Analysis of the deviation of the nonstationary availability factor of a restorable system from its stationary value (Q1974337)

Consider a restorable system with a monotone structure consisting of \(m\) independent elements having exponential time-to-failure with constant failure rates of elements \(\{\lambda_i\}\). The number of channels and the restoration procedure of the failed elements may be arbitrary. The expected values of the restoration times are finite. A criterion (for example, a structure function) is given allowing to establish whether the current state of the system is a failure. Denote by \(K(t)\) the nonstationary availability factor, i.e., the probability that the system is serviceable at the moment \(t\). The authors develop a method that allows accurate estimation of the deviation \(K(t)- K(\infty)\), i.e., the difference between the nonstationary availability factor and its stationary value, and, thefore, the rate of reaching the stationary state by the system. A numerical example is also given.