in manufacturing industries to get failure data in short period of time. The third one is called step-stress ALT,where the test condition changes at a certain time or after the termination of specific number of failures. In ALTs, the test items are tested at accelerated conditions, by applying higher levels of stress, to induce failures. Data collected at such accelerated conditions are extrapolated through statistical model to estimate the lifetime distribution at normal condition. We assume that the lifetime of the items tested at use condition follows a MWD with PDF,CDF,SF and HRF given in (1.1)-(1.4). The HRF, SF, CDF and PDF under acceerated condition are given respectively by x α−1
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
