Reliability and Profit Analysis of a Two-unit Redundant System with Periodic Rest Mechanism
Hemlata Thakur
Mathematics Department, Govt. College Rau, Indore, India.
Pradeep K. Joshi *
Mathematics Department, IPS Academy, Indore, India.
Chitaranjan Sharma
Mathematics Department, PM Govt. College of Excellence GACC, Indore, India.
*Author to whom correspondence should be addressed.
Abstract
Two-unit redundant systems have garnered significant interest in reliability studies due to their extensive use in industrial and commercial applications. Researchers have explored various configurations of these systems, focusing on metrics such as MTSF, steady-state availability, repairman busy periods, and cost analysis. This study examines the reliability measures of a system where two identical or similar units (or components) are used, with one serving as a backup for the other in case of failure, ensuring continued operation of a two-unit redundant system enhanced by a resting mechanism designed to improve performance. The system consists of two units, with one unit operating actively while the other remains in a cold standby mode. A distinctive aspect of the model is the inclusion of periodic rest for the active unit, during which it is not considered failed. The failure, repair, and rest rates are modelled using exponential distributions. Key reliability metrics such as MTSF, availability, and the busy period of the server are analyzed through linear differential equations. To evaluate the system’s performance, graphs are employed to demonstrate how varying rest rates influence reliability measures and profitability. The findings reveal that the resting mechanism plays a critical role in enhancing system availability and operational efficiency. Through this study, a mathematical basis for evaluating system performance is established, and solutions for optimizing profitability and reliability in redundant systems are provided. In future, the model could be expanded to include energy consumption and environmental factors, which are critical in modern industrial systems.
Keywords: Reliability, steady -state availability, busy period analysis, profit analysis, Mean Time to System Failure (MTSF)