Stochastic Profit Modeling of a Two-Unit Parallel System with Bad Weather Effects and Activation Time

Abstract

The present study investigates the stochastic performance and profit behavior of a two-unit non-identical parallel system operating under bad weather conditions. The system consists of unit A, which initially operates in active mode, and unit B, which remains in standby. Unit A becomes non-operative during bad weather conditions (BWC) and requires a random activation time to resume operation after the weather normalizes and necessary repairs are completed. To enhance its operational efficiency, unit A is subjected to preventive maintenance after a random interval. Priority is assigned to repair and activation activities over preventive maintenance to restore system operability, with unit A receiving higher priority than unit B. A single repairman is continuously available to attend to failed units. The failure times of both units are assumed to be independent and exponentially distributed, while the repair times follow general distributions. Employing the regenerative point technique, key measures of system effectiveness are derived, including transition probabilities, mean sojourn times, mean time to system failure (MTSF), system availability, repairman busy period, expected number of repairs performed, and the expected profit of the system.