Stability analysis of a complex standby system with constant waiting and different repairman criteria incorporating environmental failure

• Published in: Applied mathematical modelling Vol. 33; no. 2; pp. 724 - 743
• Main Authors: Wang, Wen-Long, Xu, Gen-Qi
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 01.02.2009; Elsevier
• Subjects: [formula omitted]-semigroup; Applied sciences; Exact sciences and technology; Operational research and scientific management; Operational research. Management science; Positive solution; Reliability theory. Replacement problems; Stability; Standby system; Well-posedness; Standby system; Stability; C 0 -semigroup; Positive solution; Well-posedness; C0-semigroup; Existence of solution; Redundancy; Complex system; Bounded operator; Well posed problem; Functional analysis; Semigroup; Dynamical system; Fracture criterion; Banach space; Linear operator; Steady state; Reliability
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2007.12.008

In this paper we investigate the solution of a complex standby system with constant waiting and different repairman criteria incorporating environmental failure. By using the method of functional analysis, especially, the C 0 semigroup theory of bounded linear operators on Banach space, we prove the well-posedness and the existence of positive solution of the system. Under some appropriate hypothesis, we prove that the dynamic solution of the system converges its steady state in a stronger sense.