Some aspects of the mean past lifetime of a parallel system under double regularly checking

Abstract

In this paper, a parallel system consisting of a finite number of identical components with independent lifetimes having a common distribution function is considered, when the failure time of the system is restricted to a finite interval (double regularly checking). Under these conditions, the mean past lifetime (MPL) of the system is presented and some of its properties are derived. It is shown that the underlying distribution function can be recovered from the proposed MPL. Then, a consistent estimator for MPL is presented and some of its properties are studied. This estimator also could be used for the single monitoring case or ordinary MPL. Finally, some properties of the MPL of a parallel system with nonidentical components are discussed.

Keywords:

• order statistics
• parallel systems
• reliability function
• truncated expectation

AMS subject classifications :

• 62N05

Acknowledgements

We are indebted to Professor G. Jongbloed for many valuable and helpful comments and suggested improvements.