Vijay Singh - Mathematics, Yusuf Maitama Sule University, Kano, Nigeria
Monika Gahlot - Department of Mathematics, Mewar University, Chittorgarh, Rajasthan, India

This paper studies the reliability measures of a system consisting of two subsystems in a series configuration for different types of failure and two types of repair. The subsystem-۱ has four identical units in a parallel configuration operating under ۳-out-of-۴: G policy and this has connected to subsystem-۲ which has three identical units arranged in a parallel configuration and working under ۲-out- of-۳: F, scheme. The units of subsystem-۱ are controlled by a controller for preventing failure effect and safety purposes. It is assumed that units of each subsystem have different types of failure and repair rates. The unsuitability of the environmental conditions such as overheating as a well-known natural cause of failure of any system and also weather conditions like heavy rain, thunderstorm, and catastrophic shakeups, etc. have treated as a complete failure of the system. This study considers the environmental causes of failure in the proposed repairable system as 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 the proposed system, the supplementary variable technique are used and some measures of system reliability like availability, reliability; MTTF and incurred profit function for different values of parameters are derived. Some particular cases for different values of failure rates that have explicit are also studied.

Environment failure, Human failure, Availability, MTTF, Reliability, Profit analysis, Gumbel-Hougaard family copula