Standard time is a key indicator to measure the production efficiency of the sewing department, and it plays a vital role in the production forecast for the apparel industry. In this article, the grey correlation analysis was adopted to identify seven sources as the main influencing factors for determination of the standard time in the sewing process, which are sewing length, stitch density, bending stiffness, fabric weight, production quantity, drape coefficient, and length of service. A novel forecasting model based on support-vector machine (SVM) with particle swarm optimization (PSO) is then proposed to predict the standard time of the sewing process. On the ground of real data from a clothing company, the proposed forecasting model is verified by evaluating the performance with the squared correlation coefficient (R^{2}) and mean square error (MSE). Using the PSO-SVM method, the R^{2} and MSE are found to be 0.917 and 0.0211, respectively. In conclusion, the high accuracy of the PSO-SVM method presented in this experiment states that the proposed model is a reliable forecasting tool for determination of standard time and can achieve good predicted results in the sewing process.

#### Keywords

- Standard time
- support-vector machine
- particle swarm optimization
- grey correlation analysis

In recent years, due to greater competition in the market, the product types have become more diverse and their life cycles shorter. To keep up with the business environment changes, improving the enterprise's agility and response quickly to the customer's requirements is becoming more and more important. In such a context, an efficient method for determination of standard time should be explored even further. It is very difficult to prepare manufacturing plans, short- or long-term forecasts, pricing, and other technical or managerial activities in a company without accurate standard time [1]. Standard time not only directly affects the working time and the utilization rate of the equipment, but is also the basic unit for calculating cost and remains widely used for cost management in manufacturing enterprises. Therefore, standard time prediction has direct bearing on economic accounting, production schedule control, resource optimization, production cycle shortening, cost control, and product quotation. Additionally, it ultimately promotes the labor productivity of enterprises and enhances their market competitiveness [2]. Standard time is a common language between fashion brands and manufacturers for discussions on cost, time, and floor capacity. A manager should know the time consumption of a new product processing exactly before acceptance. The term “standard time” is used to refer to time required by an average skilled operator, working at a normal pace, to perform a specified task using a prescribed method [3]. It includes appropriate allowances to allow the person to recover from fatigue and, where necessary, an additional allowance to cover contingent elements which may occur but have not been observed. Since Taylor defined standard time as the most fundamental way to represent productivity under the basic concept of “A Fair Day's Work”, many methods on the determination of standard time have been performed such as time study, activity sampling, synthetic timing, analytical estimating, and predetermined motion time systems (PTSs) [4]. Chen

The joining together of garment components, known as the sewing process, is the most labor-intensive part of garment manufacturing [10]. The sewing process needs to be carried out strictly in accordance with the production plan, which includes not only the distribution of production sites, equipment, and resources but also the arrangement of standard time. Standard time is a key indicator to measure the production efficiency of the sewing department [11]. There are a great many studies to apply the above-mentioned approach to predict standard time of the process in apparel production. Ye

Recently, machine learning techniques, such as artificial neural network (ANN) and support-vector machine (SVM), have been applied for standard time prediction. Advanced methods for determination of standard time can effectively help enterprises to reduce costs and improve production efficiency. Eraslan [1] proposed a new time estimation method based on different robust algorithms of ANNs. Kutschenreiter-Praszkiewicz [16] presented the application of neural network for unit time determination in small batch processing [16]. Chao and Danchen [17] proposed a standard time system based on neural network through the analysis of the characteristics of the standard time table [17]. The ANN has the ability to learn and approach the nonlinear function and has been considered as a powerful computing tool for establishing the mathematical relationship of the nonlinear system based on input-output data. However, the ANN has the following insurmountable shortcomings: lack of a unified mathematical theory, easy to enmesh local minimization, weak generalization ability for the small-sample data set, being prone to overfitting, etc. [18]. SVM was proposed by Vapnik

The main objective of this article is to further develop and improve the application of intelligent technology in the sewing process management, establish a prediction model using the machine learning technique, and optimize model parameters by particle swarm optimization (PSO) to forecast standard time in the sewing process. The remainder of the paper is organized as follows. In Section 2, an overview of the proposed approach is described. Section 3 presents a case study. Section 4 shows comparison analysis and presents some discussions of the results. Section 5 concludes the paper.

