International Journal For Multidisciplinary Research

E-ISSN: 2582-2160   •   Impact Factor: 9.24

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Mathematical Analysis of a Machine Repair System with Variable Repair Cost and Warm Standby Units

Author(s) Rekha Kumari
Country India
Abstract This study develops a mathematical model for a repairable machine system incorporating warm standby units and variable repair costs. In many industrial systems, machine failures can substantially affect production efficiency, system availability, and operational expenditure. The incorporation of warm standby machines provides redundancy and allows a failed operating machine to be replaced without significant interruption of service. The proposed model considers a finite number of operating machines, warm standby units, and a repair facility. Machine failures and repairs are assumed to follow exponential distributions, while the repair cost is allowed to vary according to the number of failed machines and/or the repair rate. A continuous-time Markov chain is formulated to describe the system states. Steady-state probabilities are obtained from the corresponding balance equations. Based on these probabilities, important performance measures such as system availability, utilization of the repair facility, expected number of failed machines, mean operating machines, and expected repair cost are derived. A total-cost function incorporating standby, repair, operating, and downtime costs is subsequently formulated. Numerical and sensitivity analyses can be used to investigate the effects of failure rate, repair rate, number of warm standby units, and variable repair cost on system performance. The proposed model can assist in determining economically appropriate maintenance and standby policies for industrial machine-repair systems.
Keywords Machine repair system, Warm standby, Variable repair cost, Reliability, Availability, Markov process, Cost analysis, Steady-state probability.
Field Mathematics
Published In Volume 5, Issue 3, May-June 2023
Published On 2023-06-16
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E-ISSN 2582-2160
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CrossRef DOI prefix of IJFMR is 10.36948/ijfmr

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