Generalized control-limit preventive repair policies for deteriorating cold and warm standby Markovian systems

ABSTRACT

Consider a deteriorating repairable Markovian system with N stochastically independent identical units. The lifetime of each unit follows a discrete phase-type distribution. There is one online unit and the others are in standby status. In addition, there is a single repair facility and the repair time of a failed unit has a geometric distribution. The system is inspected at equally spaced points in time. After each inspection, either repair or a full replacement is possible. We consider state-dependent operating costs, repair costs that are dependent on the extent of the repair, and failure penalty costs. Applying dynamic programming, we show that under reasonable conditions on the system’s law of evolution and on the state-dependent costs, a generalized control-limit policy is optimal for the expected total discounted criterion for both cold standby and warm standby systems. Illustrative numerical examples are presented and insights are provided.

Keywords:

• Maintenance policies
• phase-type distribution
• cold/warm system
• repair facility
• replacement
• generalized control-limit repair–replacement rule

Additional information

Notes on contributors

Yonit Barron

Yonit Barron is a Lecturer in the Department of Industrial Engineering and Management at Ariel University, Israel. She received a B.Sc. in Computer Science and an M.Sc. In Industrial Engineering & Management—both from the Technion, Israel Institute of Technology—and a Ph.D. in Statistics from the University of Haifa, Israel. Her research interests include applied probability, reliability, stochastic processes, queueing theory, service systems, inventory models, flow fluid processes, and supply chain management. Her work has appeared in IISE Transactions, Journal of Applied Probability, Annals of Operation Research, Advances in Applied Probability, European Journal of Operational Research, and Probability in the Engineering and Informational Science.

Uri Yechiali

Uri Yechiali (Professor Emeritus), is a world expert in the fields of queueing theory and stochastic modeling. He received a B.Sc. (Cum Laude) in Industrial Engineering and an M.Sc. in Operations Research, both from the Technion, Israel, and a Ph.D. in Operations Research from Columbia University, New York. He joined Tel-Aviv University in 1971 and was promoted to full professorship in 1981. He was a Visiting Professor at Columbia University, New York University, INRIA (France), and held the Beta Chair in Eurandom (Holland). His 137 scientific publications include seminal works on vacation models in queues, queues in random environment, analysis and control of polling systems, tandem Jackson networks, the Israeli queue, optimal policies for live-organ transplants, modeling genetic regulatory networks, analysis of asymmetric inclusion processes, layered queues, optimal replacement policies, and statistical mathematical programming. Prof. Yechiali supervised 41 master's and 13 Ph.D. students (most of them hold faculty positions in prestigious universities) and received several research grants from European institutes. For his excellent academic contributions, in 2004 he received a Life Achievement Award from the Operations Research Society of Israel. His current research interests are maintenance and replacement models, ASIP models, optimal allocation policies for live organ transplants, layered queues where customers act as servers, networks of retrial queues, polling systems, and queues with decomposed service.