From Reliability Engineering Handbook, Volume 2
3.1 WHAT IS A STANDBY SYSTEM?
A system is said to have units which are reliability wise in stand by when there is an active unit or subsystem to which are attached units or subsystems which stand by idly during the mission, either in a quiescent, nonoperating or warm-up mode, until they are called upon to operate at the specified output level by a sensing and switching subsystem when the active unit or subsystem, which operates from the start of the mission, fails before the mission is completed. The function of the sensing subsystem is to detect a failure in the active unit or subsystem and command the switching subsystem to switch in the standby unit or subsystem.
This is unlike the reliabilitywise parallel system in which all units start to operate simultaneously at the beginning of the mission, and the system succeeds when at least one unit is left which completes the mission successfully.
3.2 RELIABILITY OF A TWO-UNIT STANDBY SYSTEM
A two-unit standby system succeeds when ;(1) the active unit does not fail, the sensing subsystem does not fail, and the switch does not fail open during the mission, or (2) the active unit fails before the end of the mission, the sensing and switching subsystems do not fail, and the standby unit not having already failed succeeds for the remainder of the mission. The reliability block diagram of such a standby system is shown in Fig. 3.1. Probabilistically, the reliability of this system is the probability that
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