A machine learning algorithm called SVM based on statistical learning theory and SRM principle performs well for classification and regression properties [21]. Thus, SVM can be divided into support-vector classification machine and support-vector regression machine. The former usually deals with classification problems, and the latter is used for prediction. The purpose of support-vector regression machine is to analyze the function _{i}_{i}_{1}, _{1}), (_{2}, _{2}) … (_{n}_{n}_{i}^{2} represents the confidence range to smooth the fitting function and strengthen the promotion ability of fitting function. The constant

Since Eq. (1) is a convex optimization problem, the LaGrange multipliers will be introduced to obtain the LaGrange function. Then, the original problem could be transformed into the corresponding dual problem and the regression function can be obtained as follows:
_{i}_{i}

The SVM model has a good ability to solve small-sample, high-dimensional, and nonlinear problems. However, the choice of kernel function parameter _{i}_{i1}, _{i2}, …, _{iD})^{T}, is represented as the _{i}

In the formula, _{i}_{i1}, _{i2}, …, _{iD}_{i}_{i1}, _{i2}, …, _{iD}_{g}_{g1}, _{g2}, …, _{gD}_{1} and _{2} are the random number, the range is 0–1, _{1} and _{2} are the learning factors between 0 and 2, and _{id}_{max}_{max}_{max}_{max}_{max}_{min}

The process of using PSO for parameter optimization is as follows:

The population is initialized. The population size, the maximum number of iterations of the population, the penalty factor _{1} and _{2} are adopted by the linear learning strategy. The inertial weight

The position

The fitness calculation is carried out by assigning the mean squared error (MSE) as the fitness value when cross-checking the training set.

The fitness value _{i}_{best}_{i}_{best}_{best}_{i}_{best}

The individual optimal value _{best}_{best}_{best}_{best}_{best}_{best}

If the termination condition is satisfied, the iteration is stopped and the positional parameters of the optimal particle are output; that is, the optimal penalty coefficient

Input measures for machine learning algorithms are often referred to as influencing factors. The SVM model learns the relation between the influencing factors and the output values. In order to obtain the influencing factors of standard time in the sewing process more comprehensively, we conducted expert interview and literature analysis [23,24,25,26,27,28,29] to select the relevant core influencing factors. Experts were selected by a typical sampling method, and an open questionnaire was used to conduct in-depth interviews. A total of 13 interview records were obtained. The profile of these 13 interviewees is shown in Table 1.

The profile of interviewees.

Gender | Male | 6 | 46.2% |

Female | 7 | 53.8% | |

Age | 26–35 years | 4 | 30.8% |

36 years and above | 9 | 69.2% | |

Educational background | Undergraduate | 10 | 76.9% |

Graduate | 3 | 23.1% | |

Occupation | Enterprise administrator | 10 | 76.9% |

Researcher | 3 | 23.1% |

In general, many objective or subjective factors are involved in the complicated apparel manufacturing process. Based on the in-depth analysis of the relevant literature on the influencing factors of standard time in the sewing process, the influencing factors generally considered more important in most studies were extracted. First, the complexity of a garment sewing process is determined primarily by clothing style, such as type of fabric, type of seams, and the size and shape of cutting patterns. Yukari et al. [29] studied the relationship between the seam ability and mechanical properties of wool fabrics and showed that the mechanical properties of fabrics affect the quality and difficulty level of garment productions. Second, stable garment manufacturing processes require advanced production equipment and a good production condition. Third, workers’ level of effort and skill proficiency directly impact production efficiency and actual standard time in garment manufacturing. It is well demonstrated in the apparel industry that providing training for new workers or offering pre-production process is effective to improve workers’ ability to operate the equipment. Finally, a professional management team and management practices also affect the standard time in the sewing process. Higher wages or rewards motivate workers to maintain high levels of effort, encourage them to keep work interests, and enable them to develop relationships with managers or colleagues. Before making the prediction, the grey correlation analysis method was adopted to confirm the main influencing factors of standard time in the sewing process.

A multi-input and single-output support-vector regression model is formulated by constructing the relationship between the input and the output through the SVM model. The establishment of the standard time prediction model of the sewing process mainly includes training and testing. Firstly, sewing process cases are collected as sample data; then, the processed data samples are selected randomly as training sets, and the remaining samples are used as test sets. Secondly, the PSO algorithm is used to optimize the model parameters, which can be derived according to Eqs (3)–(4), and the training set is used to learn the SVM model. To this end, the relationship between standard time in the sewing process and factors that influence sewing can be established, and the continuous standard time could also be predicted by this. The flowchart of the framework is presented in Figure 1.

