Abstract
Abstract : In this report we consider different shut-off rules for series systems performance. We calculate limiting system availability under various shut-off rules. In particular, availability results for 2 and 3 unit systems with all failure and repair distributions exponential are extended to systems of arbitrary size. Consider a series of system of n components. System failure in such systems coincides with component failure. However, in many systems components can still be functioning after system failure occurs, or some components on failure will shut off others. This means that some shut-off rules can be established for system performance, such as failure of first component shuts off the second and next components or failure of second component shuts off third and higher components but not the first and so on. For example, in a 3-unit system, unit 1 on failure shuts off both unit 2 and 3, unit 2 on failure shuts off only unit 3, but not 1, and units 1 and 2 are not affected when failure of unit 3 occurs.
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