سیاست های بهینه تعمیر و نگهداری پیشگیرانه برای تجهیزات استیجاری با استفاده از کاهش نرخ خرابی

This study proposes a maintenance scheme for leased equipment using failure rate reduction method and derives an optimal preventive maintenance (PM) policy that minimizes expected total cost. Under the proposed maintenance scheme, the lessor (equipment owner) rectifies failures with minimal repairs within the lease period, and the lessor may incur a penalty when repair time exceeds a time limit as specified in the lease contract. To reduce the expected total cost, the lessor may employ PM actions to decrease the number of possible failures. In this study, an efficient algorithm is developed to derive the optimal PM policy and a closed-form solution is obtained for the case where the lifetime distribution of the equipment is Weibull. The expected total cost using the optimal PM policy under the proposed maintenance scheme is then compared with the performance of other policies under various maintenance schemes through numerical examples.

Most businesses require various types of equipment to manufacture their products or to provide service for customers. Due to rapid technological innovations, increased complexity of equipment, and the cost of professional technicians required to maintain equipment, it may not be economical for these businesses to own certain equipment. Therefore, there is a trend toward leasing instead of buying equipment (Glickman and Berger, 1976 and Nisbet and Ward, 2001). For leased equipment, the maintenance of the equipment is usually specified in a lease contract provided by the lessor (equipment owner) to ensure that the equipment could fulfill its intended purpose (Barlow & Hunter, 1960). As a result, the equipment was bundled with maintenance and offered by the lessor under a leased contract (Martin, 1997 and Murthy and Asgharizadeh, 1999). In general, two types of maintenance actions are considered in a lease contract – corrective maintenance (CM) and preventive maintenance (PM). Corrective maintenance rectifies failed equipment back to its operational status, whereas PM improves the operational status of the leased equipment, thereby decreasing the likelihood of equipment failure. There is a vast literature dealing with maintenance policies (Barlow and Hunter, 1960, Chun, 1992, Glickman and Berger, 1976, Jack and Dagpunar, 1994, Jaturonnatee et al., 2006, Murthy and Yeung, 1995, Nakagawa, 1981, Nguyen and Murthy, 1988, Pham and Wang, 1996, Pongpech and Murthy, 2006, Seo and Bai, 2004, Sheu et al., 2006, Wang, 2002, Yeh and Chen, 2006 and Yeh and Lo, 2001). In practice, minimal repair is the most commonly performed CM when restoring failed equipment (Nakagawa, 1981 and Nakagawa and Kowada, 1983). Following minimal repair, the equipment is operational; however, the failure rate remains unchanged. When the time needed for minimal repair exceeds the limit specified in the lease contract, the lessor might incur a penalty since it may cause serious damage to the lessee (equipment user). Therefore, a lessor must undertake some remedial measures to avoid costs incurred by equipment failures. Most lessors undertake PM to reduce the number of equipment failures within the lease period. Preventive maintenance is a tradeoff between PM costs and failure costs. Usually, as PM is planned, the cost of PM is less than the cost incurred when equipment fails. Numerous PM policies have been proposed and studied under various situations, such as perfect or imperfect maintenance (Brown and Proschan, 1983, Jack and Dagpunar, 1994, Jaturonnatee et al., 2006, Pham and Wang, 1996 and Sheu et al., 2006), age reduction or failure rate reduction (Chan and Shaw, 1993, Jaturonnatee et al., 2006, Nakagawa, 1981 and Pongpech and Murthy, 2006), and periodical or sequential maintenance (Chun, 1992, Jack and Dagpunar, 1994, Pongpech and Murthy, 2006, Seo and Bai, 2004, Yeh and Chen, 2006 and Yeh and Lo, 2001). Jaturonnatee et al. (2006) developed a sequential PM scheme using failure rate reduction that considers the number of PM actions, PM degree, and time epochs simultaneously. Their maintenance scheme is very general but not easy to implement in practice. For practical needs, Pongpech and Murthy (2006) reduced Jaturonnatee’s scheme to a periodical PM scheme in which the PM actions are carried out periodically with various maintenance degrees. Since this maintenance scheme is a special case of Jaturonnatee’s scheme, the resulting performance is not as good as Jaturonnatee’s. This study proposes a maintenance scheme, in which preventive maintenance actions are taken to reduce the failure rate of the leased equipment by the fixed amount specified in the lease contract. We employ a different approach to simplify Jaturonnatee’s scheme. Under our approach, the PM actions are performed sequentially with a fixed maintenance degree. As we will see later on, the performance of the proposed maintenance scheme is better than Pongpech’s scheme and is close to that of Jaturonnatee’s scheme. The remainder of this paper is as follows. The mathematical model of the proposed maintenance scheme is developed in Section 2. In Section 3, the optimal PM policy is examined and an efficient algorithm is proposed for leased equipment with general lifetime distributions. In Section 4, the optimal PM policy is derived and a reduced algorithm is proposed for the Weibull lifetime distribution. The performance of PM is evaluated via numerical examples, the expected total cost is compared with two other maintenance schemes (Jaturonnatee et al., 2006 and Pongpech and Murthy, 2006), and some practical applications are given in Section 5. Finally, conclusions are drawn in Section 6.

Under the failure rate reduction method, this study proposes a maintenance scheme for leased equipment and derives the optimal PM policy for leased equipment. Some structural properties of the optimal policy are obtained, and an efficient algorithm is developed based on these properties. Furthermore, a closed-form solution is obtained for the case where the lifetime distribution of the equipment is Weibull. From the numerical examples of the Weibull case, we found that the performance of the optimal policy with fixed maintenance degree is better than with fixed maintenance interval (periodical policy). Furthermore, when the lease period is relative long, the PM actions should be performed within the leased period since the expected cost can be reduced significantly. In this paper, the uniqueness property of the optimal PM policy is obtained for the case when the lifetime distribution is a general distribution. However, for some generalizations of this maintenance scheme, the uniqueness property might not hold or the conditions for the existence of the optimal policy might be very complicated. Some possible generalizations, such as nonlinear maintenance cost, time-dependent penalty cost, or various penalty schemes, are extended issues for the future study in this area.