Consecutive-k-out-of-n Systems

Runs, scans and URN model distributions: A unified Markov chain approach

“…Recently it has been successfully employed in a lot of diverse areas such as reliability (see Chao et at. (1995) or Papastavridis and Koutras (1994)), DNA sequencing (Arratia and Waterman (1985), Goldstein (1990)), psycholoD~, ecology, radar astronomy (Schwager (1983)) etc.…”

On a waiting time distribution in a sequence of Bernoulli trials

“…Distributions of this type are of substantial interest in radar and safety systems, time-sharing computer networks etc. In reliability theory terminology, the respective tail probabilities are survival probabilities of consecutive-2-within-k-out-of-n reliability structures (see Chao et al (1995), Papastavridis and Koutras (1993)). Also, the conditional tail distribution given the number of successes, is closely related to the generalised birthday problem, Naus (1968), Saperstein (1972).…”

Note: Pairwise rearrangements in reliability structures

“…For the r-within-consecutive-t-out-of-n system (see [9,15,18,191) Papasctavridis and Sfakianakis [16] proved i + 1 > i for 1 5 i 5 min(k -1, n -k ) and i > i + 1 for max(k, n -k + 1) 5 i 5 n -1 and pointed out that these relations cannot be established through Theorem 2.2. Nevertheless they could be easily verified, by making use of our Theorem 2.4.…”