On a class of multiple failure mode systems

Abstract

The primary objective of this work is to introduce and perform a detailed study of a class of multistate reliability structures in which no ordering in the levels of components' performances is necessary. In particular, the present paper develops the basic theory (exact reliability formulae, reliability bounds, asymptotic results) that will make it feasible to investigate systems whose components are allowed to experience m ≥ 2 kinds of failure (failure modes) and their breakdown is described by different families of cut sets in each mode. For illustration purposes, two classical (binary) systems are extended to analogous multiple failure mode structures and their reliability performance (bounds and asymptotic behaviour) is investigated by numerical experimentation.

Reliability Properties of $(n,f,k)$ Systems

“…In addition, if denotes the generating function of the sequence , then can be expressed as (2) where denotes the element of the adjoint of matrix . Therefore, should one be able to evaluate the last entry of the first row of the matrix , it is then immediate to get a formula for the generating function of the reliability of the structure.…”

“…[25], and Fu and Koutras [15]), and the consecutive -out-of system with maintenance (Papastavridis and Koutras [29]). The so-called multi-state consecutive -out-of structure, where both the system and its components are allowed to work in more than 2 operational modes, has also attracted some research interest (see, e.g., Koutras [24], Boutsikas and Koutras [2], Yamamoto et al [37]). For a survey on the consecutive -out-of systems and their generalizations, refer to Chao et al [5], and the more recent article by Eryilmaz [11]; or to the excellent monographs by Kuo and Zuo [26], and Chang et al [4].…”

Joint Distributions of Numbers of Runs of Specified Lengths in a Sequence of Markov Dependent Multistate Trials

“…, k ν -out-of-n:MFM system. According to Boutsikas and Koutras (2002), the consecutive k 1 ,k 2 , . .…”

Start‐up demonstration tests: models, methods and applications, with some unifications

“…Clearly, this framework is a generalization of the sooner waiting time problem, in which the first occurrence of one of a set of simple patterns is studied, as described earlier in Section 3.1.2. The nature of multistate start-up demonstration tests is also directly related to problems from the general theory of waiting times of patterns on multistate trials or the multiple failure mode reliability theory; see Schwager [65], Satoh et al [66], Fu [67], Koutras [68], Koutras and Alexandrou [31], Han and Aki [69], Antzoulakos [70], Boutsikas and Koutras [71], Vaggelatou [72], Milienos and Koutras [73] and Eryilmaz [25] for further details in this regard.…”

“…In Section 3.1.5, we discussed the recent unified approach of Balakrishnan et al [43] in which the class of binary start-up demonstration tests is studied under a very general framework by using the families of sets P and C . Here, we make use of the theory of multiple failure mode reliability systems [71,73] to study the case of multistate start-up tests under a similar unifying framework.…”