# JIT Production Strategy and Maintenance for Quality Deteriorating Systems
## 1 Introduction
[16] proposed an imperfect maintenance optimization model, where the system considered was assumed to be continuously monitored and subject to stochastic degradations. The objective of their model consisted of finding the optimal number of preventive maintenance actions to maximize the average availability of the system. In [PERSON] et al. [17], an optimal production plan considering the degradation of a manufacturing system following its production rate and its availability was introduced. To ensure the satisfaction of the demand, a second manufacturing system with a stochastic service level was available as production support. Indeed, the growing importance of deteriorating systems has led to an increasing interest in the development of optimization models in this domain, as observed in the presented papers. It should be highlighted that the literature has traditionally addressed availability deterioration. Nevertheless, the industrial reality shows that deterioration also impacts product quality and so it must be integrated into the decisions. Unfortunately, given the complexity of these stochastic degrading systems, alternative resolution methods such as simulation techniques are justified, since analytical solutions are cumbersome to obtain. A significant branch of the literature has applied simulation techniques to analyze unreliable manufacturing systems, since they allow us to reproduce their set of dynamics and stochastic behavior, and also because such techniques permit us to include more realistic considerations of industrial production units. For example, [PERSON] et al. [18] proposed a simulation modelling approach to address the production control problem of an unreliable manufacturing system, where, due to availability fluctuations, such machines fall short of meeting the long-term demand rate. Thus, a reserve machine is called upon for support if the finished product inventory level drops below a specific degree. In the same direction, [PERSON] et al. [19] proposed a simulation model for the joint preventive maintenance and production control policy of an unreliable production system. They compared different maintenance strategies. Another simulation model was introduced by [PERSON] et al. [20] who dealt with simultaneous production, replenishment, and raw material quality control. They compared two quality control policies, an acceptance sampling plan, and 100% inspection for lots of raw material. [PERSON] and [PERSON] [21] developed an analytical and simulation model for evaluating the performance of a production line. With their method, it is possible to model different cases such as machines having phase-type failure time distributions, serial/parallel machines, and quality control machines. A common feature of the above situation is that simulation modelling has been applied successfully in several studies, since it allows for the relaxation of unrealistic assumptions and reproduction of complex real dynamics. Nonetheless, despite the contributions of these papers, important problems remain unsolved in the interaction of production-quality-maintenance functions. More precisely, for production planning, we aim to enhance company competitiveness at implementing a JIT production strategy to improve performance through lower inventory levels and reduce the total incurred cost. The potential economic cost savings that could be obtained with the proposed joint control policy are highlighted in the comparative study section. The main research tasks devised in this paper are aligned with the extension of existing models in the production-quality-maintenance domain and the concurrent extension of analysis for these models.