Markov process approach for analyzing periodically inspected competing-risk system embodying downtime threshold

ABSTRACT

Substantially, most repairable systems undergo ignored failure, i.e. if any failure is repaired quickly then it will not be affecting systems availability. The availability and cost for a periodically examined competing-risk system is studied embedding the downtime threshold concept. If the systems downtime is not more than a pre-specified limit, the system could be considered functional during that downtime period, i.e. the breakdown could be neglected. Contrarily, if the downtime extends that limit, the system is deemed to be functional from outset of failure till the downtime exceeding the preset limit, i.e. the breakdown is deferred. Moreover, the system is presumed to have a functional state and M modes of failure. The point and limiting availabilities are being analyzed for the aforementioned system employing the Markov process approach. Additionally, long-run average cost expression is also acquired for the proposed model. An example of a protection device is then utilized to demonstrate the drafted procedure.

KEYWORDS:

• Competing-risk system
• Periodic inspection
• Availability
• Downtime threshold

Acknowledgments

The authors would like to thank the editor and the reviewers for their suggestions, which could help in improving the quality of this research paper.

Disclosure statement

The author(s) declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Funding

This work was supported by grants to the first author via Council of Scientific and Industrial Research, India [09/171(0137)/2019- EMR-1].

Notes on contributors

Himani Pant

Himani Pant is a Research Scholar in the Department of Mathematics, Statistics and Computer Science at G.B. Pant University of Agriculture and Technology, Pantnagar, India. She has completed her B.Sc.(H) Mathematics and M.Sc. (Mathematics) from Delhi University, India in the year 2015 and 2017 respectively. She has cleared Joint CSIR-UGC National eligibility test (NET) for JRF held on June 2018 and is being awarded the fellowship for the same by CSIR, India. She is pursuing Ph.D. under the guidance of Dr. S.B. Singh. Her area of research is Reliability Theory.

S.B. Singh

S. B. Singh is a Professor in the Department of Mathematics, Statistics and Computer Science, G. B. Pant University of Agriculture and Technology, Pantnagar, India. He has around 25 years of teaching and research experience to undergraduate and post graduate students at different engineering colleges and universities. Prof. Singh is a member of Indian Mathematical Society, Operations Research Society of India, ISST and National Society for Prevention of Blindness in India and Indian Science Congress Association. He is editor of the Journal of Reliability and Statistical Studies. He has authored and co-authored eight books on different courses of Applied/Engineering Mathematics. He has been conferred with four national awards. He has published his research works at national and international journals of repute. His area of research is Reliability Theory.