J Syst Sci Syst Eng (Mar 2011) 20(1): 110-118 ISSN: 1004-3756 (Paper) 1861-9576 (Online) DOI: 10.1007/s11518-010-5143-9 CN11-2983/N © Systems Engineering Society of China and Springer-Verlag Berlin Heidelberg 2011 MAINTENANCE OF MULTI-STATE PRODUCTION SYSTEMS DETERIORATED BY RANDOM SHOCKS AND PRODUCTION ∗ Won Seok YANG 1 Dae E. LIM 2 Kyung C. CHAE 3 1 Department of Business Administration, Hannam University, Daejeon, 306-791, Republic of Korea wonsyang@hnu.kr 2 Department of Industrial and Systems Engineering, KAIST, Daejeon, 305-701, Republic of Korea daeeun_lim@kaist.ac.kr () 3 Department of Industrial and Systems Engineering, KAIST, Daejeon, 305-701, Republic of Korea kcchae@kaist.ac.kr Abstract We consider the preventive maintenance of a production system that is deteriorated by random shocks and the production process itself. The degree of deterioration is modeled by discrete and finite states. Shocks arrive according to a Poisson process and deteriorate the system by random amounts. The system may deteriorate whenever it produces an item. The system is continuously monitored and repaired if the system state is at or above a predetermined level for maintenance. We analyze the lifetime, product quantity, average cost, and average profit considering revenue from the product and cost due to setup, operation, and repair. Assuming a structure of system parameters and costs, using numerical examples, we investigate the impact of production and shock arrivals on the average profit and the optimal maintenance level that maximizes the average profit. The proposed model is applicable to manufacturing tasks in which machines wear due to production, for example, press processes, milling, turning, punching, and drilling. Keywords: Multi-state deterioration, random shock, maintenance, cost-benefit analysis ∗ This paper was supported by the 2010 Hannam University Research Fund. 1. Introduction We consider maintenance of a multi-state production system deteriorated by shocks and usage. The system consists of multiple states that represent the production condition. External random shocks and production of items cause the deterioration of the system. The system is repaired if the system deteriorates to a state requiring maintenance. Multi-state deteriorating systems have been studied extensively in cases for which the states represent the relative degree of deterioration. Ohnishi et al. (1986) and Lam & Yeh (1994) considered a stochastic model that either deteriorates to the very next inferior state or suddenly fails due to random shocks in each state. They assumed that sojourn time in a state, termed a state-age, is exponentially distributed.