Stochastics and Statistics Availability and maintenance of series systems subject to imperfect repair and correlated failure and repair Hongzhou Wang a, * , Hoang Pham b a Bell Labs, Lucent Technologies, Holmdel, NJ 07733, USA b Department of Industrial Engineering, Rutgers University, Piscataway, NJ 08854, USA Received 21 June 2002; accepted 15 March 2005 Available online 23 June 2005 Abstract 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 com- ponents 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 imper- fect maintenance, International Journal of Systems Science 27(10) (1996) 1055–1062; 28(12) (1997) 1329. System avail- ability, 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. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Availability; Series system; Imperfect repair; Correlated failure and repair; Maintenance 1. Introduction The series system is one of the most important and common systems in reliability theory and applica- tions. Barlow and Proschan [1] studied the availability of the series system given that the repair at failure 0377-2217/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.03.030 * Corresponding author. Tel.: +1 973 386 7527; fax: +1 240 358 4606. E-mail address: hongzhou@lucent.com (H. Wang). European Journal of Operational Research 174 (2006) 1706–1722 www.elsevier.com/locate/ejor