The Inversion of Sets being Decisive of System Reliability : A new method and its programming
The dependence of system failure on the failures of compponents can be described by the set of the systems cut sets. Similarly the relationship between the functioning of a system and that of its components is given by the set of its path (tie) sets. If you are for instance interested in the failure mode of a systern (perhaps in search of its weak points) and the set of its path sets is known, you have to derive the set of the systems cut sets from it. As the structural redundancy of a system is uniquely determined by each of the two sets rnentioned above, anyone of them can serve to compute characteristic values of system reliability from corresponding values of its components. The smaller the fundamental sets, the simpler and shorter the computation becomes. Therefore it is expedient anyway with the exception of trivial cases to derive the set that corresponds to the given or elaborated set and to choose the smaller one. The derivation of one set from the other is called inversion. The method of inversion described in this paper has been programmed in PASCAL as a systematic and bounded searching algorithm. The presentation of a longer and structured version of this program enables the interested user to understand it and to change it as required, to translate it into another language etc. The included short form may serve for a quick copy and an easy distribution of the program.
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