This study applies periodic preventive maintenance (PM) to a repairable production system with major repairs conducted after a failure. This study considers failed PM due to maintenance workers incorrectly performing PM and damages occurring after PM. Therefore, three PM types are considered: imperfect PM, perfect PM and failed PM. Imperfect PM has the same failure rate as that before PM, whereas perfect PM makes restores the system perfectly. Failed PM results in system deterioration and major repairs are required. The probability that PM is perfect or failed depends on the number of imperfect maintenance operations conducted since the previous renewal cycle. Mathematical formulas for expected total production cost per unit time are generated. Optimum PM time that minimizes cost is derived. Various special cases are considered, including the maintenance learning effect. A numerical example is given.
Production policies have been investigated extensively with the aim of minimizing production costs [1], [2], [3], [4] and [5]. To be globally competitive, manufacturers must have a cost-effective policy that considers operating costs and the effects of restorative activities, such as repairs and preventive maintenance (PM), on damaged production systems. Maintenance is conducted when equipment fails or as planned PM. This maintenance process requires planning, scheduling, control and deployment of maintenance resources. Devarun and Sandip [6] presented a multiple-criteria decision making methodology for selecting the optimal policy in the process industry. Sheu [7] evaluated maintenance policies in deteriorating production models. Lin et al. [8] examined maintenance and production and applied an imperfect production model to decrease the number of defects.
Notably, PM, which maintains production systems in top operating conditions, is performed regularly at pre-determined intervals to minimize operating costs and risk of catastrophic failure. A sequential PM policy requires that PM is performed at unequal intervals [9] and [10]. Bartholomew-Biggs et al. [11] examined the problem of scheduling sequential imperfect PM of some equipment. Whereas a PM is performed at fixed time intervals with a periodic PM policy [12]. The perfect PM model restores a system to “as good as new” after each PM action. Tseng [13] developed a perfect maintenance policy that increases the reliability of imperfect systems. Notably, imperfect PM models assume that, after PM, system failure rate is “as bad as before PM” [14], [15] and [16]. The imperfect PM model developed by Nakagawa and Yasui [17] proposes that a PM model under which PM is either imperfect or perfect maintenance with probabilities of p and 1 − p, respectively. However, the assumption of imperfect PM is not always true. In this study, we assume the probability of PM being perfect is related to the number of imperfect maintenance operations performed since the previous renewal cycle, and the probability of PM remaining imperfect does not increase.
Failed production system must be repaired. Cui et al. [18] considered random failure of production equipment inevitable. In response to each failure, a system is repaired and maintenance costs are minimized. Major repairs reset system failure incidence (since such repairs are perfect) and the system is restored to “as good as new”. Numerous protective systems, such as circuit breakers, alarms, and protective relays, are maintained in this fashion, as described by Yang and Klutke [19].
In some cases, damage occurs following PM for human error in maintenance [20] and [21]. To model this phenomenon, this study considers three outcomes, similar to those proposed by Nakagawa and Yasui [17]. Outcome I involves imperfect PM only; outcome II involves perfect PM; and outcome III involves failed PM and a system requires major repairs. The remainder of this paper is described as follows. The cost of the production maintenance model with periodic PM is determined and an optimum policy is obtained in Section 2. Section 3 describes various special cases. Section 4 then provides a numerical result for these special cases. This study investigates the effects of these parameters on solutions. Finally, Section 5 presents concluding remarks.
This study presented a novel cost model that considers maintenance policies for a system for which PM types can be divided into imperfect PM, perfect PM and failed PM. This study analyzed how PM and repair actions impact system cost and conditions. The character of a PM process and policy facilitated generation of the hypothesis that probability of attaining perfect or failed PM depends on the number of imperfect PM actions performed since the previous renewal cycle. Analytical results of investigating optimal policy conditions demonstrate that such a policy is more general and flexible than policies proposed in literature. Special cases were examined in detail. Optimum time T∗ was identified for special cases, with reference to an example. Analytical results demonstrate the effects of input parameters on solutions. When the learning rate is estimated based on actual data, analysts can use learning curves to estimate PM costs. This information is also a valuable reference for estimating training requirements and developing PM plans. This work can be applied to machine learning. For example, historical maintenance data can be used to identify failure behavior via machine learning (data mining) and determine the optimal maintenance policy that reduces total cost.
