State-based transition probabilities for systems subject to periodic inspection interval

ABSTRACT

In this paper, we present a general formula to calculate transition probabilities for six different types of systems based on their redundancy strategy and the status of the components. The systems are under periodic inspection policy and their components are repairable. The investigated systems include system I – active redundancy without any component to be replaced or repaired; system II – active with the component(s) to be replaced and repaired; system III – active with the component(s) to be repaired; system IV – standby without any component(s) to be replaced or repaired; system V – standby with the component(s) to be replaced and repaired; and system VI – standby with the component(s) to be repaired. In addition, all components in a system are considered non-identical. To calculate the transition probabilities for systems IV, V, and VI, we first consider a system with n non-identical components and cold standby configuration (NIC-CSC) and calculate the system state probabilities using Markov theory. Then, we present the general formula transition probabilities for systems IV, V, and VI using the results of the NIC-CSC system inspection interval. We demonstrate how to calculate the transition probabilities and matrixes for the six above-mentioned systems using the provided formulas. Moreover, we use the provided formulas to optimize the inspection interval of these systems using a modified full enumeration technique.

KEYWORDS:

• Transition probabilities
• active configuration
• standby configuration
• Markov process
• inspection interval optimization

Acknowledgement

This study was funded by the Government of Canada through Canada Research Chairs (CRC) program. The authors would like to thank the Government of Canada for their support.

Disclosure statement

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

Supplemental data

Supplemental data for this article can be accessed online at https://doi.org/10.1080/16843703.2023.2236902

Additional information

Notes on contributors

Mani Sharifi

Dr. Mani Sharifi is a post-doctoral research fellow at Reliability, Risk, and Maintenance Research Laboratory (RRMR Lab) in the Department of Mechanical and Industrial Engineering at Toronto Metropolitan University. He holds a B.Sc. degree from Qazvin IAU, an M.Sc. degree from the south Tehran branch IAU, and a Ph.D. degree from Tehran Research and Science IAU in Industrial Engineering. He was the Managerial Editor of the Journal of Optimization in Industrial Engineering. His areas of interest include reliability engineering, combinatorial optimization, statistical optimization, as well as production scheduling.

Sharareh Taghipour

Dr. Sharareh Taghipour is an Associate Professor and the RRMR Lab Director at the Department of Mechanical and Industrial Engineering in Toronto Metropolitan University. She is a Tier 2 Canada Research Chair in Physical Asset Management. She obtained her Ph.D. in Industrial Engineering from the University of Toronto. She received her B.Sc. in Mathematics and Computer Science and her M.Sc. in Industrial Engineering from Sharif University of Technology, Iran. Her research interests include stochastic modeling and optimization with applications in reliability engineering, maintenance optimization, and production scheduling.

Arash Zaretalab

Dr. Arash Zaretalab holds a B.Sc. and M.Sc. degrees from Qazvin IAU and a Ph.D. degree from Amirkabir University of technology, all in Industrial Engineering. His research interests are Reliability Engineering, Combinatorial Optimization, Machining Process Optimization, Computational Intelligence, and Data Mining.