## 1 Introduction
Presently, products and processes are becoming more complex, with numerous possible assignable causes, and require more improved quality checks and multiple inspections. [PERSON] et al. [29] carried out work on integrating production, quality, and condition-based maintenance for the unreliable manufacturing system. They consider production with lot sizing and quality control done by entirely utilizing the strategy of inspection to obtain the defective proportion. Recently, [PERSON] et al. [30] integrated a production, maintenance, and control chart of a supply chain system considering a quality constraint, with a conjugated production, delivery, and maintenance optimization to minimize total cost. Advance control chart is a means of \"statistical process control (SPC) \"using pattern recognition. [PERSON] et al. [31] used the patterns of the control chart corresponding to the manufacturing process' specific factors to improve the \"control chart pattern recognition\" (CCPR) accuracy. A perfect and automatic CCPR is designed with various complex features, increasing the statistical process control. Some methodologies coordinating the process statistical control and stock issues generally pointed toward a control chart planning boundary to limit stock and quality costs and without considering the different issues that can impact the process stability as well as the products' quality. Consequently, the integrated maintenance strategy to SPC (statistical process control) based on the increasing failure rate with time and the machine's use is rarely considered in the literature. Unlike the numerous literary works, the present study deals with an original and realistic idea integrating four functions: production, delivery, maintenance, and quality. These four factors treated simultaneously contributed enormously to the computational complexity of the addressed decision problem. Firstly, we start with the relationship between production and quality, where some literary works in this area are limited presently due to not considering the maintenance strategies. Hence, the present work proposes a new vision integrating the four issues: production, delivery, maintenance, and quality, considering several constraints, since most of the existing manufacturing systems are characterized by stochastic demand, inventory, delivery, and service level. Hence the significance of this study, which shows a considerable correlation for these three concerns integrating a statistical process control approach that helps to obtain economical and dynamic maintenance planning. Otherwise, the bulk of literature works concerning production and maintenance integrated strategy considered the deterioration depending only on time, without taking the variation of the production and its impact on the degradation into consideration. Hence, our study presented that the degradation level of the manufacturing system is impacted by the production rate variation, and it is used over time simultaneously. An analytical relation of the relationship between the production and the failure level is presented in this study. Our analytical relation is a novelty in the literature, which demonstrated the progression of process failure rate with its use, regarding the process reliability continuity from one production period to another. The present study's originality is the analytic study and development to improve the application of an industrial practical case, characterized by the effect of the production variation on the process deterioration under stochastic environments, which is a novelty in the literature. Unlike other studies considering constant production rates, our proposed model discussed them differently, for example, from \"hedging point policy\" that is necessary to decide the optimal age of preventive maintenance action and the optimum level of the safety stock based on a production cadence varying between zero and demand, that considered constant, or the maximum production rate.