Consider a 2-dimensional consecutive-k-out-of-n:F system, as described by Salvia and Lasher, whose components have independent, perhaps identical, failure probabilities. In this paper, we use Janson's exponential inequalities 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 and Koutras et al. A different kind of analytic comparison is made with the upper bound of Barbour et al. We further generalize our upper bound, given identical component-failure probabilities, to suit d-dimensional systems for d ≥ 3.
