Title: Bi-level control of degraded machining system with two unreliable servers, multiple standbys, startup and vacation

Authors: Kamlesh Kumar; Madhu Jain

Addresses: Department of Mathematics, IIT Roorkee, Roorkee-247667, India ' Department of Mathematics, IIT Roorkee, Roorkee-247667, India

Abstract: This investigation deals with bi-level (N, L) switch over policy for multi-component machine repair system with two unreliable repairmen and multiple types of standbys. The repairman (R₁) turns on when N-failed units are accumulated in the system and starts repair of failed units by taking a startup rate. As soon as there is no failed unit in the system, the repairmen (R₁) goes for a vacation and returns back when he finds the number of failed units in the system greater than or equal to the threshold value N. The second repairman (R₂) turns on when there are L (>N) failed units in the system and leaves for a vacation if the number of failed units are less than L. The repairmen can also breakdown while repairing the failed units. The life time and repair time of operating/standbys units, unreliable servers, and startup time of the servers are assumed to be exponentially distributed. The transient state probabilities of the system states are obtained by using Runge-Kutta's method. Expressions for various performance indices viz. throughput, average number of failed units in the system and reliability of the system etc. are established. In order to examine the effects of various parameters, the sensitivity analysis is carried out by taking numerical illustration.

Keywords: bi-level control; machine repair; multiple standbys; queue length; startup time; vacation; Runge-Kutta method; unreliable servers; throughput; failed units; reliability.

DOI: 10.1504/IJOR.2014.064540

International Journal of Operational Research, 2014 Vol.21 No.2, pp.123 - 142

Published online: 22 Sep 2014 *

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