Redundancy Optimization for a System Comprising Two Operative Unit and N Cold Standby Units with Activation Time

Abstract

A well-known idea in the field of reliability engineering is the use of standby redundancy to raise a system's reliability and maximize profitability, ensuring the sustainability of economies and industries.To accomplish this, a reliability model is developed that incorporates a finite number (N) of cold standby units, in addition to two operational units, taking into account the activation time required to transition a standby unit to an operational state. Upon failure of either operational unit, a cold standby unit is activated to assume its responsibilities, functioning with equivalent effectiveness. The system operates with two working units at a time and if in any state there is only one operative unit available, then the system works at reduced capacity. The determination of the required number of standby units involves establishing cut-off points based on factors such as revenue, failure rates, installation costs, activation rates, etc. Computational analyses have been conducted to facilitate this process, incorporating Markov processes and various performability measures. The regeneration point technique is employed to optimize the number of standby units.