Optimal-arrangement and importance of the components in a consecutive- < e1 > k < /e1 > -out-of- < e1 > r < /e1 > -from- < e1 > n < /e1 > :F system

• Published in: IEEE transactions on reliability 1991-08, Vol.40 (3), p.277-279
• Main Authors: Papastavridis, S G, Sfakianakis, M E
• Format: Article
• Language: English
• ISSN: 0018-9529
• DOI: 10.1109/24.85439

The authors examine: the determination of an optimal consecutive < e1 > k < /e1 > -out-of- < e1 > r < /e1 > -from- < e1 > n < /e1 > :F system, under permutations of the components, and the Birnbaum-importance of components in the i.i.d. case. The authors first study (theorem 1) the optimality of a general system, with not necessarily < e1 > s < /e1 > -identical components, under permutation of the components. Then they study (theorem 2) the importance of components in the i.i.d. case. Theorem 2 is readily derived from theorem 1. The main results are given in theorems 1 and 2, and proofs are given. The assumptions are: the system and each component are either good or failed: all binary component states are mutually statistically independent, and all < e1 > n < /e1 > can be arranged in any linear order; and the system fails if and only if within < e1 > r < /e1 > consecutive components, there are at least < e1 > k < /e1 > failed ones