On the Change Point of the Mean Residual Life of Series and Parallel Systems

Abstract

This paper considers the mean residual life in series and parallel systems with independent and identically distributed components and obtains relationships between the change points of the mean residual life of systems and that of their components. Compared with the change point for single components, should it exists, the change point for a series system occurs later. For a parallel system, however, the change point is located before that for the components, if it exists at all. Moreover, for both types of systems, the distance between the change points of the mean residual life for systems and for components increases with the number of components. These results are helpful in the determination of optimal burn-in time and related decision making in reliability analysis.

Reliability analysis of a multi-state system with identical units having two dependent components

“…In literature there are many researches dealing with this function including many properties and applications (e.g. Guess and Proschan, 15 Asadi and Goliforushani, 16 Shen et al 17 ). The MRL function is also used to evaluate the reliability of k-out-of-n systems(e.g Asadi and Bayramoglu, 18 Gurler and Bairamov, 19 Raqab and Rychlik 20 ).…”

Empirical likelihood based detection procedure for change point in mean residual life functions under random censorship

“…However, few works have been carried out on the change point problem of MRL functions. Previous related work about the change point problem in MRL functions has been carried out by Ebrahimi , Xie et al , , and Shen et al , . Ebrahimi's method was developed for testing whether the MRL function has a bath‐tub curve shape and only for uncensored data.…”

“…Therefore, his method is more restricted than ours. Both Xie et al , and Shen et al , focus on the study of the relationship between the change points of the MRL function and its corresponding failure rate function with a certain shape such as a bath‐tub curve and certain distributions such as Weibull distributions. Therefore, the situations and models they considered are different from ours.…”

On the change points of mean residual life and failure rate functions for some generalized gamma type distributions

“…Bebbington et al [23] estimated the turning point for MRL of a bathtub-shaped failure distribution. Shen et al [24] examined the change point of FR and MRL functions for series and parallel systems and compared the location of the change points under increasing the number of components in systems. Recently, Shafaei et al [25] studied the change point of the MRL of some weighted models and showed that the time maximizing the MRL of the greatest order statistic precedes the time maximizing the MRL of baseline model.…”