Improved upper bounds for the reliability of d-dimensional consecutive-k-out-of-n : F systems

• Published in: Naval research logistics Vol. 45; no. 2; pp. 219 - 230
• Main Authors: Godbole, Anant P., Potter, Laura K., Sklar, Jessica K.
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc., A Wiley Company 01.03.1998; Wiley
• Subjects: Applied sciences; Approximation theory; Boundary conditions; d-dimensional consecutive-k-out-of-n : F system; Exact sciences and technology; Janson's exponential inequalities; Mathematical models; Operational research and scientific management; Operational research. Management science; Poisson and compound Poisson approximation; Probability; Reliability theory; Reliability theory. Replacement problems; Stein-Chen method; K out of n system; Upper bound; System reliability; Reliability; Multidimensional model
• ISSN: 0894-069X; 1520-6750
• DOI: 10.1002/(SICI)1520-6750(199803)45:2<219::AID-NAV6>3.0.CO;2-B

Consider a 2‐dimensional consecutive‐k‐out‐of‐n : F system, as described by Salvia and Lasher [9], whose components have independent, perhaps identical, failure probabilities. In this paper, we use Janson's exponential inequalities [5]; to derive improved upper bounds on such a system's reliability, and compare our results numerically to previously determined upper bounds. In the case of equal component‐failure probabilities, we determine analytically, given k and n, those component‐failure probabilities for which our bound betters the upper bounds found by Fu and Koutras [4] and Koutras et al. [6]. A different kind of analytic comparison is made with the upper bound of Barbour et al. [3]. We further generalize our upper bound, given identical component‐failure probabilities, to suit d‐dimensional systems for d ≤ 3. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 219–230, 1998