Interval-valued availability of a standby system with imperfect switch incorporating uncertainty & multiple failure modes

ABSTRACT

This paper examines the interval-valued availability of a standby redundant system with imperfect switching, incorporating uncertainty, i.e. the probability of successful operation of the switch is not known with accuracy. The standby system undergoes periodic inspections and is vulnerable to α number of failure modes (FMs). Every FM has a random failure time assigned to it, and once the system fails from the a^th FM, a corrective repair is executed promptly. The corrective repair takes a random amount of time${\psi }_a(a=1,2,\dots \alpha )$. Incorporating the aforesaid points, expressions for the upper and lower bounds of the model’s point and long-run availability are derived, and a sensitivity analysis is done to evaluate the impact of inspection time on the system’s availability. Lastly, the derived theorems are established by using a numerical example of a combi-boiler standby system with an imperfect switch.

KEYWORDS:

• Interval-valued availability
• standby system with imperfect switching
• uncertainty in switch
• sensitivity analysis
• multiple failure modes

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by grants to the first author through Innovation in Science Pursuit for Inspired Research (INSPIRE) fellowship from the Department of Science and Technology (DST), India. 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 degree, she received the Innovation in Science Pursuit for Inspired Research (INSPIRE) Scholarship. Currently, she is pursuing her Ph.D. at G. B. Pant University of Agriculture and Technology, Pantnagar, India and is being awarded the INSPIRE fellowship by the Department of Science and Technology (DST), India. She is pursuing her 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 26 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 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 Guest Editor of some other journals. He has authored and coauthored eight books on different courses of Applied/Engineering Mathematics and co-edited two books. He has been conferred with five national awards and the Best Teacher Award. He has published different research papers in national and international journals of repute. His area of research is Reliability Theory.