Document Type: Review Article
Mathematics, Yusuf Maitama Sule University, Kano, Nigeria
Research Scholar Mathematics, Department, Mewar University, Chittorgarh, Rajasthan, India
The reliability measures of a system consisting of two subsystems in the series configuration have been studied for different types of failures and two types of repair. The subsystem-1 has four identical units in a parallel configuration and operating under 3-out-of-4: G policy and this has connected to subsystem-2 which has three identical units arranged in a parallel configuration and working under 2-out- of-3: F, scheme. The units of the subsystem-1 are controlled by a controller for preventing failure effect and safety purposes. It is assumed that the units of each subsystem have different types of failure and repair rates. A well-known natural cause of failure of any system the unsuitability of the environmental conditions like overheating, weather conditions like heavy rain, thunderstorm, and catastrophic shakeups, etc. have treated as a complete failure of the system have also considered for this study. We have considered the environmental causes of failure in our proposed repairable system as a complete failure by which the system stops functioning. Human failure in the system is trickled as complete failure and repair employing copula (Gumbel- Hougaard family copula distribution) like another complete failed states of subsystems. To analyze our system, we have used the supplementary variable technique and derived some measures of system reliability like availability, reliability; MTTF and incurred profit function for different values of parameters. Some particular cases for different values of failure rates have explicitly been studied.