Reliability Evaluation when Redundant Sub-systems
As pointed out on Introduction, little consideration has been given so far to the modelling of systems in which redundant sub-systems are repaired prior to system failure. This omission will now be addressed, but only insofar as a brief summary of some of the associated formulae and conditions of use will be given. This topic can become quite complex from an analytical point of view; however, no attempt will be made here to give any proofs because they are covered extensively in reliability engineering literature.
Firstly, consider a two sub-system active redundant system; then, consider a system comprising one active sub-system and one cold standby sub-system.
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The use of the word cold indicates that the standby is not energised (and hence for this example cannot fail) until it is required to be used.
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For convenience, we will assume both sub-systems have the same failure rate (λ) and repair rate (μ). Assume also that both λ and μ are constant with time and that λ<<μ. The reciprocals of theses quantities are the Mean Time to Failure (MTTF or ) and Mean Time to Repair (MTTR or τ) respectively.