Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and busy time. One repairman is responsible for repairing the server failure; the repair rate is variable to adapt to whether the machines are all functioning normally or not. All the time distributions are exponential. Using the quasi-birth-death(QBD) process theory, the steady-state availability of the machines, the steady-state availability of the server, and other steady-state indices of the system are given. The transient-state indices of the system, including the reliability of the machines and the reliability of the server, are obtained by solving the transient-state probabilistic differential equations. The Laplace–Stieltjes transform method is used to ascertain the mean time to the first breakdown of the system and the mean time to the first failure of the server. The case analysis and numerical illustration are presented to visualize the effects of the system parameters on various performance indices.

Performance assessment of the complex repairable system with n-identical units under (k-out-of-n: G) scheme and copula linguistic repair approach

PurposeThis paper analyzed a complex system consisting n-identical units under a k-out-of-n: G; configuration via a new method which has not been studied by previous researchers. The computed results are more supportable for repairable system performability analysis.Design/methodology/approachIn this paper, the authors have analyzed a complex system consisting n-identical units under a k-out-of-n: G; configuration via a new method which has not been studied by previous researchers. The supplementary variable technique has employed for analyzing the performance of the system.FindingsReliability measures have been computed for different types of configuration. It generalized the results for purely series and purely parallel configurations.Research limitations/implicationsThis research may be beneficial for industrial system performances whereas a k-out-of-n-type configuration exists.Practical implicationsNot sure as it is a theoretical assessment.Social implicationsThis research may not have social implications.Originality/valueThis work is the sole work of authors that have not been communicated to any other journal before.