Analysis of the Influence of Standard Time Variability on the Reliability of the Simulation of Assembly Operations in Manufacturing Systems

Abstract

Objective:

The aim of this article is to analyze the influence of the variability of the standard time in the simulation of the assembly operations of manufacturing systems.

Background:

Discrete event simulation (DES) has been used to provide efficient analysis during the design of a process or scenario. However, the modeling activities of new configurations face the problem of data availability and reliability when it comes to seeking standard times that are effective in representing the actual process under analysis, especially when the process cannot be monitored.

Method:

The methods-time measurement (MTM) is used as a source of standard times for simulation. Assembly activities were performed at a Learning Factory facility, which provided the necessary structure for simulating real production processes. Simulation performances using different variability of standard times were analyzed to define the impact of data characteristics.

Results:

The MTM standard time presented an error of approximately 5%. The definition of the data variability of standard times and the statistical distribution impacts were shown in the simulation results, with errors above 6% being observed, interfering with the model reliability.

Conclusion:

Based on the study, to increase the adherence of a simulation to represent a real process, it is recommended to use triangular distributions with central values greater than those established via the MTM for the representation of the standard times of new assembly processes or scenarios using DES.

Application:

The study contributions can be applied in assembly line design, providing a reliable model representing real processes and scenarios.

Keywords

discrete event simulation methods-time measurement work measurement assembly workstation operations research industrial environment virtual environment

Introduction

Globalization and increased competitiveness have resulted in changes in manufacturing systems. Companies have sought to use new methods aimed at reducing time and costs in the product and process development stages. In this context, discrete event simulation (DES) has been widely used for the development of new manufacturing systems or in the analysis of scenarios for process improvement and decision making (Dode, Greig, Zolfaghari, & Neumann, 2016).

In addition to its application in process development, simulation has been used in capacity analysis (Argoneto & Renna, 2013), the identification and reduction of bottlenecks in the production flow (Atieh, Kaylani, Almuhtady, & Al-Tamimi, 2016; Yang, Bukkapatnam, & Barajas, 2013), increasing operational efficiency (Zeng, Wong, & Leung, 2012), and resource management (Lu, Petersen, & Storch, 2007). This wide use demonstrates the diversity of analysis provided through DES that facilitates process analysis, as changing real systems can be expensive in terms of cost and time (Budgaga et al., 2016).

Considering the manufacturing case, the use of simulation models is even more recommended because their analysis results in a considerable increase in time and cost, as their systems can be extremely complex due to factors such as manufacturing different items in the same line and batch processing (Fowler & Rose, 2004). Due to these characteristics, DES has been applied successfully in assembly operations in the manufacturing area because the flexibility of this type of simulation allows for the reproduction of production system complexities (Iannone, Miranda, Prisco, Riemma, & Sarno, 2016; Negahban & Smith, 2014).

DES uses a software platform to represent the system under analysis. The simulation has a stochastic nature, generating randomness through the use of statistical distributions to represent process events as the time to execute an activity or to change equipment (Tako & Robinson, 2012). These statistical distributions are defined by statistical tests to decide which configuration is appropriate for the data representation. As the software runs the process, the data will vary according the defined distribution, in this way providing the mechanism to represent the natural process variability and, as a consequence, the variability of the system as a whole. Therefore, natural variability (i.e., the number of items manufactured by a production line) can be reproduced to enable a better analysis of the system reality.

However, despite its application-related advantages, the effectiveness of a simulation study is conditioned to the reliability of the input data of the virtual system, which directly impacts the efficacy of the model defined to simulate the real system under analysis. In the case of the development of new processes or new scenarios, the difficulty associated with the availability of information on the process should be taken into consideration, as the process observation and timing are disabled, considering that the process implementation will be applied only after the virtual analysis. In assembly operations, in which scenario analysis is the most used optimization method (Prajapat & Tiwari, 2017), the availability of reliable data for the simulation of production alternatives becomes a critical factor.

