### Literature Review  
When analyzing the literature on the integration of production and maintenance strategies, we observed that several works were conducted, which makes sense given that current production systems have become more complex. For instance, [PERSON] et al. [1] studied a hierarchical decision-making process, where, in the first level, they determined the mean time to failure, and in the second level, they determined the production and maintenance rates. They assumed imperfect maintenance actions. Later, [PERSON] et al. [2] studied production and maintenance planning for a system that satisfied random demand by considering a required service level. They considered a periodic preventive maintenance option, where, at failure, a minimal amount of repair was conducted. A subsequent work conducted by [PERSON] et al. [3] treated a production system that could degrade into several discrete states, which indicated different performance states. They analyzed the trade-off of a preventive maintenance policy by considering their impact on the production rate and the buffer. [PERSON] et al. [4] considered a hybrid system, where the machine was capable of manufacturing activities, and remanufacturing, where returned products were used in production. In their study, the system was prone to deterioration and they determined production, remanufacturing, and preventive maintenance rates. [PERSON] et al. [5] studied production and repair strategies for a system subject to deterioration. They modeled quality deterioration with an aging process and several operational states. They also determined the repair efficiency to partially restore the machine after failure. More recently, [PERSON] and [PERSON] [6] developed a lot-sizing model in terms of energy, service level, and capacity constraints. They determined maintenance actions by taking into account the impact of the production rates on the level of deterioration and the increase in the failure rate. Despite the relevance of the discussed studies, more research is needed since the complex trade-offs between quality issues and the determination of production maintenance strategies were disregarded. However, companies must manage these three key functions simultaneously for economic success. There is a vast literature emerging that investigated the interaction of production, quality, and maintenance strategies. For example, [PERSON] et al. [7] determined the size of production lots and the values of the parameters of an acceptance sampling plan. They also defined overhaul rates for a deteriorating system considering an outgoing quality constraint. [PERSON] et al. [8] integrated production planning and imperfect maintenance, where process inspections were used to determine the system conditions. Their system comprised multiple products and multiple machines that deteriorated over time, producing more defects. [PERSON] et al. [9] developed a joint strategy of production and quality control for a degrading system, where preventive maintenance was conducted after inspection if the deterioration level surpassed a threshold. The strategy of quality control was based on inspecting all the units. [PERSON] et al. [10] suggested a plan for production and maintenance for a system prone to deterioration, where the quality of the products was monitored with statistical process control. Their model determined the sample size, the interval for sampling, and the limits of quality control. The deterioration degree of their system was influenced by the production rate and time. [PERSON] et al. [11] proposed a model for the simultaneous control of production planning and maintenance scheduling considering a dynamic sampling inspection. Their quality policy adjusted the sample size according to the degree of deterioration. They assumed that the deterioration process had effects on the failure rate and the failure intensity. [PERSON] et al. [12] highlighted the advantage of using a dynamic sampling strategy for quality control for cases of progressive deterioration.