A Systematic Simulation-Based Multi-Criteria Decision-Making Approach for the Evaluation of Semi–Fully Flexible Machine System Process Parameters

: Current manufacturing system health management is of prime importance due to the emergence of recent cost-effective and -efﬁcient prognostics and diagnostics capabilities. This paper investigates the most used performance measures viz. Throughput Rate, Throughput Time, System Use, Availability, Average Stay Time, and Maximum Stay Time as alternatives that are responsible for the diagnostics of manufacturing systems during real-time disruptions. We have considered four different conﬁgurations as criteria on which to test with the proposed integrated MCDM (Multi-Criteria Decision-Making)-TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution)-based simulation approach. The main objective of this proposed model is to improve the performance of semi–fully ﬂexible systems and to maximize the production rate by ranking the parameters from most inﬂuenced to least. In this study, ﬁrst, the performance of the considered process parameters are analyzed using a simulation approach, and furthermore the obtained results are validated using real-time experimental results. Thereafter, using an Entropy method, the weights of each parameter are identiﬁed and then the MCDM-based TOPSIS is applied to rank the parameters. The results show that Throughput tTme is the most affected parameter and that Availability, average stay time, and max stay time are least affected in the case of no breakdown of machine condition. Similarly, Throughput Time is the most affected parameter and Maximum Stay Time is the least affected parameter in the case of the breakdown of machine condition. Finally, the rankings from the TOPSIS method are compared with the PROMETHEE method rankings. The results demonstrate the ability to understand system behavior in both normal and uncertain conditions.


Introduction
Due to technologies that have recently emerged from Industry 4.0, industries have not only benefited but also been thrown challenges during execution. Regardless of technology advancement and functionality, recent manufacturing systems are vulnerable to unexpected disruptions such as machine breakdown, power fluctuation, loss of data, interoperability, etc. Monitoring complex manufacturing systems and dealing with these unexpected disruptions is a complex and challenging task. Prognostics and health management (PHM) is the maintenance policy that promotes better health care of complex machine systems, aiming at reducing the time and cost for maintenance, manufacturing processes, and unexpected disruption [1,2]. PHM also combines sensing and elucidates performance-related 1.
Which performance parameters influence the proposed flexible configurations most and least, with and without the breakdown of machines? 2.
How can system behavior in the case of normal and disruption conditions be understood?
On the whole, the contributions of this research paper are as follows: • Simulation analysis was conducted with the help of simulation software by varying the number of jobs from 100 to 5000 by considering cases with and without the breakdown of machines for various configurations, to compare the experimental results. • A validated proposed MCDM-TOPSIS-based simulation approach was taken to rank parameters to understand flexible system behavior in normal and uncertain conditions. Thus, the above-mentioned performance measures need to be analyzed to maintain the best health status of a system. Therefore, first an integrated MCDM-TOPSIS method was used along with an Entropy method to identify the weight of each parameter and to identify the most influencing performance measure. Thereafter, with the considered process parameters, simulations are conducted to analyze performance both with disruptions and without disruption. The proposed approach is validated with real-time experimental results [9]. The results demonstrate the ability to understand the system behavior.
The remainder of this paper is organized as follows. Section 2 provides a comprehensive overview of relevant literature. Section 3 discusses the integrated MCDM-TOPSISbased simulation methodology. Comparative results are examined in Section 4. Section 5 contains the Entropy-based TOPSIS method for simulation results. Finally, Section 6 presents conclusions and gives directions for future research.