The raw data were adapted from ZS Company, which is a privately held family owned clothing company based in China. The company was founded in 1989, owning four fashion brands, and has accumulated a great amount of sewing standard time data during its multiple years of production. After cleaning the data to remove incomplete records, the final data set consists of 105 sewing processes, including standard time and influencing factors, as shown in Table 2.

Influencing factors and standard time of the sewing process.,

^{2}) | ||||||||
---|---|---|---|---|---|---|---|---|

25 | 24 | 6 | 1,558 × 10^{−7} | 79 | 500 | 21 | 4 | |

2 | 64 | 100 | 5 | 5,503 × 10^{−7} | 99 | 260 | 33 | 3 |

3 | 58 | 48 | 5 | 7,769 × 10^{−7} | 106 | 665 | 40 | 3 |

4 | 23 | 30 | 5 | 9,357 × 10^{−7} | 110 | 320 | 44 | 9 |

5 | 32 | 48 | 5 | 4,333 × 10^{−7} | 50 | 680 | 41 | 3 |

6 | 41 | 100 | 6 | 9,216 × 10^{−7} | 109 | 345 | 41 | 5 |

7 | 32 | 44 | 5 | 4,839 × 10^{−7} | 93 | 260 | 30 | 3 |

8 | 42 | 32 | 5 | 7,247 × 10^{−7} | 99 | 708 | 39 | 4 |

9 | 69 | 152 | 5 | 7,514 × 10^{−7} | 105 | 652 | 39 | 3 |

10 | 71 | 204 | 5 | 9,011 × 10^{−7} | 112 | 380 | 42 | 5 |

11 | 49 | 160 | 5 | 1,683 × 10^{−7} | 72 | 135 | 19 | 6 |

12 | 30 | 10 | 4 | 4,893 × 10^{−7} | 94 | 260 | 31 | 5 |

13 | 51 | 92 | 5 | 7,268 × 10^{−7} | 102 | 526 | 36 | 3 |

14 | 33 | 53 | 6 | 9,115 × 10^{−7} | 108 | 264 | 39 | 5 |

15 | 27 | 12 | 6 | 9,115 × 10^{−7} | 108 | 264 | 39 | 5 |

16 | 30 | 65 | 5 | 4,012 × 10^{−7} | 46 | 380 | 36 | 2 |

17 | 32 | 40 | 5 | 7,869 × 10^{−7} | 84 | 246 | 41 | 5 |

18 | 51 | 92 | 5 | 6,589 × 10^{−7} | 90 | 342 | 36 | 3 |

19 | 15 | 10 | 5 | 4,379 × 10^{−7} | 88 | 268 | 28 | 4 |

… | … | … | … | … | … | … | … | … |

105 | 9 | 5 | 6 | 3,998 × 10^{−7} | 76 | 260 | 27 | 3 |

In order to eliminate the influence of data dimensions on the prediction results, the original data need to be preprocessed. The dimensionality reduction method used in this paper is the minimum–maximum (min–max) method, and the calculation formula is expressed as follows:
_{i}_{min}_{max}

Influencing factors are input data for machine learning algorithms. During the sewing process, as mentioned above, many factors affect the standard time, such as sewing length, stitch density, bending stiffness, fabric weight, production quantity, drape coefficient, and length of service. Before making the prediction, the main influencing factors of standard time in the sewing process were identified by grey correlation analysis. Grey correlation analysis aims to quantitatively describe the relationship or development trend between variables according to the correlation degree. The reference sequence reflecting the system's behavior characteristics and the comparison sequence affecting the system's behavior are both supposed to be determined. The data sequence that reflects the behavior characteristics of the system is called reference sequence. The data sequence composed of factors that affect the system's behavior is called comparison sequence [30]. If the correlation degree between the comparison sequence and the reference sequence is large (correlation degree > 0.6), the relationship between the two is considered to be close; on the other hand, if the correlation degree is small (correlation degree < 0.5), the relationship between the two is distant. This is used as the basis to judge the correlation. The grey correlation coefficient

When we input the _{0i} formula is as follows:
_{0i} is the grey correlation degree of the sequence _{i}_{0}. The closer _{0i} is to 1, the better is the correlation.

