Availability and cost models for sequentially inspected systems with dependent catastrophic and soft failures

Abstract

This paper introduces a novel availability and cost model designed for competing-risk systems that integrate interdependent catastrophic and soft failures. Catastrophic failures halt system operations instantly, while soft failures result in efficiency reductions. The linkage between these failure types is reflected in the fact that each soft failure instantly raises the hazard rate of catastrophic failure. The system under consideration is inspected sequentially wherein upon detecting a soft failure; an immediate minimal repair is performed. After a repair, the system is inspected again in the aforesaid way. If a catastrophic failure is discovered, the system is replaced immediately. This paper formulates expressions for upper and lower reliability limits by incorporating these aspects. Furthermore, it presents theorems that establish bounds for point availability, long-run availability, and the average long-run cost rate. The proposed framework’s validity is confirmed through a numerical case study involving a refrigerator. The outcomes highlight the effectiveness of the model in addressing systems vulnerability to interdependent failures and provide insights into its application.

Keywords:

• Reliability
• availability
• average long-run cost
• sequential inspections
• hard and soft failures

Disclosure statement

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

Additional information

Funding

This work is supported by grants awarded to the first author through Innovation in Science Pursuit for Inspired Research (INSPIRE) fellowship from the Department of Science and Technology (DST), India, under Sanction Letter No. DST/INSPIRE Fellowship/2019/IF190873.

Notes on contributors

Amisha Khati

Amisha Khati 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 completed her B.Sc. from Kumaun University, Nainital, India in 2017 and her M.Sc. (Mathematics) from G. B. Pant University of Agriculture and Technology, Pantnagar, India in 2019. While pursuing her Bachelor’s and Master’s degrees, she received the Innovation in Science Pursuit for Inspired Research (INSPIRE) Scholarship. Currently, she is doing her Ph.D. at G. B. Pant University of Agriculture and Technology, Pantnagar, India, and is a recipient of the INSPIRE fellowship provided by the Department of Science and Technology (DST), India. She is pursuing her Ph.D. under the supervision 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 University. 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 a regular reviewer of many books and International/National Journals. He has been a member of the organizing committee of many international and national conferences and workshops. He is an Editor-in-Chief of the “Journal of Reliability and Statistical Studies” and also a Guest Editor of some other journals. He has authored and coauthored eight books on different courses in Applied/Engineering Mathematics and co-edited two books. He has been conferred with five national awards and the Best Teacher Award. He has published his research papers in national and international journals of repute. His area of research is Reliability Theory.