Availability and maintenance of series systems subject to imperfect repair and correlated failure and repair

• Published in: European journal of operational research Vol. 174; no. 3; pp. 1706 - 1722
• Main Authors: Wang, Hongzhou, Pham, Hoang
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2006; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Availability; Control systems; Correlated failure and repair; Exact sciences and technology; Failure; Imperfect repair; Maintenance; Maintenance costs; Operational research and scientific management; Operational research. Management science; Optimization; Reliability; Reliability theory. Replacement problems; Repair & maintenance; Series system; Studies; Systems management; Availability; Imperfect repair; Series system; Maintenance; Correlated failure and repair; Stopping time; Renewal process; Maintenance cost; Reliability theory; System reliability; Mean time between failures; Break up time; System maintenance; Repair
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2005.03.030

The series system is one of the most important and common systems in reliability theory and applications. This paper investigates availability, maintenance cost, and optimal maintenance policies of the series system with n constituting components under the general assumption that each component is subject to correlated failure and repair, imperfect repair, shut-off rule, and arbitrary distributions of times to failure and repair. Imperfect repair is modeled through the basic idea of the quasi renewal processes introduced by H. Wang, H. Pham, A quasi renewal process and its applications in imperfect maintenance, International Journal of Systems Science 27(10) (1996) 1055–1062; 28(12) (1997) 1329. System availability, mean time between system failures, mean time between system repairs, asymptotic fractional down time of the system, etc., are derived, and a numerical example is presented to compare with the existing models by R.E. Barlow, F. Proschan, Satistical Theory of Reliability of Life Testing, Holt, Renehart & Winston, NY, 1975. Then two classes of maintenance cost models are proposed and system maintenance cost rates are modeled. Finally, properties of system availability and maintenance cost rates are studied. Optimization models to optimize system availability and/or system maintenance costs are developed, and optimum system maintenance policies are discussed through a numerical example.