Simulations have been successfully used to study and analyze systems that human work has supported (Wickens, Sebok, Li, Sarter, & Gacy, 2015; Steiner, Burgess-Limerick, & Porter, 2014), but the need to increase the reliability of operator representation in the simulation of assembly operations is still an important issue as highlighted by Dode et al. (2016). At this study, the goal is to insert human factors, such as fatigue and the operator’s learning curve, into manufacturing system modeling. Małachowski and Korytkowski (2016) also presented alternatives to incorporating the operator’s learning curve into DES. However, the authors did not address the reliability of the data sources used to represent the operator, so this remains a relevant question to be analyzed in cases where the actual values of the processes are unavailable. Thus, the need to provide reliable standard times that are effective in representing the actual processes under analysis, specifically with regard to their values and variability, is highlighted. Given this issue, the aim of this article is to analyze the influence of the variability of standard times in the simulation of the assembly operations of manufacturing systems.

To this end, the methods-time measurement (MTM) will be used, defined as a system of standard times established according to statistical bases (Cakmakci & Karasu, 2007). Currently, the MTM has been used as a data source for virtual systems, as in Kuo and Wang (2009, 2012), because it is considered an intuitive and reliable database for supporting the analysis of human movements, serving in this research as a source of standard times in the evaluated processes. The MTM contributes to facilitating human-computer interaction (HCI) with regard to the simulation software because its language is simple and intuitive, allowing the analyst to understand the process and its activities, so that it is possible to define the simulated model more closely to reality, thus improving the modeling process and the data entry in the software.

The study was carried out in the Learning Factory that Helleno et al. (2013) developed for the integral teaching of lean manufacturing concepts in the university and industry environments. A Learning Factory offers an approach to representing manufacturing works at an operational level (Barton & Delbridge, 2001), providing a facility dedicated to simulating real production processes and environments according to academic and educational purposes (Tisch, Hertle, Abele, Metternich, & Tenberg, 2015). According to Dinkelmann, Siegert, and Bauernhansl (2014) and Tisch et al. (2015), besides educational objectives, a Learning Factory may also be used for research purposes. This structure was chosen because it provided the industrial environment necessary for applying the study proposal and enabled the management of the process variables without disrupting the production.

Literature Review

The models defined through the use of DES are intended to understand how a system works over time and how it behaves under different conditions. DES models a system defined by entities, as for instance, the parts in a factory. These entities have attributes to determine how they will act in the system (Tako & Robinson, 2012), defining which equipment will be used in the manufacturing process and in which order. By means of this mechanism, a queue of events is created, and as they occur, the state of the system is affected (Alrabghi & Tiwari, 2016), with parts being produced, setups, and maintenance occurring according the simulation modeling.

The sequence and variation of these events are defined by the data input into the system. Hence, the data modeling process is an essential step of the simulation (Oliveira, Lima, & Montevechi, 2016). DES can represent the observed variations in real processes through the use of probabilistic distributions (Prajapat & Tiwari, 2017). However, the exact data for determining the statistical behavior of the variables are not always available, with part of these data being related to the standard times of the execution of activities.

The use of standard time is often necessary due to the use of operators in production lines, which provides flexibility in the processes to absorb the changes that consumers demand without the need for major operational changes. The use of labor in manufacturing systems has not yet been surpassed by the technology systems available, due to its high cost and the loss of flexibility obtained with its implementation (Małachowski & Korytkowski, 2016).

Stopwatch techniques and predetermined time systems (PTSs) consist of methods to define the standard time. Stopwatch methods provide the process variability; however, they require the systematic observation of the activities to obtain the set of values necessary to determine the operating time. Therefore, these methods represent an inappropriate approach in cases of new processes and new scenarios in which the observation may be impossible because the simulation is going to represent virtually a configuration that does not exist and, for this reason, cannot be observed. Moreover, according to Nakayama Nakayama, and Nakayama, (2002), stopwatch techniques may induce subjective impressions during the parameter definition that the analyst performs.

PTSs define movements such as grab and move, defining codes and estimated value times for their execution. When analyzing a process, it is possible to identify the standard movements necessary for its realization and, through the sum of the values assigned to these movements, to obtain the value of the total time required to perform an activity. To determine the sequence of movements, it is necessary to observe the process movements; however, because the PTSs use tabulated movements and values, systematic and multiple observations of the process are not necessary for the determination of the execution time. When the process does not exist (new process and scenarios), the sequence of movements can be determined by the definition of the process activities and, when viable, the physical simulation of movements to understand the sequence. In that case, a simple and unique simulation is sufficient for analysis but different from the stopwatch technique that requires multiple and detailed reproductions of activities to determine the process time with statistical reliability. The PTS bases provide the time with statistical reliability and eliminate the necessity of systematic process observation and evaluation of the operator activities and also still allow the working time to be estimated in the planning phase of a process (Cakmakci & Karasu, 2007).

