\bf{M/G/1} fault-tolerant machining system with imperfection

Abstract

<p style='text-indent:20px;'>The internet of things (IoT) is an emerging archetype of technology for the guaranteed quality of services (QoS). The availability of the uninterrupted power supply (UPS) is one of the most challenging criteria in the successful implementation of the service system of IoT. In this paper, we consider a fault-tolerant power generation system of finite operating machines along with warm standby machine provisioning. The time-to-failure for each of the operating and standby machines are assumed to be exponentially distributed. The time-to-repair by the single service facility for the failed machine follows the arbitrary distribution. For modeling purpose, we have also incorporated realistic machining behaviors like imperfect coverage of the failure of machines, switching failure of standby machine, reboot delay, switch over delay, etc. For the evaluation of the explicit expression for steady-state probabilities of the system, the only required input is the Laplace-Stieltjes transform (LST) of the repair time distribution. The step-wise recursive procedure, illustrative examples, and numerical results have been presented for the following different type of repair time distribution: exponential (<inline-formula><tex-math id="M2">\begin{document}$ M $\end{document}</tex-math></inline-formula>), <inline-formula><tex-math id="M3">\begin{document}$ n $\end{document}</tex-math></inline-formula>-stage Erlang (<inline-formula><tex-math id="M4">\begin{document}$ Er_{n} $\end{document}</tex-math></inline-formula>), deterministic (<inline-formula><tex-math id="M5">\begin{document}$ D $\end{document}</tex-math></inline-formula>), uniform (<inline-formula><tex-math id="M6">\begin{document}$ U(a, b) $\end{document}</tex-math></inline-formula>), <inline-formula><tex-math id="M7">\begin{document}$ n $\end{document}</tex-math></inline-formula>-stage generalized Erlang (<inline-formula><tex-math id="M8">\begin{document}$ GE_n $\end{document}</tex-math></inline-formula>) and hyperexponential (<inline-formula><tex-math id="M9">\begin{document}$ HE_n $\end{document}</tex-math></inline-formula>). Concluding remarks and future scopes have also been included.