Bayesian estimation of reliability indexes for cold standby system under general progressive Type II censored data

This paper aims to deal with the estimation of the empirical Bayesian exact confidence limits of reliability indexes of a cold standby series system with (n+k−1) units under the general progressive Type II censoring scheme.

Assuming that the lifetime of each unit in the system is identical and independent random variable with exponential distribution, the exact confidence limits of the reliability indexes are derived by using an empirical Bayes approach when an exponential prior distribution of the failure rate parameter is considered. The accuracy of these confidence limits is examined in terms of their coverage probabilities by means of Monte-Carlo simulations.

The simulation results show that accuracy of exact confidence limits of reliability indexes of a cold standby series system is efficient. Therefore, this approach is good enough to use for reliability practitioners in order to improve the system reliability.

When items are costly, the general progressive Type II censoring scheme is used to reduce the total test time and the associated cost of an experiment. The proposed method provides the means to estimate the exact confidence limits of reliability indexes of the proposed cold standby series system under this scheme.

The application of the proposed technique will help the reliability engineers/managers/system engineers in various industrial and other setups where a cold standby series system is widely used.