**1. Introduction**

Climate change is a serious challenge facing the world today. Since the industrial revolution, energy consumption has increased year by year. With the increase in carbon dioxide emissions, the global temperature is gradually rising. Carbon dioxide-based greenhouse gas emissions are the main cause of global warming [1,2]. Thus, controlling carbon emissions and mitigating global warming has become an important global issue and is gradually becoming a global consensus. Taking China as an example, to cope with climate change, carbon peaking and carbon neutrality goals have been proposed to promote the construction of an ecological civilization and achieve high-quality development [3].

By comparing the carbon emissions of various industries, it can be found that the manufacturing industry has long accounted for a large proportion, with relevant data showing that over 70% of the carbon dioxide emissions from China come from industrial production or generative emissions [4,5]. As a result, industry, especially the manufacturing sector, has become the main battleground for reducing carbon emissions in China and the key to achieving carbon peak and neutrality targets. As the main body of the national economy, the manufacturing industry needs to carry out green and low-carbon transformation and

**Citation:** Yang, L.; Liu, Q.; Xia, T.; Ye, C.; Li, J. Preventive Maintenance Strategy Optimization in Manufacturing System Considering Energy Efficiency and Quality Cost. *Energies* **2022**, *15*, 8237. https:// doi.org/10.3390/en15218237

Academic Editors: Brian D. Fath and Nicu Bizon

Received: 17 August 2022 Accepted: 2 November 2022 Published: 4 November 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

development to achieve carbon peak and neutrality targets and realize green manufacturing and intelligent manufacturing [6]. Hassan T et al. [7] found that technology to improve energy efficiency is a crucial method to achieve lower carbon emissions and mitigate global warming. Thus, it is critical to improve energy efficiency in the manufacturing system.

Energy consumption in manufacturing is mainly from production equipment. Thus, we need to pay close attention to the energy efficiency of production equipment. Maintenance plays a crucial role in the normal operation of equipment, and maintenance activities affect the reliability of equipment, indirectly affecting the energy efficiency of the equipment. For this reason, it is crucial to take into account energy efficiency in the optimization of maintenance strategies, gradually achieving a transition from condition-centered maintenance to energy-centered maintenance [8]. Many maintenance methods have been proposed in previous studies, such as breakdown maintenance where maintenance is performed after the equipment has failed to return to its normal function. However, this type of maintenance can affect the production schedule, so preventive maintenance is proposed, which predicts the status of equipment and maintains the equipment in advance to keep it in continuous production [9]. As the detailed literature review below shows, there is a wide range of literature that focuses on the cost of preventive maintenance and the quality of the products produced by the equipment. However, only a few focus on the energy consumption and environmental impact of maintenance, and even fewer articles combine cost, quality, and energy consumption. This paper proposes a new preventive maintenance strategy model. The innovation of this paper is that not only the cost is considered in maintenance activities but also the quality loss cost is introduced to constrain the product quality of equipment, the energy consumption is modeled and calculated, and the recovery of defective products is taken into account. The maximization of energy efficiency and the minimization of maintenance costs are taken as the overall optimization objectives to develop the maintenance strategy.

The remainder of the paper is organized as follows. Section 2 presents a short literature review and shows the contributions of this paper. Section 3 describes the problems associated with equipment maintenance and makes some assumptions about the model. Section 4, a multiobjective decision model is constructed in four steps based on identifying decision variables and optimization objectives and then solved according to the NSGAII algorithmic process. Section 5 validates the model using a numerical case. Conclusions, managerial impacts, and future research scopes are discussed in Section 6.

#### **2. Literature Review**

Quality control in equipment maintenance has been studied by scholars for a long time. The relationship between maintenance and quality is discussed, and a broad framework is proposed. Two approaches to connecting and modeling this relationship are discussed in the article. The first approach is based on the idea that maintenance affects the failure modes of the equipment and that it should be modeled with the concept of imperfect maintenance. The second approach is based on the quality approach of Taguchi [10]. Subsequent scholars began to link maintenance and quality closely together. On the one hand, excessive maintenance can lead to unnecessary costs. On the other hand, if the equipment is not correctly maintained, this will lead to failures and result in defective products. In an integrated model of maintenance and quality, the literature [11] correlates the failure rate of equipment with the quality of the product to obtain a function of the variation of the product quality. The control of quality is also reflected in costs such as quality loss and maintenance thresholds, and these models can minimize the total cost and ensure high quality products [12–14].

Scholars have researched energy consumption and environmental impact in equipment maintenance. Jiang et al. [15] considered the ecological impact of equipment degradation, the excessive emissions of equipment, and the energy consumption and obtained maintenance thresholds and inspection intervals that were optimal considering energy consumption and CO2 emissions by minimizing the average expected cost. Tlili et al. [16]

considered the penalties to be incurred when equipment degradation exceeds a critical level and developed two inspection strategies (periodic and nonperiodic), with separate preventive maintenance thresholds and inspection sequences obtained to reduce cost. Chouikhi et al. [17] proposed a condition-based maintenance strategy for production systems to reduce excess greenhouse gas emissions, translated environmental constraints into maintenance thresholds, and determined optimal maintenance inspection cycles by minimizing maintenance costs. Huang et al. [18] developed a data-driven model from the date of distributed sensors to integrate energy conversation and maintenance to determine the optimal level of maintenance. Liu et al. [19] considered the maintenance of wind turbines and correlated energy consumption with the operating costs of equipment to obtain a maintenance strategy by minimizing the expected costs. Horenbeek et al. [20] developed an economic and ecological analysis tool covering a wide range of maintenance policies. The model developed was validated using the example of a turning machine tool. Saez et al. [21] studied the relationship between production environment, quality, reliability, productivity, and energy consumption and proposed a modeling framework for manufacturing systems that integrates systems, machines, and parts.

