Collaborative Optimization of a Matrix Manufacturing System Based on Overall Equipment Effectiveness

Abstract

When several traditional flow-shop lines operate in parallel, the operation mode with no communication between production lines will no longer be the optimal production paradigm. This paper describes matrix manufacturing systems (MMS) in a general manner from the perspective of related works, comparing different manufacturing organizational forms and their characteristics. Subsequently, MMS are extracted during the parallel production of multiple surface mount technology (SMT) lines. An overall equipment effectiveness (OEE) online calculation model and a collaborative optimization method are proposed based on the OEE of the MMS. The innovative idea of this study is to divide existing multiple parallel SMT lines into MMS. The efficiency of each matrix unit (MU) was calculated, and a collaborative optimization method was proposed based on an indicator (OEE). In this paper, an example of eight SMT lines is presented. The partitioning of MUs, OEE calculation of each MU, and the low OEE unit collaborative optimization method are described in detail. Through a case study, the architecture of the collaborative optimization model for the MMS was constructed and discussed. Finally, the improvement in the OEE proved the effectiveness and usability of the proposed architecture.

1 Introdution

The “Outline of the 14th Five-Year Plan (2021–2025) for National Economic and Social Development and the Long-Range Objectives Through the Year 2035 of P.R. China” issued by the State Council of the People’s Republic of China in 2021 states that the direction of discrete job-shops should be guided by “improving factor allocation efficiency,” breaking through “development of personalized customization,” and achieving full-stage and full-factor collaboration. It supports “intelligent solutions for discrete job-shop problems” and promotes the “construction of an industrial Internet+ intelligent manufacturing industry ecology.” Job-shops are often characterized by difficulties in scale, structural complexity, and intensive equipment. Current production decision-making methods, which mainly focus on a planned or centralized approach, often lose their guiding significance because of frequent disturbances. Therefore, a new collaborative optimization method based on events or indicators has become an international consensus.

From a quantitative perspective, industrial process indicators such as on-time delivery rate, operation rate, product qualification rate, work in progress, inventory quantity, quality indicators, capacity load rate, output value, and total labor productivity are widely discussed. For product-oriented manufacturing job-shops, three indicators (production capacity, equipment efficiency, and machining quality) [1]) focus on increasing unit time productivity by continuously reducing downtime, lowering ineffective waste, and improving quality [2]. However, the various process indicators mentioned above (except for the on-time delivery rate, which can be precisely predicted through advanced planning scheduling (APS)) rely heavily on post-event statistical methods such as overall equipment effectiveness (OEE), process capability indicator (CP), and statistical process control (SPC). The excessive reliance on post-event statistics and manual experience indicates that these methods cannot obtain real-time and accurate calculations, nor can they provide the requisite support for subsequent decisions based on the indicators. For example, although many existing control systems have their own OEE functions that adopt a fixed interval for the division of downtime (unplanned downtime, planned downtime, changeover time, and normal production downtime intervals), the application effects are not sufficient. In the existing calculation mode of the well-known surface mount technology (SMT) enterprise AKM Co., Ltd. in China, downtime of less than three minutes is considered the normal production interval, approximately 20 minutes is regarded as the changeover time, about two hours is the planned downtime, and other time intervals are considered unplanned downtime. Many drawbacks of the model are encountered daily at AKM. For example, if skilled workers finish the changeover job in 10 minutes, the system incorrectly classifies the line change time as unplanned time, which affects the OEE and has a continuous impact on subsequent decisions. The transformation of post-event statistics and excessive reliance on manual experience into real-time and smart calculation models using collaborative optimization indicators or methods has become a major problem in current process control.

