Reliability Modeling and Switching Decision Optimization for Standby Systems with Switching Time Redundancy

Switching time redundancy is crucial for optimizing the performance of standby systems, where a redundancy period commences upon the failure of the online operating unit, requiring the standby unit to activate within a designated random time interval to ensure operational continuity. This paper examines a two-unit warm standby system that integrates switching time redundancy. System failure can occur due to simultaneous failures of both units or failure of the standby unit's activation within the allowed redundancy period. The proposed warm standby system model with switching time redundancy is especially pertinent in critical applications, such as hospitals, where backup generators are vital for maintaining a continuous power supply to life-support systems and other essential functions. Our primary aim is to identify the optimal switching timing for the standby unit's transition to the online mode, striking a balance between key trade-offs: early activation may lead to excessive wear and increased operational costs, whereas delayed activation could result in detrimental downtime. We propose switching strategies aimed at (a) maximizing expected system lifetime and (b) maximizing expected operational profit. Numerical examples illustrate the practical applicability of these strategies and offer valuable guidance for effective operations management within warm standby systems.