The above studies are based on the maintenance cost, where the energy consumption and the environmental impact are regarded as the threshold or other influencing factors in the maintenance cost. The modeling and calculation of the specific energy consumption of equipment are not involved. In terms of modeling the energy consumption of equipment, Yan et al. [22] proposed a method for modelling the energy consumption of a machine tool, using the model to obtain the energy consumption of the machine tool during and after maintenance and converting the energy consumption into carbon emissions, thus effectively controlling the impact on the environment. Zhou et al. [23] analyzed the energy consumption of machine tools commonly found in manufacturing, dividing the machine tool energy consumption model into three parts: a linear cutting energy model, a process-oriented machining energy model, and cutting energy consumption for various specific parameters. After summarizing the power consumption characteristics of heavy machine tools, Shang et al. [24] developed a generic power consumption model for heavy machine tools to predict the power consumption and assess the energy consumption state and developed corresponding energy saving strategies, but they did not take into account the variation of energy consumption. Zhou and Yi [25] have linked energy consumption to equipment degradation, elaborated on the variability of energy consumption, and introduced energy quality thresholds to create an energy-oriented decision model. Mawson and Hughes [26] used new technologies such as digital twins to simulate the energy consumption of equipment. Using a digital twin strategy, Bermeo-Ayerbe et al. [27] proposed an online data-driven energy consumption model. Xia et al. [28] modelled the energy consumption of machine tools and tools and proposed an energy-oriented machine tool maintenance and tool replacement strategy to save energy. Aramcharoen and Mativenga [29] carried out a detailed analysis and calculation of the energy consumption of the entire process of machining a machine, including machine start-up, workpiece set-up, machine warm-up, tool change and cutting, and machine shutdown.

In terms of the energy efficiency calculation of equipment, Zhou et al. [30] proposed the concept of effective energy efficiency by considering the energy saving opportunities arising from machine downtime, obtained the optimal maintenance threshold based on the energy saving opportunity window to maximize energy efficiency, and verified the superiority of the model by comparison. Xia et al. [31] modeled the energy attributes to obtain the multiattribute model (MAM), used the energy savings window (ESW) and constructed the MAM-ESW maintenance policy model by considering energy consumption, mass production, and maintenance. Brundage et al. [32] proposed a control scheme where energy opportunity windows were inserted into various machines to reduce the energy consumption and increase profits. Xia et al. [33] proposed a selective maintenance model for energy-oriented series-parallel systems to find a maintenance strategy for each equipment to maximize the energy efficiency. Hoang et al. [34] defined the concepts of the energy efficiency index (EEI) and remaining energy-efficient lifetime (REEL), calculated the various energy consumptions of equipment, and constructed a model to maximize the energy efficiency index. Frigerio and Matta [35] proposed an aggregate control policy framework that determines the optimal control policy by calculating the energy consumption in each machine state and minimizing the expected energy required by the equipment.

The above literature analysis shows that fewer studies integrate equipment maintenance costs, energy efficiency, and product quality, which still need more attention and research. Most of the existing papers examined several of these components. The main contributions of this article include: (1) a preventive maintenance decision optimization model that takes into account energy efficiency, product quality, and maintenance cost with preventive maintenance thresholds and maintenance efficiency as decision variables; (2) a link between preventive maintenance costs, equipment operation energy consumption, and equipment failure rates to obtain more realistic variable preventive maintenance costs and variable operation energy consumption; (3) a recovery model for defective products produced by equipment to reduce energy consumption, which describes the reduction in the number of defective products to be recovered as the equipment degrades by introducing a recovery factor.

#### **3. Problem Description and Hypotheses**

#### *3.1. Problem Description*

In reality, equipment cannot be restored to a new health state after use; it is in continuous degradation, and the failure probability of equipment is increasing. The failure rate function of equipment can be obtained by simulating the historical data of equipment. The degradation of equipment failure rate is influenced by controllable factors such as maintenance activities and production schedules and uncontrollable factors such as changes in the production environment. The specific impact of maintenance activities will be described in the hypothesis section, and the impact of the production schedule on equipment degradation can be obtained through historical data analysis. As for the impact of environmental changes in the field, only the degradation of equipment under normal environmental conditions is considered in this paper because the environment in which equipment is located varies and is full of randomness.

Generally speaking, the life cycle of production equipment is relatively long. For the convenience of calculation, the time interval between the brand-new condition of equipment and the next replacement is selected as a period to be considered in this paper. During the operational cycle of equipment, only three maintenance actions are adopted, including breakdown maintenance, preventive maintenance, and replacement, as shown in Figure 1. The different conditions of equipment will determine the adopted type of maintenance actions, and the effect of each type of maintenance varies. When equipment reliability reaches the preventive maintenance threshold, preventive maintenance will be executed, and equipment cannot be restored to a new health state but a state between the new state and the state before adopting maintenance. Breakdown maintenance occurs when equipment fails during preventive maintenance intervals. It is impossible that preventive maintenance is always carried out when the number of preventive maintenance reaches a certain amount. The equipment needs to be replaced to reduce the maintenance cost and improve energy efficiency.

Similarly, in actual production, the product quality decreases as the equipment degrades, and as the equipment continues to operate, the number of defective products will increase, resulting in a large portion of the cost of quality loss. Therefore, the problem of recycling defective products is considered in this paper by introducing the recovery coefficient because recycling defective products can save a part of the energy consumption.

**Figure 1.** The variation in equipment failure rates and maintenance actions.
