Authors: Madhu Jain; G.C. Sharma; Varsha Rani
Addresses: Department of Mathematics, IIT Roorkee, Roorkee 247 667, India ' Department of Mathematics, I.B.S., Khandari, Agra 282 002, India ' Department of Mathematics, St. John's College, Agra 282 002, India
Abstract: This investigation is concerned with the transient analysis of machine repair problem with M operating units and multi types of warm spares. In case when all spares are being used, the failure of units occurs in degraded fashion. Each unit is assumed to fail in two modes. When all permanent repairmen are busy, the caretaker who brings the failed units for repair departs from the system after waiting for sometime in the queue due to impatience. For transient state, Chapman-Kolmogorov equations governing the model are constructed. Various performance measures such as expected number of failed units in each mode, average number of operating units in the system, average number of idle and busy repairmen in the system, operative utilisation factor, etc., are obtained. The cost minimisation problem to determine the optimum number of spares in terms of various cost elements has been formulated. We used Runge-Kutta technique to find the numerical solution for the transient model. The sensitivity analysis is performed to observe the effect of different parameters on various performance indices.
Keywords: machine repair; two mode failure; warm spares; Runge-Kutta technique; queue size; cost analysis; performance prediction; cost minimisation; machine failures.
International Journal of Operational Research, 2015 Vol.22 No.2, pp.167 - 193
Available online: 06 Feb 2015 *Full-text access for editors Access for subscribers Purchase this article Comment on this article