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A set of general formulas is proposed for the probability of failure ondemand (PFD) assessment of MooN architecture (i.e. k-out-of-n) systems subjectto proof tests. The proof tests can be partial or full. The partial tests (e.g.visual inspections, partial stroke testing) are able to detect only some systemfailures and leave the others latent, whereas the full tests refer to overhaulswhich restore the system to an as good as new condition. Partial tests mayoccur at different time instants (periodic or not), up to the full test. Thesystem performances which are investigated are the system availabilityaccording to time, the PFD average in each partial test time interval, and thetotal PFD average calculated on the full test time interval. Following thegiven expressions, parameter estimations are proposed to assess the systemfailure rates and the partial test effectiveness according to feedback datafrom previous test policies. Subsequently, an optimization of the partial teststrategy is presented. In the 2oo6 system given as example, an improvement ofabout 10% of the total PFD average has been obtained, just by a better(non-periodic) distribution of the same number of partial tests, in the fulltest time interval.

Probability of Failure of Safety-Critical Systems Subject to Partial Tests