Literature Review
This section offers an overview of the relevant literature on PHM of flexible machine systems and an integrated MCDM-TOPSIS method simulation approach on manufacturing systems. As manufacturing systems are disrupted due to their own natural characteristics or unexpected downtimes, health management for machines is considered to be a vital approach for better performance, as mentioned by [24,25]. Based on the mentioned problematic condition, [12,26] proposed a method to control disruptions and predict the failure time of each machine in a parallel configuration by adjusting the workloads on individual machines. This transformation has led to a lot of studies on maintenance methodologies related to manufacturing systems [27]. The health status of a machine can be evaluated by conventional prognostics and diagnostics approaches, and these are essential in the case of machine health management in Industry 4.0 [28,29].
Generally, manufacturing systems can be designed differently according to company strategy, boundary conditions, and the goals mentioned in [30]. Among all the existing manufacturing system configurations, semi-fully flexible real-time configurations, i.e., one-degree, two-degree, semi-flexible, and fully flexible configurations, are considered in the literature for the simulation analysis [9]. The above-mentioned configuration provides routing flexibility, so that the system can use two or more machines to perform the same task, and assess the system's ability to handle many changes, such as a substantial increase in capacity and machine failure [31].
From the various literature [32,33], it has been shown that six performance parameters need to be considered that influence the above-mentioned four configuration performances. These parameters influence a flexible machine system performance, as machine availability can be an important determinant of the delivery speed and delivery dependability, because unexpected machine downtime will not only increase lead time but also disrupt the production plan [33]. Such disruptions can be detrimental to a Just-in-Time (JIT) manufacturing environment. Alongside that, the average stay time of jobs, Maximum Stay Time of jobs, maintenance costs, and production cost force firms to analyze the performance of their systems systematically and efficiently regarding the availability of machines [13]. Simulation analysis for these performance parameters helps with visualizing and understanding system behavior for real-time manufacturing systems mentioned by [34][35][36][37][38]. A comparison of various features of this present study with other recent studies is shown in Table 1, below. A method needs to be used for ranking the performance parameters from most influenced to least, which furthermore can help with increasing manufacturing system performance and product quality. The integrated MCDM method considers all standards and the importance that decision-makers place to determine the most satisfactory solution based on performance evaluation [35]. Refs [35,36] mention that different MCDM tech-niques have been used to solve problems related to decision-making or ranking among alternatives. An Entropy method was presented by the [37] and was used in this paper for finding the weight of each criterion. An integrated MCDM methodology based on the TOPSIS method was used in this paper to rank the parameters. Among the various MCDM techniques, the TOPSIS method is best suited for decision-making problems since it has been observed that the TOPSIS method is preferred for considering the quantitative criteria mentioned by [17].
The main principle of the TOPSIS method is that the selected alternative should be the shortest distance from the positive ideal solution and the largest distance from the negative ideal solution. To determine the attribute weight for the TOPSIS method, the Entropy method is frequently used [21,22]. Generally, the Entropy method is used to calculate the weights of each criterion when decision-makers have conflicting views on the value of weights.

Methodology
In this paper, the performance process parameters were analyzed using the simulation analysis approach, and then the results were validated using real-time experimental calculation results. Later, an integrated MCDM method was selected to rank the parameters, because MCDM is a well-known technique for solving complex real-life problems of diverse alternatives using several criteria to rank or choose the best or worst alternative.
Different MCDM techniques can be used for solving decision-making problems, but TOPSIS is the best suited, and it has been observed that the TOPSIS method is preferred for considering quantitative criteria. The Entropy method is used in conjunction with the TOPSIS method. The Entropy method is applied to calculate the weight of each criterion and the TOPSIS method is used for evaluating the alternatives (parameters) based on these criteria. Various key parameters that influence flexible machine systems are shown in Figure 1, below.
A method needs to be used for ranking the performance parameters from most influenced to least, which furthermore can help with increasing manufacturing system performance and product quality. The integrated MCDM method considers all standards and the importance that decision-makers place to determine the most satisfactory solution based on performance evaluation [35]. [35,36] mention that different MCDM techniques have been used to solve problems related to decision-making or ranking among alternatives. An Entropy method was presented by the [37] and was used in this paper for finding the weight of each criterion. An integrated MCDM methodology based on the TOPSIS method was used in this paper to rank the parameters. Among the various MCDM techniques, the TOPSIS method is best suited for decision-making problems since it has been observed that the TOPSIS method is preferred for considering the quantitative criteria mentioned by [17].
The main principle of the TOPSIS method is that the selected alternative should be the shortest distance from the positive ideal solution and the largest distance from the negative ideal solution. To determine the attribute weight for the TOPSIS method, the Entropy method is frequently used [21,22]. Generally, the Entropy method is used to calculate the weights of each criterion when decision-makers have conflicting views on the value of weights.

Methodology
In this paper, the performance process parameters were analyzed using the simulation analysis approach, and then the results were validated using real-time experimental calculation results. Later, an integrated MCDM method was selected to rank the parameters, because MCDM is a well-known technique for solving complex real-life problems of diverse alternatives using several criteria to rank or choose the best or worst alternative.
Different MCDM techniques can be used for solving decision-making problems, but TOPSIS is the best suited, and it has been observed that the TOPSIS method is preferred for considering quantitative criteria. The Entropy method is used in conjunction with the TOPSIS method. The Entropy method is applied to calculate the weight of each criterion and the TOPSIS method is used for evaluating the alternatives (parameters) based on these criteria. Various key parameters that influence flexible machine systems are shown in Figure 1, below. In the experimentation analysis, the number of jobs has been taken as 5000, and the values of each individual parameter have been calculated. After that, the simulation analysis was conducted with the help of simulation software by varying the number of jobs from 100 to 5000. The obtained simulation results are mostly near the experimental values. Finally, the parameters of simulation results were ranked by influence on the flexible machine systems, from most to least. Figure 2 outlines the overview of the integrated MCDM-based simulation approach. In the experimentation analysis, the number of jobs has been taken as 5000, and the values of each individual parameter have been calculated. After that, the simulation analysis was conducted with the help of simulation software by varying the number of jobs from 100 to 5000. The obtained simulation results are mostly near the experimental values. Finally, the parameters of simulation results were ranked by influence on the flexible machine systems, from most to least. Figure 2 outlines the overview of the integrated MCDMbased simulation approach.

