Residual Lifetime of Repairable Systems and Phase type Approximation

ABSTRACT

This paper considers a repairable system whose periods of operations and repairs alternate during the run time. The residual lifetime of the system and its age, when the system operates at time $\mathit{t}$, are proposed, and their properties are investigated. Under the condition that the system is under repair, the remaining time until the end of system repair time and the elapsed time of a repair are studied. Since computing a renewal function is not straightforward, we use phase-type approximation to find the best-fitted distribution of corresponding random variables. We provide some examples and utilize a real data set to demonstrate the results.

KEYWORDS:

• Alternating renewal process
• phase-type renewal process
• repairable system
• reliability residual lifetime
• availability
• phase-type distribution

Acknowledgements

The authors acknowledge the associate editor and the anonymous reviewers for their helpful comments and suggestions that improved the presentation of this paper.

Disclosure statement

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

Additional information

Notes on contributors

Sareh Goli

Sareh Goli is an assistant professor in the Department of Mathematical Sciences at Isfahan University of Technology. Her research interests are Applied Probability, Reliability Modeling of Systems, Reliability Theory, and Quality Control.

Safieh Mahmoodi

Safieh Mahmoodi received her B.Sc. in Statistics from Shiraz University (SU), M.Sc. in Mathematical Statistics from Isfahan University of Technology (IUT), and Ph.D. in Probability Theory and Stochastic Processes from SU, Iran. Also, she spent one year as a postdoctoral researcher at the University of Libre de Bruxelles (ULB), Belgium. She is with the Department of Mathematical Sciences, IUT, as an associate professor. Her research interests include Stochastic Processes and Modeling, particularly Stable Processes, Markov Processes, and Time Series Analysis also subjects related to Theory and Applied Probability with a focus on Queuing Theory.