Let Xn be a random variable enumerating the number of appearances of a specific pattern in a sequence of n Bernoulli trials. A new method is presented for obtaining the conditional distribution of Xn given the number of successes in the n trials. The method is applied to three fixed-length run...

In the present article, we deal with the problem of developing a systematic procedure for evaluating the general reliability bounds developed recently by Fu and Koutras (Statist. Probab. Lett. 22 (1995) 137). More specifically, we prove that, the identification of the optimal bounds can be...

In this article a minimal path upper bound and a minimal cut lower bound on the reliability of a coherent system are derived for the case of independent (but not necessarily identical) components. Coupling these bounds with the classical Esary and Proschan's (1963) bounds, some limit theorems...

Esary and Proschan (1963) proposed a lower bound (resp. upper bound) for the reliability of a general coherent system, which was expressed via system's minimal cut (resp. path) sets. In this article we provide a lower bound based on the minimal path sets and an upper bound based on the minimal...