Improved upper bounds for the reliability of d‐dimensional consecutive‐k‐out‐of‐n : F systems
利用Janson指数不等式，为二维及更高维连续k-out-of-n:F系统推导出更紧的可靠性上界，并通过数值和解析比较验证其优于现有上界。
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.