The standard time in the sewing process was taken as the reference sequence, and the influencing factors are the comparison sequences. MATLAB can be used to calculate the related grey correlation degree. According to Table 3, the influencing factor with the maximum correlation degree for the standard time of the sewing process is the sewing length (0.823), and the influencing factor with the minimum correlation degree is the seam density (0.613). When the grey correlation degree is 0.8–1.0, there is a high degree of correlation between the reference sequence and the comparison sequence; when the grey correlation degree is 0.6–0.8, the reference sequence and the comparison sequence have a relatively high degree of correlation; when the grey correlation degree is <0.5, the correlation between the reference sequence and the comparison sequence is weak. Because none of the influencing factors is <0.6, this paper selects the above seven factors as the input vector of SVM.

Grey correlation degree of influencing factors for standard time.

1 | Sewing length | 0.823 |

2 | Stitch density | 0.613 |

3 | Bending stiffness | 0.714 |

4 | Fabric weight | 0.705 |

5 | Production quantity | 0.686 |

6 | Drape coefficient | 0.723 |

7 | Length of service | 0.657 |

A total of 105 samples were collected in the construction of the standard time prediction model of the sewing process. In this case study, 88 samples were selected randomly as training samples, and 17 samples were used as testing samples to train and test the PSO-SVM model. The MATLAB and LIBSVM toolbox were used to implement the SVM model according to the construction process. When the PSO-SVM program was written, the initial parameters of the model were set. The standard PSO with 20 particles (SIZEPOP = 20) and 200 iterations was used (MAXGEN = 200). The value range of _{1} = _{2} = 1.5. The machine environment was an i5-2430M central processing unit (CPU) with a frequency of 3.90 GHz and a memory of 4.0 GB, running on the Windows 7 operating system. After initialization, the calculation program was processed to read the sample data of the training set. The kernel parameter

For the sewing process, the PSO-SVM model with radial basis kernel function is introduced to predict the standard time. MSE and squared correlation coefficient (^{2}) are introduced as performance criteria for prediction assessment. The comparison between the actual and predicted values in the training set is shown in Figure 2. In Figure 2, x-axis represents the sample size of the training set, and y-axis the standard time of the sewing process. Then, the regression prediction was made for the test data of randomly selected test samples. The comparison between the actual value and the predicted value is shown in Figure 3. As shown in Table 4, in the training experiment, the ^{2} criterion is 0.917. In the testing experiment, the ^{2} is 0.852. Irrespective of whether the process involved is the training data experiment or testing data checking, the prediction model of the standard time of the sewing process based on PSO-SVM optimization algorithm achieves higher prediction performance. Therefore, the prediction model of PSO-SVM has excellent generalization ability and can obtain a scientific prediction result for standard time of the sewing process.

Performance of the PSO-SVM model.

^{2} | ||
---|---|---|

Training samples | 0.0211 | 0.917 |

Test sample | 0.0844 | 0.852 |

MSE, mean square error; PSO, particle swarm optimization; SVM, support-vector machine.

In order to further validate the performance of the model, we also presented a BP neural network to make a prediction experiment. The forecasting result is shown in Figure 4. As shown in Table 5, MSE of the BP neural network is much higher than that of SVM, and ^{2} of SVM is closer to 1. It is obvious that the prediction result of SVM is much better than that of the BP neural network. Thus, it is proven that SVM can be effectively applied to the prediction problem of a small sample while maintaining sufficient accuracy.

The comparison of the forecasting results by the BP neural network and PSO-SVM.

^{2} | ||
---|---|---|

PSO-SVM | 0.0211 | 0.917 |

BP neural network | 0.1066 | 0.528 |

MSE, mean square error; PSO, particle swarm optimization; SVM, support-vector machine.

In the SVM theory, determining the model parameters such as penalty parameter

Comparison of the prediction results with different parameter optimization methods.

PSO | 101 | 0.01 | 0.0358 |

Cross validation | 128 | 0.01 | 0.1157 |

MSE, mean square error; PSO, particle swarm optimization.

This study includes seven independent variables identified as the influencing factors of standard time in the sewing process, which are sewing length, stitch density, bending stiffness, fabric weight, production quantity, drape coefficient, and length of service. By means of the grey correlation analysis, the results showed that there is a significant correlation between the seven factors and the standard time of the sewing process. The MSE and R^{2} have been used to measure the effectiveness of the model in predicting standard time. It was found that the model in this study can predict the standard time of the sewing process quickly and accurately. By comparing the cross validation parameter selection method, it can be proven that the PSO algorithm performs better among the tested methods on the basis of higher accuracy.

