Distribution of time to failure of consecutive k-out-of n:F systems

It is shown that by modifying the path-evaluation technique due to R.C. Bollinger and A.A. Salvia (1985) it is possible to compute the cumulative distribution function (CDF) of the lifetime of any consecutive k-out-of-n:F system recursively, obtaining it as a mixture of the distributions of the failure times of the various paths. The distribution of the failure time given a path is a convolution of exponential distributions with the distributions of failure times of systems made up of disjoint modules in series, where each module is either a subsystem for which the recursive computation has already been done or an s-coherent system with nonoverlapping min-cut sets whose failure time CDF can be easily found