Estimation of the limiting availability of a repairable series system with stationary dependent sequences

Abstract

The independence assumption would lead to poor estimation of the availability and even misleading conclusions when dependence actually exists. In this paper, we provide the estimation of the limiting availability of a repairable series system when the failure times and repair times are two independent sequences of stationary dependent random variables. Furthermore, consistency and asymptotic normality of the estimator of the limiting availability are derived under some regular conditions. Finally, we investigate the limiting availability for a first-order exponential moving average (EMA1) process and a first-order exponential autoregressive (EAR(1)) process. Simulations are presented to study the impact of dependence on the estimation of the limiting availability.

Keywords:

• Availability
• series system
• dependent sequences
• consistency
• asymptotic normality

2010 Mathematics Subject Classifications:

• 62F40
• 62J02
• 62J20

Acknowledgments

The authors are grateful to the editor, the associate editor and the anonymous referee for their valuable comments that have vastly improved this paper.

Disclosure statement

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

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant number 12071233], [grant number 11926347], [grant number 11971247], the PhD Candidate Research Innovation Fund of Nankai University and Natural Science Foundation of Colleges of Jiangsu Province [grant number 18KJB110003].