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In this paper, we propose a machine repair problem with constant retrial policy, wherein if a failed machine finds the repairman busy upon arrival, it enters into an orbit. The machines in the orbit form a single waiting line, and only the one at the head of the orbit repeats its request for repair. The failure times of operating machines and the repair times of failed machines follow exponential distributions. It is assumed that retrial times are generally distributed. We used the supplementary variable technique to obtain explicit expressions for the steady-state probabilities of the number of failed machines in the orbit. We performed sensitivity analysis of the machine availability and operative efficiency with respect to system parameters and the number of machines in operation. The analysis of the busy period and the waiting time were also presented. Finally, we developed a cost model and formulated a cost minimization problem. [ABSTRACT FROM AUTHOR]

In this paper, we study a repairableK-out-of-(M+W) retrial system withMidentical primary components,Wstandby components and one repair facility. The time-to-failure and time-to-repair of the primary and standby components are assumed to be exponential and general distributions, respectively. The failed components are immediately for repair if the server is idle, otherwise the failed machines would enter an orbit. It is assumed that the retrial times are exponentially distributed. We present a recursive method using the supplementary variable technique and treating the supplementary variable as the remaining repair time to obtain the steady-state probabilities of down components at arbitrary epoch. Then, a unified and efficient algorithm is developed to compute the steady-state availability. The method is illustrated analytically for the exponential repair time distribution. Sensitivity analysis of the steady-state availability with respect to system parameters for a variety of repair time distributions is also investigated. [ABSTRACT FROM AUTHOR]