On conditional spacings and their properties under coherent system setting

Abstract

This paper introduces the concepts of conditional spacings and normalized conditional spacings when an $(n-k+1)$-out-of-n system or a general coherent system having independent and identically distributed (IID) components just fails at time t. First, we obtain the marginal reliability and joint reliability of conditional spacings, and then conduct some comparisons of conditional spacings. We also investigate the dependent and ISO${}^{\ast }$ properties of the conditional spacings. Finally, the case when the lifetimes of components are IID exponential is discussed in detail.

Keywords:

• Conditional spacings
• coherent systems
• comparisons
• IID
• MTP${}_2$ dependence

2020 Mathematics Subject Classifications:

• Primary 60E15
• secondary 62G30

Acknowledgments

The authors also express their sincere thanks to the two anonymous referees for their useful comments and suggestions on the previous version of this manuscript which led to this improved version.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was partially funded by National Natural Science Foundation of China under grant No. 72161009, and partially by Natural Science Foundation of Hainan Province of China under grant No. 122MS057 and No. 121QN227.