Stochastic Analysis of a Three-Unit Non-Identical Repairable System with Simultaneous Working of Cold Standby Units

  • S. Kadyan Department of Statistics, M. D. University, Rohtak, India
  • Suresh Chander Malik Department of Statistics, M. D. University, Rohtak, India
  • Gitanjali Department of Applied Sciences, M.S. Institute of Technology, Delhi, India
Keywords: Repairable system, non-identical units, simultaneous working of cold standby units, stochastic analysis


Here, stochastic analysis of a repairable system of three units has been carried out by taking one unit in operation (called main unit) and two identical units (called duplicate units) in cold standby. The switch device is used to convert the standby units into operative mode. A single server is hired to handle repair activities of the units who visits the system instantly whenever needed. The repair done by the server is perfect and thus the repaired unit follows the same lifetime distribution as the original. The constant failure rates are considered for both main and the duplicate units while their repair time distributions are taken as arbitrary. Some important reliability measures including mean sojourn times (MST), transition probabilities (TP), mean time to system failure (MTSF), availability, expected number of repairs for both kinds of units separately, expected number of visits by the server and busy period analysis of the server due to repair are determined using semi-Markov process (SMP) and regenerative point technique (RPT). The arbitrary values of the parameters are considered to examine the behaviour of some significant reliability measures through graphs. The possible application of the system model can be visualized in a power supply system of a house where a set of solar panels are kept in spare for their simultaneously working when main power supply is discontinued.


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Author Biographies

S. Kadyan, Department of Statistics, M. D. University, Rohtak, India

S. Kadyan is a Ph.D. student at M.D. University Rohtak (India) since 2019. Her Ph.D. work centres on Reliability Modelling. She has attended good number of conferences and presented her research work.

Suresh Chander Malik, Department of Statistics, M. D. University, Rohtak, 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 the 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.

Gitanjali, Department of Applied Sciences, M.S. Institute of Technology, Delhi, India

Gitanjali received her Ph.D. degree in the subject Statistics from M.D. University Rohtak (India). Presently she is working as Assistant Professor in Department of Applied Sciences, MSIT, New Delhi. She has published good number of research papers in the field of Reliability theory and Modelling.