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

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 systemʹs MFF are found easily from the first step of the Boolean fault tree functionʹs Shannon decomposition. This way one finds a general theory of a systemʹs 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 treeʹs 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.