Erik E. Kostandyan, Leonard R. Lamberson, and Azim Houshyar

k parallel r-out-of-n systems, maximum ordered random variable, Beta distribution, Weibull distribution

A “k parallel r-out-of-n:F" system is structured with “k" parallel subsystems where each subsystem will function if at least “r" out of “n" components function within each subsystem. The time-to- failure distribution for “k parallel r-out-of-n:F" systems is developed providing for both the probability density function and cumulative distribution function. This allows one to ﬁnd any quantile of the time-to-failure distribution to predict when the system should fail for a given probability level. The method is easy to implement using a well-known spreadsheet function for the Beta distribution.

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