Among the PTSs, the MTM stands out as one of the most used time systems (Alrabghi & Tiwari, 2016) and is therefore applied as an international standard for work performance. Another PTS called the work factor (WF) is also applied in industry, but its methods consider the execution time for a more skilled operator versus considerations related to the MTM, so the values determined via the WF are on average 20% smaller than those established via the MTM (Lehto & Buck, 2007).

The objectives of the MTM application are linked to the standardization and optimization of work efficiency (Kuo & Wang, 2009). Besides that, the times that the method defines are used to determine the work rates in the industry (Di Gironimo, Di Martino, Lanzotti, Marzano, & Russo, 2012), thus providing a standard of comparison for the performance of a process. By using the MTM analysis, proposed changes in the processes can be immediately quantified concerning the operating time (Kuhlang, Edtmayr, & Sihn, 2013) through the analysis of the sequence of movements, providing the time values necessary for the simulation.

The MTM has been applied to the analysis of assembly line movements as in the studies of Kothiyal and Kayis (1995), Tseng and Tang (2006), Kernbaum, Franke, and Seliger (2009), Kuo and Wang (2009), Desai and Mital (2010a), and Baraldi and Kaminski (2011). In addition, the method has been applied in the analysis of maintenance procedure movements, such as in Desai and Mital (2010b), Desai and Mital (2011), and Di Gironimo et al. (2012).

The accuracy of the MTM was assessed in the studies of Knott and Sury (1986) and Kothiyal and Kayis (1995). Knott and Sury compared the tabulated times with the real times collected in the study, finding positive and negative differences among the cases verified. In the study of Kothiyal and Kayis, the authors reported that the MTM records the times of the activities in an underestimated way, defining less time than necessary for the accomplishment of the tasks. The times observed in the studies of Kuo and Wang (2009) and Di Gironimo et al. (2012) were also higher than those determined via the MTM.

In current studies, such as Desai and Mital (2011), Kern and Refflinghaus (2013), and Bedny and Harrys (2013), the MTM has been applied with deterministic values for the execution times of activities, without considering the variability inherent in human activities. However, for the DES application, the system must take into account the variability of the processes to obtain greater reliability regarding the reality. Therefore, variability in the standard time values used in the modeling is necessary to consider.

Robinson (2004) stated that when the probabilistic curve of an event is unknown, uniform and triangular distributions can be used to represent the data. According to Banks and Chwif (2011), the triangular distribution is usually applied to simulate the process time at the beginning of a simulation project, in the absence of exact data.

However, these distributions are considered approximations regarding the actual distribution of operating times, which, according to Murrel (1961) and Dudley (1963), should be determined with a normal distribution in which, for experienced operators, the highest occurrence frequency is concentrated in values positioned to the left of the mean. However, according to Banks and Chwif (2011), manual service times generally follow the lognormal distribution. Despite this application, the use of the triangular distribution may result in errors when representing a process whose real distribution would be lognormal, as shown in Figure 1.

Figure 1.

Operation represented as a lognormal and simulated as triangular (Banks & Chwif, 2011).

However, errors resulting from the approximations made via the substitution of real values for the uniform and triangular approximation curves may not affect the simulation results. According to Banks and Chwif (2011), the incorrect definition of the distribution curve of a variable may not result in significant differences in the simulated model, as the choice among a lognormal, uniform, or triangular is possibly indifferent in the simulation results.

Research Methods

Participants

The systematic execution of activities was conducted with production engineering students representing the operators’ performance. Of 37 students who collaborated, 73% were male, 100% of the sample was between 19 and 22 years, and none had experience working with assembly-line activities.

This research complied with the American Psychological Association Code of Ethics and was approved by the institutional review board at Universidade Metodista de Piracicaba. Informed consent was obtained from each participant.

Procedures

The approach defined for the study was divided into five stages as shown in Figure 2. Stages I, II, and III were performed in the assembly line structured in the Learning Factory. Plant simulation software was adopted in this study as the virtual modeling environment used in Stage V. The plant simulation system, which uses a discrete event-based framework for dynamic process modeling, has been widely applied in the production environment as presented in Owida Byrne, Heavey, Blake, and El-Kilany (2016).

Figure 2.

Research methods.

