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

Abstract

Purpose -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 þ k 2 1) units under the general progressive Type II censoring scheme. Design/methodology/approach -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. Findings -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. Practical implications -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. Originality/value -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.

Hierarchical Bayes Estimation of Reliability Indexes of Cold Standby Series System under General Progressive Type II Censoring Scheme

“…Figure 1 shows a functional diagram of the series system. Barot and Patel (2014) have considered such a series system and placed it on a life testing experiment under general progressive Type II censoring scheme by assuming that every unit has the failure rate kλ with the probability density and cumulative distribution functions, respectively, as…”

“…This censoring scheme is extremely useful in both industrial life testing and clinical settings. The numerous articles dealing with inference procedures under this censoring scheme have been found in the journals (e.g., Balakrishnan & Sandhu, 1996;Fernández, 2004;Kim & Han, 2009;Barot & Patel, 2014).…”

“…Xu, Kang, and Shi (2002) discussed Bayesian and multiple Bayesian analysis of reliability performances for the series system. Barot and Patel (2014) derived the exact confidence limits of the reliability indexes for a cold standby series system under general progressive Type II censoring scheme using an empirical Bayesian approach.…”

The beta compound Rayleigh distribution : Properties and applications

“…Shajaee et al [2] obtained the empirical Bayes estimates for parameter and reliability function associated with the CR distribution under record data. Barot and Patal [3] compared the maximum likelihood and Bayes estimates of the reliability parameters corresponding to the CR distribution under progressive type-ii censored data. Abd-Elmougod and Mahmoud [4] studied the CR distribution with constant partially accelerated life tests under an adaptive type-ii propgressive hybrid censored data.…”

The Kumaraswamy compound Rayleigh distribution : properties and estimation

“…Shajaee et al [2] obtained the empirical Bayes estimates for parameter and reliability function assciated to compound Rayleigh distribution under record data. Barot and Patal [3] compared the maximum likelihood and Bayes estimates of the reliability parameters corresponding to compound Rayleigh distribution under progressive type-ii censored data. Abd-Elmougod and Mahmoud [4] studied the compound Rayleigh distribution with constant partially accelerated life tests under an adaptive type-ii propgressive hybrid censored data.…”