A Closed-Form Solution for the Number of Minimal s -Cutsequences in a Consecutive- k -out-of- n: F System.

Bollinger and Salvia proposed an approach to study the failure time distribution of a consecutive- k -out-of- n: F system by studying the number of minimal s -cutsequences. They gave recursive equations to compute this number. In this paper we show that the recursive equations have a closed-form solution. Reader Aids: 1) Purpose - Derive exact closed-form solution; 2) Special math needed for explanations - elementary combinatorics and probability; 3) Special math needed to use results - none; and 4) Results useful to - Reliability analysts and theoreticians.