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Availability of a Special 2-unit Series System

This paper deals with some availability problems of a special 2-unit series system. The purpose is threefold: 1) To point out an interesting, practical situation of 2-unit series system in which failure of one unit shuts off the other, but not vice versa. 2) To dispel an erroneous notion that all availability expressions, ranging from the one extreme of `neither shutting off the other at failure' to the other extreme of `both shutting off the other at failure', depend only on the means of the random quantities involved. A case is shown where the availability depends on the Laplace transform of a distribution as well as on the means. 3) To establish the credibility of the two extreme cases as the tight upper and lower bounds for the intermediate cases in most practical applications. All random variables are assumed s-independent. The solution uses supplementary variables.