Analysis of the two-unit cold standby repairable system with damage and repair time dependency via matrix-exponential distributions

ABSTRACT

In this paper, two-unit standby repairable system is studied via matrix-exponential distributions. The system under concern consists of one active and one standby components, and fails if either a damage size upon the failure of the active component is larger than a repair limit or the repair time of the failed unit exceeds the lifetime of the active unit, whichever happens first. Under the assumption that the damage size and repair time are statistically dependent, the Laplace transform of the system’s lifetime is obtained. The Laplace transform is shown to be rational under particular cases, and the reliability evaluation of the system is performed via well-known distributional properties of the matrix-exponential distributions. The problem of estimating the unknown parameters of the operation time and repair time distributions is also discussed based on system’s lifetime data.

KEYWORDS:

• Matrix-exponential distribution
• moment estimator
• maximum likelihood estimator
• reliability
• repairable system

Acknowledgments

The authors thank the anonymous referees for their helpful comments and suggestions, which were useful in improving the paper.

Disclosure statement

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

Additional information

Notes on contributors

Coskun Kus

Coskun Kus completed his Ph.D. at Selcuk University (Turkey). He is currently working as a professor at Department of Statistics at Selcuk University. His research interests are reliability theory, statistical inference and distribution theory. He has published papers in various journals including Computational Statistics and Data Analysis, Journal of Applied Statistics and Journal of Statistical Computation and Simulation.

Serkan Eryilmaz

Serkan Eryilmaz completed his Ph.D. at Ankara University (Turkey) in 2002. He is currently working as a professor at Department of Industrial Engineering and serving as vice president for research at Atilim University, Ankara. He is the present co-chair of the System Reliability Technical Committee of the European Safety and Reliability Association. He  currently serves as a member of the Editoral Board of Reliability Engineering and System Safety and an Area Editor of the IISE Transactions-Quality & Reliability Engineering. His research interests include reliability engineering, applied probability, stochastic modeling and renewable energy systems. He is the author of more than 180 publications. He was honored by TUBITAK (Scientific and Technological Research Council of Turkey) Science Incentive Award due to his highly qualified studies on system reliability in the field of stochastic models/processes in operations research.