In this study, collaborative optimization refers to the real-time or prior indicator calculation method and data/model-driven decision-making method instead of relying on post-event statistics and excessive reliance on manual experience. The development of this study is based on actual engineering projects in the flow-shops of the China Electronics Technology Group Corporation No. 29 Institute, the SMT flow shops of Inventec (Chongqing) Co., Ltd., and the SMT flow-shops of AKM. Although the processes of the three factories are quite different, their manufacturing nature is very similar (flow-shops on SMT). As is publicly known, flow-shops are the most likely to improve production capacity; however, a survey found that the equipment OEE of all three companies did not reach 85%, and in many cases, it was below 30%. The efficiency of traditional flow-shops has received extensive discussion from the research team. Although a flexible manufacturing system (FMS) can significantly improve efficiency, it is difficult to control, especially when facing numerous disturbances in the APS, which significantly reduces manufacturing efficiency. Therefore, researchers wonder whether there could be a hybrid manufacturing system that would increase production indicators (such as OEE or CP) to a higher level while retaining the flow-shop features as much as possible. The flexibility presented in this paper can be regarded as the reconfiguration of functions inside the manufacturing unit as well as the path selection of subsequent processes. Therefore, the concept of matrix manufacturing systems (MMS) is proposed, and the characteristic details of MMS are tracked in the second section.

The main idea of this research is to apply an indicator (online OEE) based on MMS for collaborative optimization. The remainder of this paper is organized as follows. Section 2 provides a brief review of the challenges faced by MMS, OEE, and collaborative optimization. An online OEE calculation method is proposed in Section 3, and a collaborative optimization model of the MMS based on the online OEE is elaborated. The details of the implementation of the collaborative optimization model are described in Section 4. Finally, a summary and future work are presented in Section 5.

2 Literature Review

This section describes the characteristics of MMS, OEE, and collaborative optimization. Furthermore, it discusses the state of the art and challenges in OEE and collaborative optimization.

2.1 Matrix Manufacturing System

With continuous improvement at the industrial level, the traditional manufacturing mode faces many difficulties in meeting market changes. Simultaneously, dynamic market demand, large-scale batch customization demand, and high-performance quality demand have promoted the transition from traditional manufacturing systems to next-generation manufacturing systems. Manufacturing systems with flexible and reconfigurable characteristics have become an important way to overcome these changes; examples include the reconfigurable manufacturing systems (RMS) in the BMW Munich factory and the RMS in FESTO, Germany.

In recent years, with the development of information technology, the concept of manufacturing systems has been constantly updated, such as the MMS solutions proposed by the German company KUKA Robotics (Figure 1). The construction of matrix units (MUs), which can be quickly configured and switched to suit different production needs, equipment collaboration, and AGV intelligent logistics, can address problems such as peak capacity utilization rate and resource bottlenecks. MMS have been successfully applied in the manufacturing process of Volkswagen frame structures, increasing efficiency by 20% [3].

Figure 1

KUKA MMS (integrates warehouse, AGV tooling station and circulation unit), partly applied in Augsburg factory

2.1.1 Related Works on MMS

The MMS has the characteristics of high flexibility and strong adaptability, allowing it to respond quickly to changes in jobs, allocate resources reasonably, and improve resource utilization. So far, research on MMS has just begun and is mainly concentrated in Germany, at institutions such as Braunschweig University of Technology, Karlsruhe Institute of Technology, University of Stuttgart, University of Magdeburg, Dortmund University of Technology, and Vienna University of Technology [4]. For production lines with multivariate, variable batch, fast cycle, and nonlinear production demand characteristics, the MMS seems to be a viable solution. Related studies have also been conducted.

In the manufacturing system design phase, Michael et al. [5] believed that higher changeability is expected from an MMS to cope with high product variants. To provide the required degree of changeability, the options for change must be considered. Christian et al. [6] proposed a control system architecture for an MMS to balance flexibility and high production throughput. A simulation analysis was conducted by Renna [7], comparing the performance measures and benefits of the MMS and RMS with those of flow-shops, as shown in Table 1. (+ indicates an increase compared with dedicated flow, and − indicates a decrease. The work in process, WIP). The results show that MMS has a great advantage in terms of throughput rate, throughput time, WIP, and waste-time management.

