Analysis of a two-unit maintained series system with imperfect detection of failures

A two-unit series system with two detectors, one for each unit, is considered. Detectors are subject to two failure modes: not detecting a failed unit and giving false alarms. Failure time, repair-time of units, fault identification time and alarm confirmation time all follow arbitrary distributions. We employ the technique of the semi-Markov process and obtain the steady-state availability and the expected cost rate of the system. A particular case is included.