The goal of Stage I was to define the assembly line configuration, because the structure used in the work offers flexibility for determining the division and order of activities to reach the study goals. For the correct implementation of MTM-1, according to Di Gironimo et al. (2012), the process presents a short cycle time (less than 3 min) as a prerequisite. Thus, the distribution of activities between operators must guarantee that each is going to work for less than 3 min at each part being processed. In addition to this requirement, the process must be defined with consideration of the resource constraints.

The division of activities into movements, performed via the MTM, should be applied after the analysis of the entire structure of activities, including the logical organization of cognitive and motor actions (Bedny, Karwowski, & Voskoboynikov, 2015). Therefore, during Stage I, the best sequence of task execution was analyzed and defined before the application of the MTM took place.

Stage II subsequently sought to obtain the probability distribution of the assembly-line data for its comparison with the MTM values. To achieve this goal, two scenarios were defined: operator in the learning period (Scenario 1) and trained operator (Scenario 2). Statistical procedures were executed to determine the number of participants to perform Scenarios 1 and 2, giving confidence to the result.

The probability distribution of each scenario was determined for every operator following the statistical tests usually applied in simulation studies. Stage III refers to the application of the MTM’s standard movements in the defined sequence, as well as the definition of the standard time.

The comparison between the values obtained via the operators’ time was developed in Stage IV, simultaneously with the comparison between the values and distributions obtained in each scenario. The probability distributions to be introduced in the MTM values were also defined at this stage of the research, taking into account the analysis of the distributions observed in the process.

The DES model was developed in Stage V to represent the assembly line and, based on the human times verified in the scenarios, validate the proposed distributions for the MTM. During the modeling process, the conceptual model was developed according to the instructions that Robinson (2015) provided, and the verification and validation process were carried out following the guidelines of Sargent (2013). The results of the simulations regarding the different proposals for the distributions of the MTM and the values that the method originally defined were compared to define the appropriate approach for the use of the MTM in DES.

Results and Discussions

In Stage I, the process structure was identified via the assembly of a pilot product. During this pilot, the activities were timed to base the division of tasks between the workstations. The process configuration was defined with three workstations as shown in Figure 3, resulting in a simplified assembly line. Workstations 1 and 2 were analyzed concerning the process time and MTM values. The third workstation received outputs from workstations 1 and 2.

Figure 3.

Assembly line configuration.

In Stage II, 31 operators were selected to carry out the activities so as to allow a comparison of the results. The systematic execution of the process was carried out in 2 days, with 1 day for each workstation to avoid the interference of possible fatigue at the time of the second workstation execution if it was performed the same day.

On the first day, a training exercise was executed, showing the operators the basic assembly sequence to be followed. After that, operators performed the process for the first time to understand the assembly requirements. The execution of the process followed, collecting the data for Scenario 1: learning with 150 executions of Workstations 1 and 2. In this period, the authors observed that the operators’ skills with and knowledge of the assembly sequence appeared to be under development. The next day, the process execution was carried out to collect data for Scenario 2: trained with 150 executions of Workstations 1 and 2.

The results of this initial experiment were analyzed to determine the number of participants necessary to represent the operators’ performance according Equation 1:

n = (\frac{Z_{α / 2} * σ}{ϵ})

(1)

where n represents the sample size, Z is the critical value according the confidence determined by α, σ represents the deviation of an initial sample, and ϵ represents the acceptable error. The initial deviation was determined by the media of the 31 operators for the two workstations. The deviation was defined as 7.68 s. With a 95% confidence interval and 2.5 s of acceptable error, the sample size was defined as 37 participants. To complete the data, the same systematic execution of the process was conducted with six more participants.

The results of each execution were analyzed, and the outliers were identified by examining the box plot graphs. Using the graphs, the outlier was identified, considering the median as a reference and 25% of the data above and under this value as the first and third quartiles. Based on the difference of these quartiles, the values of the second and fourth quartiles were defined, and the outlier was the data plotted above these quartiles. In the simulation data, the outlier can originate from a measuring error or an anomaly in the process, the loss of a part during the assembly process, or some outside interruption.

Anderson Darling and Kolmogorov–Smirnov statistical tests were performed. These tests verify if a family of distributions can represent a sample of data measuring the difference between each statistical distribution and the sample data probabilistic distribution. These tests can show, for example, whether the normal distribution can represent a sample of data. As a result, the tests show which statistical curves could represent the human data, together with the respective parameters for this representation. For the definition of the most appropriate curves between the ones considered appropriate by the tests, the simulation analysts apply graphical comparisons between the observed values and the values of each of the possible representative curves. Therefore, the chosen curve is defined by a combination of statistical tests and visual selection. The distributions defined for each of the proposed scenarios are presented in Table 1.