Table 1 The performance measures of RMS & MMS compared to the dedicated flow

Halldor et al. [8] utilized a novel approach by applying visual simulations to illustrate the operation and potential challenges of an MMS in a real-world context. The simulations demonstrated how the system could adjust the production capacity and functionality in response to changing demands by utilizing robotic arm movements, manual labor, and mobile manipulators. Patrick et al. [9] believed that MMS aim to achieve efficient production by implementing flexible material flow among stations. Liu et al. [10] introduced the AGV capacity and latest delivery time to reduce the cost of the total objective, consisting of the AGV cost, travel cost, and penalty cost in the MMS.

2.1.2 Comparison of Organizational Forms for Manufacturing Systems

Ref. [11] provides a brief comparison of organizational forms for manufacturing systems, as shown in Table 2. The primary principles of MMS and matrix RMS are the flow principle and performance principle, respectively, with no directed material flow. The advantages include (1) the combined use of different kinds of resources and (2) shorter transport distances compared with job-shops and shorter intermediate storage. However, these changes increase coordination and control expenditures and may lead to higher space consumption than other production organizations.

Table 2 Comparison of organizational forms for manufacturing systems [11]

2.1.3 Characteristics of MMS

Based on the above analysis, the characteristics of MMS are summarized as follows:

• (1) The reconfiguration capability of a matrix unit (MU) is driven by the task. Several capabilities based on the task are preset in the MU, and these capabilities can be switched between one another. In Figure 2, A B, C, and D show the preset capabilities. Preset capabilities can be the same (e.g., AABC) or different (e.g., ABCD). Additionally, the MU can reserve space to introduce non-preset capabilities (e.g., equipment or tooling). In total, the MU must have the ability to switch and reconfigure according to different tasks.

• (2) The reconfiguration capability of an MMS is driven by the orders. Driven by the predicted orders in a large production cycle, the orders are divided into minimum process steps. Depending on the type and quantity of the minimum process steps and the sequence constraints, the MMS is reconfigured into several job combinations, including flow-shops, job-shops, and flexible job-shops (Figure 3). According to the concept of multi-agents, four agents are used in the system-level reconfiguration of the MMS:

Figure 2

Structure of the MU

Figure 3

Reconfiguration capability in the MMS

Agent 1 Order grouping to reform the MMS into several other organizational forms.

Agent 2 Job-shop scheduling agent.

Agent 3 Job selection agent.

Agent 4 Machine selection agent.

Agents 3 and 4 jointly complete the flexible job-shop scheduling. Additionally, system-level matrix reconstruction may be performed again in different job cycles if necessary.

2.1.4 Research Challenges of MMS

The essence of an MMS is to reasonably combine MUs according to the processes. Some of the new challenges are discussed below:

• (1) Process steps in granularity research of MU: As shown in Figure 2, ABCD represents the preset capability or mini-process step. The division of process step granularity directly determines the set of ABCD and job-shop scheduling, which is the first step in all other studies.

• (2) Internal capability combination: The combination of internal capabilities within a unit and the quantity and type of units can lead to reconstruction, resulting in complex coupling constraints such as reconstruction time.

• (3) (3) Operational research: This involves considering unit switching capacity and switching time.

2.2 State of the Art and Challenges in OEE

Under the initiative of total productive maintenance, OEE is widely used as a key performance indicator for measuring system efficiency. Based on the availability rate ($A$), performance rate ($P$), and quality rate ($Q$), OEE tracks improvements or declines in equipment efficiency with the goal of reducing equipment downtime and improving factory maintenance tasks. OEE is a powerful tool for identifying and eliminating production process losses, achieving intelligent manufacturing, and improving production system availability [12]. The formulation is shown in Table 3, and the main application scenarios and effects of OEE are illustrated in Figure 4.