Comparative Results
Here, S1, S2… S6 indicates the sources from where jobs can be assigned to processors. The flexible machine systems consist of N number of identical machines in which the system must operate simultaneously to complete the given number of jobs shown in Figure  3. Figure 3a presents the one-degree flexible system in which, if any machine fails, then the remaining number of jobs can be adjusted on an adjacent connected machine. Figure  3b represents the two-degree flexible system in which, if any machine fails, then the remaining number of jobs can be adjusted on two adjacent connected machines depending upon the availability of machines. Here, the availability of machines has been increased in the case of two-degree flexible configuration compared to one-degree flexible configuration. Figure 3c,d represents the semi-flexible and fully flexible machines, in which the availability of machines is more compared to the one-degree flexible system than the twodegree flexible system [9].

Comparative Results
Here, S1, S2 . . . S6 indicates the sources from where jobs can be assigned to processors. The flexible machine systems consist of N number of identical machines in which the system must operate simultaneously to complete the given number of jobs shown in Figure 3. Figure 3a presents the one-degree flexible system in which, if any machine fails, then the remaining number of jobs can be adjusted on an adjacent connected machine. Figure 3b represents the two-degree flexible system in which, if any machine fails, then the remaining number of jobs can be adjusted on two adjacent connected machines depending upon the availability of machines. Here, the availability of machines has been increased in the case of two-degree flexible configuration compared to one-degree flexible configuration. Figure 3c,d represents the semi-flexible and fully flexible machines, in which the availability of machines is more compared to the one-degree flexible system than the two-degree flexible system [9].

Experimental Analysis
The values of each parameter have been calculated by considering the number of jobs as 5000 and, as mentioned below in Table 2, to obtain that level a majority of machines break down at least once. Throughput time is the actual time taken to manufacture a product, and it can be calculated by multiplying the average stay time by the total number of jobs per machine compared with the existing literature values [9]; similarly, throughput rate is the rate at which units move from start to finish, and it can be calculated by dividing the output by the Throughput Time. The Availability is the amount of time in which the machine runs and is available for production, and can be calculated by Equation (1).

M TB F A vailability M TB F M TTR
The average stay time and Maximum Stay Time can be calculated from the bell curve by considering a 99.97% confidence level since the processing time follows the normal distribution. The system use can be defined as the proportion of time that the manufacturing system is used, and system use is calculated by Equation (2).

Experimental Analysis
The values of each parameter have been calculated by considering the number of jobs as 5000 and, as mentioned below in Table 2, to obtain that level a majority of machines break down at least once. Throughput time is the actual time taken to manufacture a product, and it can be calculated by multiplying the average stay time by the total number of jobs per machine compared with the existing literature values [9]; similarly, throughput rate is the rate at which units move from start to finish, and it can be calculated by dividing the output by the Throughput Time. The Availability is the amount of time in which the machine runs and is available for production, and can be calculated by Equation (1).
The average stay time and Maximum Stay Time can be calculated from the bell curve by considering a 99.97% confidence level since the processing time follows the normal distribution. The system use can be defined as the proportion of time that the manufacturing system is used, and system use is calculated by Equation (2). various configurations from a single degree to fully flexible are shown in Figure 3. The processing time, mean time between failures (MTBF), and Mean Time to Repair (MTTR) follow the normal distribution, and the time required to repair a machine has been considered to be constant.

