Efficient analysis of warm standby systems using central limit theorem

In a warm standby sparing system, the standby units have time-dependent failure behavior; they have different failure parameters or in general distributions before and after they are used to replace the on-line faulty units. Such time-dependent behavior makes the reliability analysis of warm standby system a challenging task. Existing approaches to analyzing the reliability of warm standby systems include Markov-based methods, simulation-based methods, and combinatorial me thods. Those approaches, however, have one or more of the following limitations: 1) requiring long computation time especially when results with high degree of accuracy are desired, 2) requiring exponential time-to-failure distribution for system components, and 3) involving difficult tasks of computing convolution of multiple integrals. In this paper, based on the central limit theorem, a computationally-efficient approximate method is proposed for the reliability analysis of warm standby systems. The proposed approach has no limitation on the time-to-failure distributions for the system components. Several case studies using different time-to-failure distributions and system sizes are performed to demonstrate the application of the proposed approach.