Table 3 Basic Components of OEE

Figure 4

Main application scenarios and effects of OEE. Ref. [13]: Job-shops. Ref. [14] : Diffusion line. Ref. [15]: Peugeot assembly lines, Ref. [16]: Welding line. Ref. [17]: Aerospace alloy joint line. Ref. [18]: Pipe-cutting machine. Ref. [19]: Accumulator. Ref. [20]: Injection machine. Ref. [21]: Roll grinding machine. Ref. [22]: CNC milling machine. Ref. [23]: GT22 generator

In recent years, OEE, as a systematic performance measurement indicator, has found effective application in industries such as semiconductor and automobile manufacturing, as shown in Table 3. This phenomenon has been studied by numerous research institutions.

However, the review revealed that data processing mostly relies on offline processes. In this model, OEE serves as a post-event indicator with no guiding significance for process control. To address this problem, machine learning must be employed to construct the feature space and design an online algorithm for multiclass downtime identification to enable real-time monitoring. Only with online calculation of OEE can the manufacturing system make decisions based on the real-time OEE indicator. For example, in an MMS, real-time OEE can serve as an indicator of MU efficiency. When the real-time OEE is low, an MU, as an independent smart unit, can proactively seek job tasks, thereby improving the overall efficiency of the MMS.

2.3 State of the Art of Collaborative Optimization

Collaborative optimization is pivotal for improving production efficiency and product quality in modern job-shop operations. Several key aspects identified through the literature review are discussed below.

2.3.1 Collaborative Optimization in Monitoring and Controlling

Multi-agent collaboration: Global optimization is achieved using multi-agents (such as robots and automated equipment). Zhang et al.[24] emphasized collaborative problem-solving among intelligent agents with interdependent task allocation to achieve optimal global solutions.

Multistage/Line collaboration: Effective control across production stages or lines is essential for efficiency. Wei et al.[25] advocated for joint processing across workshops to address capacity limitations and minimize delays. Zhao et al.[26] proposed collaborative parallel segmented models to enhance system efficiency.

Production and maintenance collaboration: Jiang et al.[27] explored the joint optimization of scheduling and maintenance to minimize downtime and costs.

Design and manufacturing collaboration: Fan et al.[28] suggested smart factory models to integrate design and manufacturing across enterprise levels. Zhou et al.[29] developed a framework for the design and manufacturing processes based on the integration of models, data, and knowledge. This framework spans the lifecycle of design and manufacturing, emphasizing top-level design concepts.

2.3.2 Collaborative Optimization in Scheduling

Distributed job-shop collaboration: Coordination between job-shops enhances resource utilization and task efficiency. Du et al.[30] proposed a Q-learning-based collaborative optimization algorithm to address scheduling challenges in distributed flow-shops.

Multi-objective collaboration: In flexible job-shops, balancing multiple objectives such as cost, time, and quality is crucial. Research [31, 32] has highlighted the importance of constructing multi-objective functions and developing scheduling mechanisms for technical research and optimizing manufacturing execution performance. The formulation of these multi-objective functions closely correlates with scheduling scenarios involving parameters such as makespan, delivery times, delays, energy consumption, and costs. Lang et al.[33] discussed multi-objective optimization in flexible job-shop scheduling, focusing on balancing cost, time, and quality to enhance production performance.

Multi-resource collaboration: Coordinating automated guided vehicles (AGVs) is essential for preventing collisions and ensuring timely production in flexible job-shops. Innovative strategies, such as time-window approaches [34] and priority-based wait strategies [35], optimize AGV path planning and scheduling.

A comparison of traditional and collaborative optimization methods is shown in Table 4.

Table 4 Comparison of optimization method

3 Collaborative Optimization Model of MMS based on OEE

3.1 Introduction of the SMT Line

Comparing the flow-shops of the China Electronics Technology Group Corporation No. 29 Institute, the SMT flow-shops of Inventec, and the SMT flow shops of AKM, all exhibit the characteristics of a flow-shop for SMT. This section uses the Inventec notebook assembly flow-shops as an example.

