A numerical model with age reduction factor for warm spare

Reliability analysis of industrial systems working in critical situation is complicated due to dynamic behaviors such as sequence-dependency, spares, redundancy management. Systems designed to achieve a desired high reliability often require a high degree of redundancy, standby, and dynamic redundancy management. This paper focuses on modeling the warm spares through a numerical approach. An age reduction factor based on failure accumulating effect is proposed to model the warm spare. The model is validated when the input events within the warm spare gate follows the exponential distribution. The proposed method is further applied to a real system.