The Theory of Delayed Repair for all Systems with 2 or 3 Components
This is a report on the derivation of the probability distribution of residual life time after certain (hardware) component failures. For redundant systems, typically fault tolerant computers, it may be necessary or economical to start repairs only after certain tolerable faults, knowing that in most cases repairs will be finished prior to system failure. In such cases the distribution function of residual life is the probability of not meeting this goal. All systems with 2 or 3 components are discussed at length to give 1) easy to understand results for such simple systems, 2) many examples to test more general methods. Complete results are given for the case of s-independent components, especially for the exponential case, and for cold standby, where appropriate. For the general case of s-dependent components, a general approach is outlined and shown to work with two selected examples.
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