Stochastic comparisons of lifetimes of fail-safe systems with dependent and heterogeneous components under random shocks

Abstract

A fail-safe system is a $(n-1)$-out-of-n system whose lifetime is represented by the second-order statistic. This work studies stochastic comparisons of lifetimes of fail-safe systems with dependent and heterogeneous components, where the components are subjected to random shocks instantaneously. The results are derived for a general semiparametric family of distributions of the component lifetimes. We derive sufficient conditions for the comparison results under the usual stochastic order, and we provide counterexamples to show that under those conditions, similar comparisons cannot be made under the hazard rate order.

Keywords:

• Fail-safe system
• order statistics
• majorization
• stochastic order

2020 Mathematics Subject Classifications:

• Primary 62G30
• 60E15
• Secondary 62N05

Acknowledgments

The authors are thankful to the Editor-in-Chief, the Associate Editor and the anonymous Referees for their valuable suggestions which lead to an improved version of the manuscript.

Disclosure statement

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

Data availability statement

No new data were created or analysed in this study.