Abstract
This paper is concerned with machine repair system having on line units along with mixed standby units under the care of single unreliable server. Whenever any unit fails, it is immediately replaced by a standby unit if available. In case when all standbys are used, the failure of remaining on line units occurs in degraded fashion. The server is turned on when there are N or more failed units present in the system; it is turned off when the system has no failed unit. The server is subject to breakdowns and repairs. The life time and repair time of failed units and the server are exponentially distributed. The governing equations are constructed using appropriate birth-death rates. After taking Laplace transform of set of equations, we employ matrix method to determine transient probabilities. Various performance indices such as expected number of standby units, expected number of failed units, probability of server being idle, busy or broken etc. are determined. Expressions for the system reliability and mean time to system failure are established in terms of transient probabilities. Cost function is also facilitated which may be helpful for system designer to achieve effective system descriptors. Numerical results are provided for various system characteristics to examine the effects of different parameters.
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