سیاست های تعمیر و نگهداری پیشگیرانه برای محصولات استیجاری تحت هزینه های نگهداری مختلف

This paper investigates the effects of preventive-maintenance cost functions on the optimal preventive-maintenance policy for a leased product with Weibull life-time distribution. During the lease period, any product failures are rectified by minimal repairs and may incur a penalty to the lessor, if the time duration for performing a minimal repair exceeds a pre-specified time limit. To reduce repair costs and possible penalty, preventive-maintenance actions are scheduled in the lease contract. The objective of this paper is to derive the optimal preventive-maintenance schedule and maintenance degrees such that the expected total cost is minimized. Some structural properties of the optimal policy are obtained and an efficient algorithm is provided to search for the optimal policy. For the cases where the preventive maintenance cost is a constant or a linearly increasing function, the effects of the preventive-maintenance cost function on the optimal policy are investigated in detail both theoretically and numerically.

This paper derives the optimal preventive-maintenance policy for a leased product with Weibull life-time distribution and investigates the effects of preventive-maintenance cost function on the optimal policy. Due to the increase in complexity of products/systems and rapid advances in technological innovation, performing maintenance actions for such complex products now requires expensive equipments and special professional technicians, which is not economical for a company to keep. Therefore, there is a trend to lease products instead of owning them (Desai and Purohit, 1998 and Fang and Huang, 2008). For a leased product, the maintenance actions are usually provided by the lessor (the one who owns the product) and specified in a lease contract to ensure that the product could fulfill its intended performance requested by the lessee (the one leasing the product). In general, there are two types of maintenance considered in a lease contract – corrective maintenance (CM) and preventive-maintenance (PM). CM actions are employed to rectify failed products back to operational status, and PM actions are used to improve the operational status of a product to avoid failures (Barlow and Hunter, 1960 and Valdez-Flores and Feldman, 1989). The articles in Dekker, 1996, Dekker and Scarf, 1998, Pieskalla and Voelker, 1976, Sherif and Smith, 1981 and Valdez-Flores and Feldman, 1989 are excellent reviews of maintenance models for products subject to stochastic failures. In developing a maintenance model, minimal repair is the most commonly used corrective maintenance action to restore a failed product (Nakagawa, 1981 and Nakagawa and Kowada, 1983), since the failure rate of the product remains unchanged after performing a minimal repair. Various maintenance models involving minimal repair can be found in Boland and Proschan, 1982, Nakagawa, 1981, Nakagawa and Kowada, 1983 and Sheu, 1991. For a leased product, minimal repairs are carried out by the lessor to restore a failed product back to its operational condition. When the time required to perform a minimal repair exceeds a pre-specified amount of time, there is a penalty to the lessor to compensate the loss to the lessee. Therefore, there is a need for the lessor to provide some remedial measures to avoid the costs of minimal repairs and penalty incurred by product failures. To reduce the number of product failures and possible penalties within the lease period, PM actions are widely employed since the cost for carrying out a planned PM action is usually less than the cost incurred by a product failure. Various PM models have been proposed for different situations such as perfect or imperfect PM (Barlow and Hunter, 1960, Jack and Dagpunar, 1994 and Pham and Wang, 1996), and periodical or sequential PM (Chun, 1992, Jack and Dagpunar, 1994 and Yeh and Lo, 2001). For the imperfect PM, the maintenance degree for each PM action is characterized by age-reduction or failure rate-reduction methods (Barlow and Hunter, 1960 and Pham and Wang, 1996). Using the age-reduction method, the age of the product after taking a PM action becomes a certain amount of time younger than before. On the other hand, using the failure rate-reduction method, the failure rate of the product is reduced by a certain amount after a PM action. In this paper, the age-reduction method is adopted since it is easily measured and implemented in practice. Using the age-reduction method, a mathematical cost model is developed and the optimal PM policy is derived such that the expected total cost in the lease period is minimized. Furthermore, the effects of the PM cost function on the optimal PM policy are investigated in detail. The remainder of this paper is organized as follows. The mathematical model is developed in Section 2 for the case when the failure density is Weibull. In Section 3, the properties of the optimal PM policy are investigated, and an efficient algorithm is provided for searching the optimal policy when PM cost is a general function of the maintenance degree. Furthermore, closed-form solutions of the optimal policy are obtained for the special case when PM cost function is constant or linearly increasing. The performance of the optimal PM policy is evaluated through numerical examples in Section 4. Finally, some conclusions are drawn in the last section.

In this paper, we derive the optimal PM policy for a leased product with Weibull life-time distribution. Under the age-reduction maintenance scheme, we focus on investigating the effects of the PM cost function on the optimal PM policy. Given a general PM cost function, we show that there exists an unique optimal policy such that the expected total cost during the lease period is minimized. Under the optimal policy, PM actions are carried out at time epochs x∗, 2x∗, 3x∗, … , n∗x∗ with same maintenance degree x∗. An efficient algorithm is provided in this paper to search for the optimal policy (n∗, x∗) when β > 1. Furthermore, when the PM cost function is constant, C p(x ) = a > 0, we found that the optimal policy is a periodical PM policy. That is, PM actions should be performed at time epochs View the MathML sourceLn∗+1,2Ln∗+1,3Ln∗+1,…,n∗Ln∗+1 with same maintenance degree View the MathML sourceLn∗+1. And, the optimal number of PM actions n∗ decreases as the PM cost increases. However, when the PM cost linearly increases as the maintenance degree increases, i.e., Cp(x) = a + bx, we found that the PM actions are performed periodically at the beginning of the lease period and it is not worthwhile to perform any PM actions near the end of the lease period. The numerical results also show that n∗ decreases as the marginal cost b increases.