10.4 Approximation Method
This section presents fast approximation models based on the central limit theorem (CLT) for reliability analysis of 1‐out‐of‐n homogeneous and heterogeneous cold standby systems. Refer to  for the extension of the approximate model to a more general k‐out‐of‐n cold‐standby system requiring k primary and online components. Refer to  for another extension of the approximate method for reliability analysis of warm standby systems.
10.4.1 Homogeneous Cold Standby System
Consider a homogeneous cold standby system with n s‐identical components with A1 being the primary component and A2, …, An being cold standby spares, which are used in the order of their indices. Specifically, when A1 fails at time T1, it is replaced by A2; when A2 fails at time T1 + T2, it is replaced by A3, and so on. The replacement is assumed to happen instantaneously. The time durations T1, T2, … are assumed to be...