# Profit Analysis of a Standby Repairable System with Priority to Preventive Maintenance and Rest of Server Between Repairs

• Chhama Aggarwal Department of Statistics, M.D. University, Rohtak-124001, India
• Nitika Ahlawat Department of Statistics, M.D. University, Rohtak-124001, India
• S.C. Malik Department of Statistics, M.D. University, Rohtak-124001, India
Keywords: Cold standby redundancy, stochastic process, rest of the server, preventive maintenance, priority, reliability characteristics and profit analysis

### Abstract

The paper aims to bring out the profit analysis of a system with cold standby redundancy of two identical units. In the system, we keep one unit productive and the other is to backup the operation. The system requires preventive maintenance after a specific time. In addition to that, the server is allowed to rest between two consecutive repairs. The repairs are done to increase the efficiency and productivity level of the system. The repair and rest times follow arbitrary distributions while the random variable related to failure time of the unit follows negative exponential distribution. The provision of priority has been made for the preventive maintenance over repairs. Some important reliability characteristics are studied in steady state by using the approach of stochastic processes. The revenue per unit time and the cost per unit time for which server is busy in repairs and maintenances are considered for determining the profit incurred to the system.  The results are shown graphically and numerically to highlight the effect of different parameters on some significant reliability characteristics.

### Author Biographies

Chhama Aggarwal, Department of Statistics, M.D. University, Rohtak-124001, India

Chhama Aggarwal is a Ph.D. student at the Department of Statistics in Maharshi Dayanand University since October, 2018. She received her B.Sc. (H) Mathematics and M.Sc. in Mathematics degrees from University of Delhi, Delhi.

Nitika Ahlawat, Department of Statistics, M.D. University, Rohtak-124001, India

Nitika Ahlawat is a Ph.D. student at the Department of Statistics in Maharshi Dayanand University since December, 2019. She received her B.A. in Mathematics and Statistics and M.Sc. in Statistics degrees from M.D. University, Rohtak (Haryana).

S.C. Malik, Department of Statistics, M.D. University, Rohtak-124001, India

S. C. Malik is presently working as Professor & Head, Department of Statistics, M.D. University, Rohtak (Haryana). His field of research specialization are Reliability Theory, Sampling and Applied Statistics. He has a long research and teaching experience in subject of Statistics. He has supervised 40 Ph.D. students in the fields of reliability theory, sampling theory and applied statistics. Dr. Malik has been invited by various academic institutions to deliver talks and to present research papers at conferences/seminars/symposiums/workshops held in India and abroad including USA, UK, Portugal, Singapore, Germany, Hong-Kong, France, Spain, Netherland, Belgium, Austria, Italy, Japan, Switzerland and Nepal. He is reviewer of various journals specifically for the journals in the areas of Reliability, Operations Research and Statistics. Prof. Malik has been a member/life member of various academic/professional bodies. He is a founder President of Indian Association for Reliability and Statistics (IARS) and also Chief Editor of the UGC listed journal IJSRE being published by IARS.

Published
2021-03-30
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Articles