Table 1:

Statistical Distributions Definition

Scenario	Statistical Distribution	Percentage of Use (Between 37 Operators)
1: Learning	Lognormal	81.1%
	Weibull	10.8%
	Normal	8.1%
2: Trained	Lognormal	86.5%
	Erlang	8.1%
	Weibull	5.4%

According to the results, most cases could be represented by the lognormal, with the exception of 18.9% of operators in the learning scenario and 13.5% of the cases in the trained scenario. Banks and Chwif’s (2011) assertion that manual service times can usually be represented by a lognormal distribution could be applied to the study conditions because it is the chosen distribution for most cases. Analyzing Table 1, it was found that lognormal was the distribution considered appropriate for most scenarios, especially the trained scenario, which was considered to be the closest to a stable industrial process. The statements that Murrel (1961), Dudley (1963), and Knott and Sury (1986) made in relation to the normality of the manual process were not verified, because the normal curve was defined as the most adequate for the representation of the processes in only 8.1% of the cases in the learning scenario.

However, according to the statistical tests, more than one curve was usually considered acceptable for the representation of a given group of data. Although it was not defined for the representation of the values in the simulation, the normal curve was considered adherent to the data in 89% of the cases in the learning scenario and 81.1% of the cases in the trained scenario. However, according to Law (2008), normal function is rarely considered the correct function for the representation of manufacturing processes.

All operators’ times to assemble one part are given in Figure 4 as the mean, minimum value, maximum value, and deviation in each situation.

Figure 4.

Sample statistics.

In analyzing Figure 4, it can be seen that all the statistics present a decrease in values between the learning and trained scenarios. The decrease of the deviation value between the scenarios may indicate the stability of the process with less process time difference. These results might be a consequence of the learning experience, because the operators became better trained during the assembly sequences. According to Małachowski and Korytkowski (2016), repetition of activities leads an operator to become more familiar with parts and tools, thus resulting in less process time.

During the experiments, the authors observed differences in values between operators’ performances, showing that personal characteristics can influence process time. This confirmed the researchers’ perception that an operator’s characteristics might influence processing time and, consequently, the accuracy of the MTM values.

In Stage III, the MTM analysis was done based on the sequence of activities defined for each workstation. Through the identification of the sequence of performed movements, the MTM values were defined as 73.75 s for Workstation 1 and 37.45 s for Workstation 2.

In Stage IV, the differences between the mean values of the sample and the MTM values were evaluated. Table 2 shows the deviation between MTM and the values in each scenario.

Table 2:

Difference Between the Human Data and MTM

Scenario	Workstation 1			Workstation 2
Scenario	Mean (s)	MTM Value (s)	Deviation (s)	Mean (s)	MTM Value (s)	Deviation (s)
Learning	84.35	73.75	−10.60	49.35	37.45	−11.90
Trained	77.32	73.75	−3.57	38.77	37.45	−1.35

Regarding the accuracy of the MTM, Table 2 shows that all mean values of the samples for the Trained scenario, considered similar to a usual industrial environment, are higher than the values determined via the MTM. In addition to the accuracy of the MTM, the errors originating from the identification of movements, cases, and distances that the researchers performed can also be considered a source of differences between the observed values and the MTM.

Table 3 shows the percentage of difference among the minimum, maximum, and mean values of the sample for both operators in the experienced scenario compared with the value determined in the MTM for each of the workstations. In addition, at the end of the table is presented the mean difference of each of the values regarding the MTM.

Table 3:

Percentage Difference Between Sample Statistics for Trained Scenario and MTM

Work Sequence	Minimum Value (s) of Trained	% of Difference Considering MTM	Mean (s) of Trained	% of Difference Considering MTM	Maximum Value (s) of Trained	% of Difference Considering MTM
Workstation 1	68.74	93.21%	77.32	104.84%	87.45	118.58%
Workstation 2	32.74	87.42%	38.77	103.52%	56.01	149.56%
Mean		90.32%		104.18%		134.07%

