Assuming that the joint distribution of the lifetimes of online unit and standby unit and the repair time of a failed unit in a two unit warm standby system is trivariate exponential, measures of system performance such as system reliability, MTBF, point availability and steady state availability are obtained. see Marshall and Olkin (J Amer Statist Assoc 62:30–44, 1967). Further, a 100(1-α) % asymptotic confidence interval for steady state availability of the system and an estimator of system reliability based on moments are obtained. Numerical work is carried out to illustrate the behaviour of steady state availability as well as the system reliability based on moments by simulating samples from trivariate exponential distribution.
Steady state availability Standby system Multivariate central limit theorem Slutsky theorem