Time-dependent reliability analysis for repairable consecutive-k-out-of-n:F system

Abstract

In a repairable consecutive $C(k,n:F)$ system, after the system operates for a certain time, some components may fail, some failed components may be repaired and the state of the system may change. The models developed in the existing literature usually assume that the state of the system varies over time depending on the values of n and k and the state of the system is known. Since the system reliability will vary over time, it is of great interest to analyse the time-dependent system reliability. In this paper, we develop a novel and simple method that utilizes the eigenvalues of the transition rate matrix of the system for the computation of time-dependent system reliability when the system state is known. In addition, the transition performance probabilities of the system from a known state to the possible states are also analysed. Computational results are presented to illustrate the applicability and accuracy of the proposed method.

Keywords:

• Repairable consecutive-k-out-of-n:F system
• transition rate matrix
• time-dependent reliability
• time-dependent transition performance probability

Disclosure statement

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

Additional information

Funding

H. K. T. Ng's work was also supported by a grant from the Simons Foundation [Grant Number 709773].

Notes on contributors

Gökhan Gökdere

Gökhan Gökdere is currently an Associate Professor of Statistical Science with the Fırat University, Elazıg, TURKEY. His research interests include reliability and statistical inference.

Hon Keung Tony Ng

Hon Keung Tony Ng is currently a Professor of Statistical Science with the Southern Methodist University, Dallas, TX, USA. His research interests include reliability, censoring methodology, ordered data analysis, nonparametric methods, and statistical inference. He is a Fellow of the American Statistical Association, an elected senior member of IEEE, and an elected member of the International Statistical Institute.