The determination of the parameters of the curves in relation to the MTM was defined by means of the results presented in Table 3. All values were defined using the percentage of difference between MTM and the sample statistics. The minimum value was defined based on the mean of the minimum values (90.32%), using 90% and 95% of the MTM as the minimum values for the proposed distributions. Differences around 18.58% and 49.56% were presented in the maximum value. Workstation 2 presented a larger difference, resulting in an elevated mean value. We verified that sometimes more attempts were required to assemble a specific part at this workstation, resulting in this value. Most of the actual data collected from the participants were represented by the lognormal, and this curve has a right tail with lower incidence of probability (i.e., its higher values have a low probability of occurrence). This format is not observed by the uniform curves, in which the probability of distribution is the same throughout the whole stretch, and even with the triangular the probability difference also decreases more sharply to the right of the graph compared with lognormal. Therefore, the values defined were lower than those observed (i.e., between 120% and 125% was defined for the maximum value in the triangular distributions and 115% and 120% for the uniforms).

The central value for one of the triangular distributions was defined as a value higher than the MTM, because the mean values observed in the process were higher than the standard time that the MTM defined. The mean value was established based on the value of 104.18%. Because the difference between the sample and the MTM was less than 5%, the values used were established within 100% and 105% of the MTM.

Considering these values, two configurations of uniform and triangular curves were tested, and their configuration parameters are shown in Table 4.

Table 4:

Values According to the MTM for the Proposed Distributions

Proposed Distribution	Values Regarding MTM
Proposed Distribution	Minimum	Mode	Maximum
Uniform 1	90%*MTM		115%*MTM
Uniform 2	95%*MTM		120%*MTM
Triangular 1	90%*MTM	100%*MTM	120%*MTM
Triangular 2	95%*MTM	105%*MTM	125%*MTM

A comparison between the proposed uniform and triangular curves and the two operators’ lognormal curves, as an example of the adherence of the proposed curves, is shown in Figure 5. Graphically, differences between operators can be observed, showing that the proposed curves can be more adequate for a set of data than other types of curves. The continuous curve represents the proposed distributions.

Figure 5.

Comparison between uniform and lognormal distributions.

In relation to the probability distributions proposed for the MTM, it can be seen through the evaluation of Figures 5 and 6 that the graphical arrangement of the triangular curve is more similar to the lognormal curve than the uniform curve. However, the uniform curve covers a larger area in cases where the deviation of the process is wider. Because the graphical analysis was defined for only two operators, the results regarding the general adherence cannot be made, although the analysis of similarity with the lognormal curve is valid for most of the cases in which it was defined for human data representation.

Figure 6.

Comparison between triangular and lognormal distributions.

In Stage V, the conceptual model considered few simplifications as represented in Figure 7. The inventories were not considered to increase the dependency between the workstations and, therefore, provided a better visualization of the impact of using different data in the simulations. Production takes place at Workstations 1 and 2, which only begin the production of a new unit if Workstation 3 is free to process the items released by the previous workstations.

Figure 7.

Conceptual model.

The data of each operator were used in different simulations, and the mean result among the 37 operators was determined. In this way, it would be possible to evaluate which proposed distribution (Uniform 1, Uniform 2, Triangular 1, or Triangular 2; presented in Table 5) is closer to the real process, which was represented as the mean among operators. In addition, a simulation using the MTM deterministic values was elaborated. Table 5 presents the results obtained for a week of operation.

Table 5:

Simulation Results With Different Probability Distributions

Parameters	Mean of Operators	MTM	Uniform 1	Uniform 2	Triangular 1	Triangular 2
Working time workstation 1	93.28%	90.01%	91.17%	88.41%	92.03%	94.73%
Working time workstation 2	51.59%	45.77%	41.11%	41.22%	46.18%	49.82%
Production (pieces)	1919	1930	1925	1792	1929	1919
Mean time workstation 1 (s)	76.13	73.64	75.41	78.54	74.62	77.16
Mean time workstation 2 (s)	41.85	37.45	38.55	36.73	37.21	39.53

According to the results presented in Table 6, it can be noticed that the uniform curves presented smaller values for the working time than the simulation did using the values that the MTM determined when compared with the average values of the operators. It can also be noticed that the values that the triangular curves represent are closer to the average of the operators, with the results of Triangular 2 being closest to the desired values. This curve had its central parameter set at a value above that determined with the MTM (105% of the MTM).