As shown in Figure 5, the loading station first delivers a printed circuit board (PCB) or flexible printed circuit board (FPC) to the automatic solder paste printer. The initial inspection is performed using a solder paste inspection (SPI) machine to detect parameters such as thickness. The PCB/FPC is then transferred to the chip mounter to mount electronic components, such as the CPU. After reflow soldering, an automated optical inspection (AOI) machine checks the position of the components. Next, the CPU pins are glued and encapsulated using a glue dispensing machine, with fast solidification performed in an ultraviolet (UV) curing oven and a vacuum oven. Subsequently, the glue dispensing process is inspected at the X-ray station, focusing on indicators such as bubbles and pin deformation. Finally, the appearance and electrical performance of each product are inspected manually. Each failed inspection chip (Not Good, NG) generated during the detection process is marked and repaired.

Figure 5

Inventec notebook assembly flow-shops and SMT process

The SMT line represents a typical flow shop with certain matrix and unit characteristics. For instance, chip mounting, reflow soldering, and AOI can be considered a unit because these three processes are consistent. The unit can also be divided into a processing unit (chip mounting and reflow soldering) and an inspection unit (AOI). The same classification applies to the loading station, printing station, SPI, glue dispensing station, UV, vacuum oven station, and inspection stations (X-ray /appearance electrical inspection). When multiple SMT lines exist in a workshop (e.g., AKM has nearly 40 SMT lines), the final configuration is an MMS. MUs are no longer transmitted by an adapter but by AMRs or mobile robots with loading functions.

3.2 OEE Online Calculation Model

The online OEE calculation model is illustrated in Figure 6. The cycle time, production cycle, number of parts, number of NG parts, and number of second-pass parts used for the calculation were obtained through on-site measurements, analysis, or MES statistics. Four types of downtime (production, planned, changeover/inspection, and unplanned) were collected using a data-driven classification method involving the synthetic minority oversampling technique and multilayer perceptron (SMOTE-MLP). SMOTE [36] addresses unbalanced data issues, while MLP [37] serves as a classifier that moves beyond traditional offline calculation methods, enabling online calculations of the availability rate, performance rate, quality rate, and OEE [38]. Details of the SMOTE-MLP are as follows:

Figure 6

OEE online calculation model

SMOTE is an algorithm used to artificially synthesize new minority class samples. Unbalanced datasets are a significant challenge for machine learning and artificial intelligence. When there are many more samples in one class than in another, the machine learning model tends to be biased toward the larger class, resulting in poor classification performance. SMOTE is a powerful and widely used solution for imbalanced data. The algorithm operates as follows:

• (1) For each sample x in the minority class, the Euclidean distance is used to calculate its distance to all the samples, identifying its k-nearest neighbors.

• (2) The sampling ratio is set according to the sample imbalance ratio. For each minority sample x, several samples are randomly selected from its k-nearest neighbors, denoted as φ.

• (3) For each randomly selected neighbor φ, a new sample is constructed with the original sample using the formula φ (new) = φ + rand(0,1) × ( x -φ).

The SMOTE diagram is shown in Figure 7.

Figure 7

The SMOTE diagram

An MLP is a classifier and a feedforward neural network consisting of an input layer, multiple hidden layers, and an output layer. Each layer contains several neurons, with adjacent layers connected by weights. Each neuron in the MLP performs the following operations:Linear transformation:

The linear combination of input signals is weighted.

Nonlinear activation: The linear combination is activated using a nonlinear function. Commonly used nonlinear activation functions include the rectified linear unit (ReLU), which is effective for addressing the gradient vanishing problem and is often the first choice for activation functions; sigmoid, frequently used in the output layer of binary classification tasks; and softmax, a standard choice for the output layer in multiclass tasks.

3.3 MMS Division and OEE Control of the SMT Line

Based on SMT processing and inspection, several MUs can be divided as shown in Figure 8: the loading and printing unit, SPI unit, chip mounting and reflow soldering unit, AOI unit, glue dispensing and UV/vacuum oven unit, X-ray unit, and inspection unit. Among these, the inspection unit features various detection capabilities, such as appearance inspection 1 and 2 and electrical inspection. Additionally, the processing and inspection units can be further subdivided into finer granularities, as depicted in Figure 9.

