Time to Failure and Availability of Paralleled Systems with Repair

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Abstract
This paper discusses reliability properties of some simple paralleled or redundant systems, where repair is possible in case of failure. We are assuming here that a ``failure'' may always be instantly identified, and the appropriate steps taken. In certain problems such an assumption is not warranted. The ``systems'' discussed are composed of two identical ``subsystems,'' e.g., computers, or radars, and the system is considered to be in a state of failure when, and only when, both subsystems are simultaneously in such a state. Such system design strategies have been proposed for various applications, but have received little analysis. Two measures of reliability are discussed: 1) the time to system failure, measured from an instant at which both subsystems are operative, and 2) the long-run availability of the system, where the latter means the average fraction of the time during which the system is able to perform its function. Analysis is based on the assumption of ``random'' (Poisson-like) failure for the subsystems (for theoretical justification see Drenick [2]), and independent but otherwise arbitrarily distributed repair times. It is of some interest that several of the important operational measures deduced, depend in detail upon the form of the distribution of repair times, as it is summarized in its Laplace transform, and not simply upon certain simple averages or moments of repair time.

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