Reliability of linear and circular consecutive-\(k\)-out-of-\(n\) systems with shock model. (English. French summary) Zbl 1327.62495

Belaloui, Soheir; Bennour, Besma

Afr. Stat. 10, 795-805 (2015).

Summary: A consecutive \(k\)-out-of-\(n\) system consists of an ordered sequence of \(n\) components, such that the system functions if and only if at least \(k\) \((k\leq n)\) consecutive components function. The system is called linear (\(L\)) or circular (\(C\)) depending on whether the components are arranged on a straight line or form a circle. In the first part, we use a shock model to obtain the reliability function of consecutve-\(k\)-out-of-\(n\) systems with dependent and nonidentical components. In the second part, we treat some numerical examples to show the derive results and deduce the failure rate of each component and the system.

MSC:

62N05	Reliability and life testing
68M15	Reliability, testing and fault tolerance of networks and computer systems
68M20	Performance evaluation, queueing, and scheduling in the context of computer systems
90B25	Reliability, availability, maintenance, inspection in operations research
60K10	Applications of renewal theory (reliability, demand theory, etc.)

Keywords:

linear and circular consecutive-\(k\)-out-of-\(n\) system; reliability function; failure rate; shock model