In the production of apparel manufacturers, especially for the sewing process, experience is often used to estimate the standard time, which is subjective and lack of scientific basis. Although a large amount of data has been accumulated in production, it cannot be combined with the results. As a machine learning model, the proposed PSO-SVM method can establish the potential relationship between the influencing factors and the standard time. With the development and accumulation of big data in the apparel industry, the managers are able to apply the proposed prediction model to obtain a more accurate result for the standard time in the sewing process.

#### Comparison of the prediction results with different parameter optimization methods.

PSO | 101 | 0.01 | 0.0358 |

Cross validation | 128 | 0.01 | 0.1157 |

#### The comparison of the forecasting results by the BP neural network and PSO-SVM.

^{2} | ||
---|---|---|

PSO-SVM | 0.0211 | 0.917 |

BP neural network | 0.1066 | 0.528 |

#### Grey correlation degree of influencing factors for standard time.

1 | Sewing length | 0.823 |

2 | Stitch density | 0.613 |

3 | Bending stiffness | 0.714 |

4 | Fabric weight | 0.705 |

5 | Production quantity | 0.686 |

6 | Drape coefficient | 0.723 |

7 | Length of service | 0.657 |

#### Performance of the PSO-SVM model.

^{2} | ||
---|---|---|

Training samples | 0.0211 | 0.917 |

Test sample | 0.0844 | 0.852 |

#### The profile of interviewees.

Gender | Male | 6 | 46.2% |

Female | 7 | 53.8% | |

Age | 26–35 years | 4 | 30.8% |

36 years and above | 9 | 69.2% | |

Educational background | Undergraduate | 10 | 76.9% |

Graduate | 3 | 23.1% | |

Occupation | Enterprise administrator | 10 | 76.9% |

Researcher | 3 | 23.1% |

#### Influencing factors and standard time of the sewing process.,

^{2}) | ||||||||
---|---|---|---|---|---|---|---|---|

25 | 24 | 6 | 1,558 × 10^{−7} | 79 | 500 | 21 | 4 | |

2 | 64 | 100 | 5 | 5,503 × 10^{−7} | 99 | 260 | 33 | 3 |

3 | 58 | 48 | 5 | 7,769 × 10^{−7} | 106 | 665 | 40 | 3 |

4 | 23 | 30 | 5 | 9,357 × 10^{−7} | 110 | 320 | 44 | 9 |

5 | 32 | 48 | 5 | 4,333 × 10^{−7} | 50 | 680 | 41 | 3 |

6 | 41 | 100 | 6 | 9,216 × 10^{−7} | 109 | 345 | 41 | 5 |

7 | 32 | 44 | 5 | 4,839 × 10^{−7} | 93 | 260 | 30 | 3 |

8 | 42 | 32 | 5 | 7,247 × 10^{−7} | 99 | 708 | 39 | 4 |

9 | 69 | 152 | 5 | 7,514 × 10^{−7} | 105 | 652 | 39 | 3 |

10 | 71 | 204 | 5 | 9,011 × 10^{−7} | 112 | 380 | 42 | 5 |

11 | 49 | 160 | 5 | 1,683 × 10^{−7} | 72 | 135 | 19 | 6 |

12 | 30 | 10 | 4 | 4,893 × 10^{−7} | 94 | 260 | 31 | 5 |

13 | 51 | 92 | 5 | 7,268 × 10^{−7} | 102 | 526 | 36 | 3 |

14 | 33 | 53 | 6 | 9,115 × 10^{−7} | 108 | 264 | 39 | 5 |

15 | 27 | 12 | 6 | 9,115 × 10^{−7} | 108 | 264 | 39 | 5 |

16 | 30 | 65 | 5 | 4,012 × 10^{−7} | 46 | 380 | 36 | 2 |

17 | 32 | 40 | 5 | 7,869 × 10^{−7} | 84 | 246 | 41 | 5 |

18 | 51 | 92 | 5 | 6,589 × 10^{−7} | 90 | 342 | 36 | 3 |

19 | 15 | 10 | 5 | 4,379 × 10^{−7} | 88 | 268 | 28 | 4 |

… | … | … | … | … | … | … | … | … |

105 | 9 | 5 | 6 | 3,998 × 10^{−7} | 76 | 260 | 27 | 3 |

_{1−x}Fex-SDC composite anode by using PSO-SVR. In: 4th International Conference on Advanced Materials Research and Manufacturing Technologies.

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