Figure 8

MMS division of SMT lines

Figure 9

MMU division of SMT line with finer granularity

Traditional SMT flow-shops are represented as black blocks in Figure 8. The MMS are indicated by the red block. The selection of the next process is based on online OEE rather than relying solely on the conveyor. The application paradigm for online OEE is illustrated in Figure 10.

Figure 10

Online OEE application paradigm

As shown in Figure 10, various data acquisition modules were initially added to the unit to collect decision features for OEE calculation. These modules can be classified into embedded collection, PLC-based control, and monitoring information collection. The main decision features collected for classification are divided into normal, planned, unplanned, and changeover times.

Subsequently, machine learning algorithms are applied to achieve highly accurate classification of downtime types. After several iterations, the usability and efficiency of the algorithm in terms of classification accuracy and computation time were validated.

The unit efficiency was then calculated in real time. The OEE standard formula, combined with a machine learning-based downtime classification model, is used to categorize the downtime. Online OEE is classified into three categories: red, yellow, and green, representing idle, good efficiency, and excellent efficiency, respectively. The ranges for OEE are as follows:

• Red: [0, 40%]

• Yellow: (40%, 50%]

• Green: (50%, 100%]

Finally, a collaborative optimization model for the MMS is proposed based on the OEE levels. Existing flow-shops are generally reluctant to modify their line structures unless a new plant is constructed. Therefore, a collaborative robot arm is integrated according to the MMS division logic. These robotic arms provide additional tasks to red and yellow OEE units within the same process to increase efficiency, allowing the MU to actively request tasks based on OEE. This integration provides the unit with the capability to make decisions and opens up possibilities for further use of deep learning in MMS. The red unit, having more job insertions, is prioritized for task allocation, while the yellow unit is allocated with a delay. The decision results are then communicated to the executor who implements them.

4 Implementing and Case Study

4.1 OEE Feature Analysis and Data Acquisition

Taking the AOI unit as an example, the decision factors include the time each carrier enters and leaves the manufacturing unit, the number of PCBs/FPCs carried on each carrier, working cycle time, and the number of pins detected by the AOI on each carrier. Five-dimensional factors can be obtained from the PLC of the AOI. An RS485-to-wireless transmission device is designed to store the collected signals in a database. (Considering that some imported AOI machines do not have open PLC ports, alternative embedded acquisition modes can be used. For example, carrier entry and exit times can be captured using RFID, and cycle time can be determined by measuring spindle work time).

For the AOI unit, the feature vectors are formed as follows:

[Time interval between two carriers, material change between two carriers]

The feature factors are the five-dimensional factors mentioned above.

4.2 OEE Online Training

Machine learning algorithms classify downtime into normal production downtime, planned downtime, unplanned downtime, and changeover time. The MLP was selected due to the large number and high frequency of SMT downtime classification samples (an average of 70,000 per day). Other algorithms, including the linear support vector machine (LSVM), radial basis function support vector machine (RBF-SVM), decision tree, random forest, AdaBoost, and naive Bayes (NB), were used for comparison. The running environment consists of an Intel® Core™ i5-8250U CPU @ 1.60 GHz and 8 GB RAM. Considering accuracy and processing time, the MLP classification model based on SMOTE exhibited excellent performance (99.70%, 18 ms).

4.3 Collaborative Optimization

Using the AOI unit data as an example, the calculation results are presented in Table 5. Lines 1 and 3 are seriously idle, line 5 has good efficiency, and the remaining lines have excellent efficiency (Data available at https://pan.baidu.com/s/1X4-0qgqqbbkJU5ECgHeshw).

