Reliability analysis of heating ventilation and air conditioning systems using the trend renewal process

Reliability analysis of repairable systems such as heating, ventilation, and air conditioning (HVAC) equipment must account for multiple failure modes and the reality of imperfect repairs. Traditional models like the non-homogeneous Poisson process (NHPP) or the classical renewal process assume extreme repair effects (minimal or perfect), which can misrepresent systems where maintenance actions return the equipment to an intermediate condition (neither “as good as new†nor “as bad as old†). To address this gap, we apply the Trend Renewal Process (TRP) model to capture the failure dynamics of HVAC systems with multiple failure modes (refrigerant leak, electrical, and mechanical failures), as a case study. The TRP generalizes conventional models by combining a time-dependent trend component with a renewal distribution; specifically, we develop a Weibull–Weibull TRP formulation and derive its conditional intensity function for each failure type. The model parameters for each failure mode are estimated through maximum likelihood estimation (MLE) using real-world failure data from NASA’s Rocket Propulsion Test Program HVAC systems. The results demonstrate that HVAC systems exhibit increasing failure rates and partial repair effectiveness, characterized by parameters indicating moderate aging trends and imperfect renewals. The Weibull–Weibull TRP model effectively captured the variability and dynamics of different HVAC failure modes, providing a realistic framework for reliability prediction and maintenance optimization. Despite limitations due to data availability and categorization accuracy, this approach is robust, highlighting opportunities for further refinement with more comprehensive datasets. The observed system-level failure stream aggregates heterogeneous component processes (a superposition). We therefore use the TRP as a parsimonious approximation rather than an exact superposition model. Adequacy is evaluated against a minimal-repair NHPP baseline via a likelihood-ratio test and residual diagnostics.