A recursive algorithm evaluating the exact reliability of a consecutive κ-within- m-out-of- n:F system

Abstract

A consecutive κ-within- m-out-of- n:F system consists of n linearly ordered components e 1,3. e n . The system fails if among any m subsequent components there are k or more failed ones. A recursive algorithm is presented evaluating the reliability of the system whose components are independent and have unequal failure probabilities. This algorithm is computer implementable for “not too large m” (e.g. m ≤ 15 for PC machines).