Table 5 Online monitoring of OEE of AOI Unit

Subsequently, the collaborative optimization decision-making module allocates jobs for insertion based on these three states. The enterprise has eight SMT lines with similar processes but varying configuration parameters due to different processes. The AOI unit was previously operated as a surface-chip mounting and reflow soldering unit. The primary reason for the low OEE of the AOI unit was the delay in unit and material delivery caused by the previous operation, with a delay ranging from 0 to 3 minutes. Although this waiting time does not cause downtime, it severely reduces the unit’s performance rate (P). The main cause of the waiting time was the unequal pace between the previous operation and the AOI unit. The collaborative optimization decision-making module allocates jobs based on the three states or the OEE. For instance, in the scenario depicted in Table 5, a decision-making agent was added to the AOI units in lines 1, 3, and 5. During production wait periods, products with identical processes are inserted (sources include parts for return jobs, NG parts returned to the line, and FPCs pre-produced on Line 9 without AOI units, etc.). The job insertion process involves the reflow soldering unit and the AOI unit being synchronized; if there is output from the upper unit, it will not be passed downward until the AOI unit completes job insertion. Once the AOI unit finishes inserting jobs, the connecting machine is released. Based on this model, the efficiency of a low-OEE unit can be effectively improved. The insertion rate can be calculated from the gap between the target result and the current result. If the target OEE is over 80% and the existing OEE is 30%, the number of jobs required per unit time can be calculated using Table 3. To facilitate understanding, fixed-ratio insertion was used in this study. For example, the insertion rate for the red unit was set to 2:1, meaning that one product is inserted for every two consecutive products produced by the AOI unit. The insertion rate for the yellow unit was set to 5:1, as shown in Figure 11.

Figure 11

Collaborative optimization of MMS

4.4 Statistics and Analysis

According to international standards, the OEE of world-class manufacturers should exceed 85%. However, as noted in the literature review, there remains a significant gap between the OEE of SMT and the top international levels. From the perspectives of A, P, and Q, the statistical results for A are below 90%, primarily due to frequent changes associated with multiple small-batch jobs. Enterprise research indicates that the highest frequency of changes in a line can exceed 10 times per day. Each changeover substantially reduces the OEE due to mold replacement and parameter adjustment. The statistical results for Q are generally above 95% (some reach up to 97%, and many lines achieve 100%), indicating that Q is acceptable.

Many practitioners focus on optimization scheduling, merging similar jobs, and reducing changeover time as primary methods to improve OEE, as these strategies can effectively enhance A. However, our analysis reveals that, among A, P, and Q, the main bottleneck is P, rather than A. In other words, P is the primary factor limiting OEE improvement. P represents the proportion of effective equipment startup time. A low performance rate indicates that the capacity of many pieces of equipment is not fully utilized, leading to frequent idle and waiting conditions. This is the main reason for low OEE.

An MMS offers a viable solution. By assigning additional jobs to the red and yellow units using the same process, the low-OEE unit’s performance is improved through job insertion, as detailed in Table 6. The SMT MMS monitoring is illustrated in Figure 12 (only two SMT lines are depicted in Figure 12).

Table 6 Comparison of the OEE of the unit before and after collaborative optimization

Figure 12

Two lines of MMS based on OEE

5 Conclusions

In this study, SMT parallel lines were innovatively divided into MMS, and active scheduling was implemented based on real-time OEE indicators. The contribution of this study is the detailed description of a collaborative optimization method based on the OEE of an MMS. An example involving eight SMT lines was presented. The OEE of three lines increased by 8.6%, 15.7%, and 18.6%, respectively. We believe this study will inspire future research in this area. The MMS approach is particularly noteworthy.

However, this research has limitations. It only applies to SMT flow-shops, and job shops and flexible job shops require further investigation with respect to MMS. Future research should consider two perspectives:

• (1) An MU can exhibit multiple processing capabilities through presetting. Exploring the switching of preset capabilities in scheduling and addressing delays caused by function switching are important areas for further investigation.

• (2) The OEE enables the MU to think. Future research should explore whether additional indicators can be integrated and how artificial intelligence methods, such as deep Q-networks could be used to develop advanced solutions like AlphaGo in manufacturing systems.