# JIT Production Strategy and Maintenance for Quality Deteriorating Systems
## 1 Introduction
[6], the authors dealt with the problem of joint determination of the optimal lot sizing and production control for an unreliable production system, where the quality control of lots produced was conducted using an acceptance sampling plan. [PERSON] et al. [7] addressed the problem of optimal joint assignment of buffer sizes and inspection station placement for an unreliable transfer line. In their model, the location of one station is fixed to inspect finished parts, while the location of the other station is chosen to optimize the total per unit time average cost. More recently, [PERSON] et al. [8] presented a model for the joint production and repair activity planning for a manufacturing system which produces defectives. In their formulation, they used an intensity control model that allowed them to implement different types of repairs, such as imperfect and minimal repairs. It is evident that quality and production modeling has been demonstrated to provide considerable advantages, as seen in these papers. Nevertheless, maintenance strategies must also be considered in these models, since these three key functions are highly coupled and optimal decisions can only be reached when these functions are captured and addressed simultaneously. The coupling of production and maintenance strategies has been the subject of several studies in recent years. For instance, [PERSON] et al. [9] proposed a framework based on failure mode effect analysis and Petri nets to analyze and predict the uncertain behavior of an industrial system. The authors aim to understand the behavioral dynamics of the system and adapt maintenance practices to improve system reliability and maintainability aspects. The control of production systems subject to maintenance was addressed by [PERSON] et al. [10], where a preventive maintenance plan was provided in order to decrease the failure rate. They took into account the influence of delivery time, and they obtained the optimal delivery and production plans with the corresponding preventive maintenance periods. [PERSON] et al. [11] studied the problem of integrating imperfect preventive maintenance and production planning. They considered the existence of nonconforming items in the produced lots and machine inspection for maintenance and restoration purposes. [PERSON] et al. [12] developed an analytical model in order to determine an integrated maintenance and production plan under a required service level which takes into consideration the influence of the production rate on the failure rate. As can be noted, one drawback of these papers is that their focus has only been on production and maintenance strategies. Nonetheless, manufacturing companies must manage several functional areas successfully in order to ensure efficient coordination and effective decision-making, according to [PERSON] et al. [13]. Furthermore, given the repercussions of deterioration processes on the control strategy, their effects must be minded. In a manufacturing environment, deterioration is a common phenomenon which impacts not only the production system but also may influence the product quality. Therefore, to ensure a rational exploitation of production systems, integrated models must assess the effects of degradation to keep high product quality and performance. Recent years have seen considerable growth in interest in deteriorating systems. For instance, [PERSON] et al. [14] presented a method to determine the optimal production, repair/replacement, and preventive maintenance policies for a deteriorating manufacturing system. In their model, preventive maintenance is available to improve the reliability of the machine. In the same vein, [PERSON] et al. [15] dealt with the combined production and maintenance plans for a deteriorating manufacturing system. They took into account the deterioration of the failure rate according to the production rate of the machine to derive an optimal maintenance schedule. [PERSON] et al.