Algorithms for Strict Consecutive-k-out-of-n:F Systems

A recursive formula is given for calculating the failure probability for consecutive-k-out-of-n:F systems such that isolated strings of failures of length less than k (which do not cause system failure) do not occur, or are immediately corrected; ie, when system failure occurs it is because all failures present are in strings of length at least k. For the i.i.d. case an exact formula is given for the failure probability of the system.