A short Boolean derivation of mean failure frequency for any (also non-coherent) system

Winfrid G. Schneeweiss

Reliability Engineering and System Safety, 2009, vol. 94, issue 8, 1363-1367

Abstract: For stationary repairable systems it is shown that the probabilistic weights for the individual components’ mean failure frequencies (MFFs) that can be added to yield the system's MFF are found easily from the first step of the Boolean fault tree function's Shannon decomposition. This way one finds a general theory of a system's MFF and the case of coherence covered in standard textbooks is shown to be a subcase. Unfortunately, elegant rules for calculating system MFF from any polynomial form of the fault tree's Boolean function are only known for the coherent case, but repeated here, because they are not yet found in many textbooks. An example known from literature is treated extensively with great care.

Keywords: Mean failure frequency; Non-coherence; BDD; Shannon decomposition; Fault tree; Boolean algebra; Boolean difference (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:94:y:2009:i:8:p:1363-1367

DOI: 10.1016/j.ress.2008.12.001

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