Stochastic modelling and reliability analysis of a three-unit non-identical repairable HVAC system with warranty considerations

This paper presents a stochastic model for a three-unit, non-identical, repairable HVAC system comprising two identical air-conditioning units operating in parallel for cooling and a distinct ventilation unit for fresh air circulation. Using the regenerative point technique within a semi-Markovian framework, the model evaluates system reliability and economic performance under a finite warranty period. Failure and repair times are exponentially distributed with constant parameters, and repair of the non-identical unit is prioritized during the warranty period, with costs covered by the manufacturer. Analytical expressions for Mean Time to System Failure (MTSF), steady-state availability, and expected profit are derived to characterize system behaviour. Numerical evaluation demonstrates the impact of repair prioritization and warranty conditions on system performance, providing quantitative insights for optimizing reliability, maintainability, and cost-effectiveness of HVAC systems to sustain indoor air quality.