Warm-Up Period
The number of replications for the simulation was determined as 20 and the length of each replication was 1 h with a warm-up period of 8 h for a one-degree flexible configuration, as shown in Figure 4a in the case of no breakdown of machines. The warm-up period for the two-degree flexible configuration, semi-flexible, and fully flexible configurations without the breakdown of machines are 8 h, 13 h, and 10 h, as shown in Figure 4b-d, respectively. Similarly, the warm-up period with the breakdown of machines for various configurations is shown in Figure 5. The warm-up period for one-degree and two-degree flexible configuration, semi-flexible, and fully flexible configurations following the breakdown of machines are 6 h, 14 h, 11 h, and 14 h as shown in Figure 5a-d, respectively. The warm-up period has been obtained by applying Welch's procedure [38] to estimate a steady-state mean. The technique often suggested for these kinds of problems is called the warm-up period or initial data deletion. The main idea is to delete the initial observations from the run and use the remaining observations to obtain the steady state. The number of replications has been calculated with the help of the following Equation (3) [38].
where X(n) represents the sample mean, s represents sample standard deviation, and n represents the number of replications, and t n−1,1−α/2 is the upper and 1 − α/2 critical points where the warm-up period is in the case of breakdown for one-degree configuration of 6 h. Then, the desired confidence interval for 95% confidence level is 6 ± t 19,0.025 7.504 √ 20 . From the results, it can be observed that the 20 simulations are enough from the initial approach mentioned in [38]. The warm-up period has been identified from the plot as shown in the figure below for various configurations.

Parameter Analysis
Various parameters, such as Throughput Rate (TR) in throughput/hour, Throughput Time (TT) in seconds, System Use (SU) as a percentage, Availability (A), Average Stay Time (T avg ) in seconds, Maximum Stay Time (T max ) in seconds, have been generated with the help of simulation software for one-degree, two-degree, semi-flexible, and fully flexible configurations without and with the breakdown of machines. The number of machines has been varied from 100 to 5000, and the simulation results have been presented for various configurations in Tables 3-6, respectively. The collected values of the parameters' effect on flexible machine systems are represented in Table 7. These values were generated using the simulation procedure for various configurations without and with machine breakdown by considering the number of jobs as 5000. Initially, different normally distributed Mean Time Between Failure (MTBF) values for the different machines (processors) and constant MTTR (Mean Time to Repair) as 1 day and normally distributed processing time has been considered to obtain random failure. Figure 6A-D represents the simulation results of various parameters (throughput rate, system use, and average stay time) for various configurations without the breakdown of machines. Similarly, Figure 7A-D represents the simulation results of the above-mentioned parameters with the breakdown of machines. These simulation results have been generated by arranging the machines as per the configuration and data have been provided in the simulation software with the help of MTBF, MTTR, and processing time for each machine.

Proposed Entropy Weight-Based TOPSIS Method
In this paper, the frequently used normalization methods Entropy and TOPSIS methods, as these two methods are used in combination with each other, have been analyzed for the collected simulation data. The Entropy method is used to calculate the weights of each criterion when decision-makers have conflicting views. The weights calculated by the Entropy method are also called objective weights. The Entropy method shows how much different alternatives approach one another in respect to a certain criterion. The best advantage of the Entropy method is the avoidance of human factor interference on the weights of indicators. With this advantage, the Entropy method has been widely used in recent years. The Entropy method consists of four steps, as mentioned below. Equations (4)-(7) are formulas to calculate the weights of each criterion are as follows [21,22]. The TOPSIS method is used to find a ranking for each individual alternative. The TOPSIS

Proposed Entropy Weight-Based TOPSIS Method
In this paper, the frequently used normalization methods Entropy and TOPSIS methods, as these two methods are used in combination with each other, have been analyzed for the collected simulation data. The Entropy method is used to calculate the weights of each criterion when decision-makers have conflicting views. The weights calculated by the Entropy method are also called objective weights. The Entropy method shows how much different alternatives approach one another in respect to a certain criterion. The best advantage of the Entropy method is the avoidance of human factor interference on the weights of indicators. With this advantage, the Entropy method has been widely used in recent years. The Entropy method consists of four steps, as mentioned below. Equations (4)- (7) are formulas to calculate the weights of each criterion are as follows [21,22]. The TOPSIS method is used to find a ranking for each individual alternative. The TOPSIS method is used to obtain the solution which is nearest the positive ideal solution and farthest from the negative ideal solution. The application of the TOPSIS method in ranking various factors that affect flexible unit systems has been reported in the literature. Various steps involved in the TOPSIS method are explained below with the help of Equations (8)-(14) [21,22].

