Some statistical characteristics of a repairable, standby, human & machine system

This paper presents a model for a 2-unit s-identical system with one operating-unit (OU) online and the other, warm standby-unit (SU) human machine system. The failure rates for both the OU & SU (common-cause, human error, and hardware failures) are constant, whereas the repair times are arbitrarily distributed for a failed system. Linear ordinary differential equations are used to obtain a general expression for system steady-state availability for failed system by taking the repair time distributions as Gamma. Generalized expressions for system reliability, and time-dependent availability are presented. Graphs demonstrate the impact of human error on system steady-state availability for various distributions, and some physical meaning is given. As time increases, the time-dependent availability decreases for exponential repair time distribution for different values of initial human error rate.