Table 6:

Confidence Interval of Simulations

Simulation	Mean	Deviation	Variation Regarding the Mean of Operators
Mean of operators	1919.13	0.82
MTM	1930		0.57%
Uniform 1	1925.22	0.42	0.32%
Uniform 2	1792.43	12.95	−6.60%
Triangular 1	1929.98	0.63	0.57%
Triangular 2	1919.25	0.76	0.01%

In analyzing the quantity of pieces, the values presented a small variation between the simulations, ranging from 1,792 to 1,930 pieces. This analysis could invalidate the affirmation that Banks and Chwif (2011) made, that the definition of the probability curve for the simulation data representation may not present significant differences in the model results.

To deepen the analysis of this result, the variability of the model regarding the quantity of pieces produced through the performance of simulation rounds was verified. Table 6 shows the mean and standard deviations of the number of pieces produced.

The results showed that the simulation with Triangular 2 resulted in a closer variability compared with the average between operators. Uniform 2 presented the farthest results compared with the mean values of the operators.

Table 6 also shows the variations in percentage in the average results in relation to the average of operators. It can be verified that in the Uniform 2 case, the variation difference is higher than 6%, showing that its use in the simulation is not feasible for representing the processes under analysis. The Triangular 2 curve presented a difference percentage close to zero, showing its validity in representing the actual data of the process with a low error rate. Due to the differences in values, the impact of the choice of the distribution curve and its values on the simulation reliability are highlighted.

Thus, through the evidence presented, it can be stated that the triangular curve with a central value greater than that established via the MTM is considered more adequate for the representation of the MTM values in DES considering the case under analysis. In practical industry cases, the percentage placed above the values established via the MTM should be measured to adapt the method to the workplace reality.

Conclusion

The objective of this article was to analyze the influence of the variability of standard times in the simulation of the assembly operations of manufacturing systems. By means of the research results, it can be verified that the average of the working times observed in the analysis presented higher values than those determined via the MTM tables. Thus, the need to adapt the method to workplace reality to approximate the simulation analysis can be emphasized. The variation observed between the human data and MTM may originate from fatigue, recovery, or tolerance values; nevertheless, the study scope does not involve the origin of the variation, focusing instead on the scale of it.

It was also verified that the inadequate choice of the distribution curve of the values used in the simulation may incur errors in the data, with a difference of up to 6% being observed in the study between the curves and values analyzed.

In addition, the application of a triangular curve—with a central value greater than the deterministic value of the MTM—presented results closer to the real data observed than the simulation using the deterministic values of the MTM. Therefore, it is considered an adequate variability curve for the DES analysis and brings greater reliability to the simulated models.

In this way, it is recommended to use triangular curves with central values greater than those established via the MTM for the representation of standard times during the scenario analysis or in the planning stages of assembly processes using DES. In addition to its application in assembly processes, the proposed approach can be extended to maintenance operations that, according to Desai and Mital (2010b), mostly include disassembly and assembly activities, which can be represented by the MTM.

Key points

This approach to using standard times in simulations may have more reliability in the design of new processes or scenarios.

The use of the MTM as a standard time resource is analyzed, with the accuracy of the method presented.

The impact of different data and probabilistic distributions at simulation results is showed regarding errors above 6% in the simulation.

Footnotes

Rafaela Heloisa Carvalho Machado holds a Master’s degree (2017) in production engineering from the Universidade Metodista de Piracicaba - UNIMEP. She has experience in the areas of simulation, production management and human factors.

André Luís Helleno holds a Master’s degree (2004) and a PhD (2008) in production engineering from the Universidade Metodista de Piracicaba - UNIMEP. He completed a doctoral intern (2005) and postdoctoral degree (2011) at Technische Universität Berlin, Germany.

Maria Celia de Oliveira holds a Bachelor’s Degree in Mathematics from the Universidade Metodista de Piracicaba - UNIMEP (2004). She holds a PhD in production engineering from the Universidade Metodista de Piracicaba - UNIMEP (2012) and completed an internship at the Technische Universität Berlin, Germany (2010).

Mário Sérgio Corrêa dos Santos holds a Master’s Degree (2004) in mechanical engineering from the Fundação Educacional Inaciana Padre Sabóia de Medeiros - FEI (2014) and is a PhD student at the Universidade Metodista de Piracicaba - UNIMEP.

Renan Meireles da Costa Dias is a graduate student at Universidade Metodista de Piracicaba - UNIMEP. He has experience in the areas of simulation and methods-time measurement and is part of the process engineering research team.

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