Weight Calculation by Entropy Method
Step 1. Normalize the decision matrix The performance value of a th alternative and b th criteria in Equation (4) is indicated by A ab = (a = 1, 2, . . . . . . , m; b = 1, 2, . . . , n) and the normalized matrix is shown in Table 8. Step 2. Entropy value of E b for b th criteria Entropy value E j of b th criteria can be obtained by Equation (5) and is shown in Table 9.
where K = 1/ ln x is a constant to satisfy the condition 0 ≤ E b ≤ 1 and 'b' indicates the number of alternatives or factors. Step 3. The degree of divergence of average information The degree of divergence of average needs to be discovered using Equation (6). The degree of diversity value matrix is calculated and shown in Table 10. Step 4. The weight of Entropy of b'th criteria The weight of criterion can be calculated by Equation (7) and is represented in Table 11.

Ranking the Parameters by TOPSIS Method
Step 1. Normalization of the decision matrix.
The normalization matrix can be calculated by Equation (8). The normalized decision matrix is formed and shown in Table 12.
The associated weights W b are multiplied with the normalized matrix and taken from each parameter to be obtained by following Equation (9). The weighted normalized decision matrix is formed and shown in Table 13. Step 3. Determining positive ideal solution and negative ideal solution.
The positive ideal solution and the negative ideal solution are determined using Equations (10) and (11) respectively. The positive ideal and negative ideal solution matrix is formed and shown in Table 14.
where K is the index of set of benefit criteria and K | is the index of cost criteria. Step 4. Finding the Euclidean distance from positive ideal solution and negative ideal solution. The Euclidean distance from positive ideal solution and negative ideal solution can be computed by the below Equations (12) and (13), respectively. The Euclidian distance matrix from positive ideal solution and negative ideal solution is formed and shown in Table 15. Step 5. Calculating the relative closeness (performance score).
The relative closeness is calculated from the ideal solution using Equation (14).
Equation (14) indicates the relative closeness in which the higher value indicates the best rank and lower value indicates the worst rank. The relative closeness value matrix is formed based on obtained value, and ranks the parameters as shown in Table 16. Table 16. Matrix of relative closeness and ranking of the parameters.

Ranking the Parameters by PROMETHEE II Method
PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) is a MCDM method, and it has been widely used to rank the alternatives in many decisionmaking problems [39]. This method is based on a pair to pair of possible decisions along with each criterion. Various possible decisions need to be evaluated according to different criteria, which is to be maximized or minimized.
Step 1. Determination of pairwise comparisons deviations. It can be calculated by Equation (15). d j (m, n) = g j (m) − g j (n) (15) where d j (m, n) is the difference between the evaluations of m, n on each criterion.
Step 2. Application of preference function is shown in Equation (16).
where S j (m, n) indicates the preference of alternative m with regard n on each criterion.
Step 3. Calculation of global preference index can be calculated by Equation (17).
where π(m, n) defined as the weighted sum of each criterion, w j denotes the weight associated with the j'th criterion.
Step 4. Calculation of outranking flows can be calculated by Equation (18).
Step 5. Calculation of net outranking flow can be calculated by Equation (19).
where φ(a) indicates the net outranking flow.
The comparison between the TOPSIS and PROMETHEE II rankings without breakdown and with a breakdown of machines is shown in below Table 17, and the comparison between the TOPSIS and PROMETHEE II rankings without breakdown and with breakdown plots is shown in Figure 8a,b.

Conclusions and Future Directions
In this paper, the maximum number of jobs has been taken as 5000 in a real-time experiment and values of mentioned six parameters, i.e., throughput rate, Throughput Time, system use, Availability of machines, average stay time, and Maximum Stay Time, have been obtained. To compare these experimental results, simulation analysis was conducted with the help of simulation software by varying the number of jobs from 100 to 5000 by considering the breakdown of machines and no breakdown for various configurations. Later, the Entropy method was used for simulation results to compute the weights of each criterion, and the integrated MCDM-TOPSIS method was employed to rank the parameters from the most affected to the least affected by considering breakdown and no breakdown of machines. From the obtained results, it can been observed that the Throughput Time of 431,921.51 s is the most affected performance parameter and Availability, Av-

Conclusions and Future Directions
In this paper, the maximum number of jobs has been taken as 5000 in a real-time experiment and values of mentioned six parameters, i.e., throughput rate, Throughput Time, system use, Availability of machines, average stay time, and Maximum Stay Time, have been obtained. To compare these experimental results, simulation analysis was conducted with the help of simulation software by varying the number of jobs from 100 to 5000 by considering the breakdown of machines and no breakdown for various configurations. Later, the Entropy method was used for simulation results to compute the weights of each criterion, and the integrated MCDM-TOPSIS method was employed to rank the parameters Funding: This work has been, also, supported by the FCT within the RD Units Project Scope: UIDP/04077/2020 and UIDB/04077/2020.