4.1. System Description and Variable Identification
Arunima Sportswear Ltd. (Ashulia, Dhaka, Bangladesh), a renowned garment factory in Bangladesh, has been chosen for this study. A garment style, i.e. Kid’s Pant, having twenty-one operations, was selected for this research work. Twenty-eight operators were involved in the assembly line. The conceptual model of the assembly line was developed through observation and consulting with production personnel. The conceptual model, as depicted in Fig. 2, is simply the sequence of operations of the garment. The number in the circle refers to the operations according to their position in the list (Table 1).
There are a number of system variables, such as processing time (the time required to complete each task in the assembly line), entities per arrival (number of cutting parts arriving in the line at a time), machine breakdown (machine failure time), rework, operator’s absenteeism, operators fatigue, machine delay, etcetera. Some of these factors have been considered in this study.
4.2. Data Collection and Analysis
In this experiment, data were collected on task processing time, interval time between entities, machine breakdown time, operator absenteeism, and rework time. The interval time of entities arrival and the number of entities per arrival were collected from the floor. A bundle of 36 pieces of garments part were fed into the line every 10 minutes. Task processing time was collected through work-study; twenty processing times were taken for each task. The apparatus used in collecting time were a stopwatch, clipboard, pen, and paper. Rework time was also determined similarly, and the number of defective parts was collected from quality-checking documents. For machine breakdown time, we took the help of ‘Data entry Personnel’, who keeps records of the machine failure time of every operator on a daily basis. Finally, operators’ absenteeism information was taken from the human resource department.
4.3. Modelling of Inputs
Prior to being used in the following stage, the raw data of processing time were analyzed using Arena Input Analyzer software and stored in Table 1. The program offers a variety of integrated distribution functions that automatically fit the histogram of the actual data. For instance, the processing time analysis result for the ‘2 N set hip pocket’ operation, as in Fig. 3shows that the distribution function for this particular task is expressed as 0.45 + 0.22 * BETA (1.72, 2.04) with a minimum square error of 0.001504.
Table 1
Fitted processing time distribution
Opn
|
Operations Description
|
Resource
|
Qty
|
Processing Time Distribution
|
1
|
2N Hem Hip Pocket
|
2 N Fixed Bar
|
1
|
TRIA(0.28, 0.313, 0.46)
|
2
|
Hip pkt Deco & Attach Lather Join
|
Cycle Sewing M/C
|
2
|
NORM(0.545, 0.0527)
|
3
|
Crease Hip Pocket
|
Iron
|
2
|
0.5 + WEIB(0.158, 2.75)
|
4
|
Mark Hip Pocket Position
|
Helper
|
1
|
NORM(0.345, 0.0302)
|
5
|
2N Set Hip Pocket
|
2N Lock Stitch
|
2
|
0.45 + 0.22 * BETA(1.72, 2.04)
|
6
|
Mark Front pocket & J Stitch
|
Helper
|
2
|
TRIA(0.51, 0.6, 0.81)
|
7
|
2N Front pocket & J Stitch Deco
|
2 N Fixed Bar
|
2
|
NORM(0.845, 0.103)
|
8
|
Assembly Part Match Body
|
Helper
|
1
|
0.27 + 0.19 * BETA(1.99, 3.2)
|
9
|
Safety Stitch Outseam
|
5 Thread O/L
|
1
|
TRIA(0.4, 0.514, 0.6)
|
10
|
2N Top Stitch Outseam
|
Feed of the Arm
|
1
|
0.43 + 0.22 * BETA(1.66, 1.47)
|
11
|
Gusset Mark
|
Helper
|
1
|
NORM(0.294, 0.0222)
|
12
|
Gusset join
|
5 Thread O/L
|
2
|
0.53 + LOGN(0.115, 0.0675)
|
13
|
Waistband Elastic Tack
|
1N Lock Stitch
|
1
|
0.31 + WEIB(0.105, 2.15)
|
14
|
Serge Hem
|
3 Thread O/L
|
1
|
0.29 + ERLA(0.0128, 4)
|
15
|
Hem Elastic Tack
|
1N Lock Stitch
|
1
|
0.32 + 0.24 * BETA(2.02, 3.57)
|
16
|
Hem Elastic Join
|
1N Lock Stitch
|
1
|
0.42 + LOGN(0.134, 0.0775)
|
17
|
Waistband Elastic Join
|
1N Lock Stitch
|
1
|
0.49 + LOGN(0.102, 0.0624)
|
18
|
Attach Care Label
|
1N Lock Stitch
|
1
|
0.18 + 0.13 * BETA(2.1, 3.22)
|
19
|
Top Stich Waistband
|
Waistband M/C
|
1
|
0.33 + WEIB(0.0968, 1.94)
|
20
|
Hem Bottom
|
1N Lock Stitch
|
2
|
TRIA(0.68, 0.689, 1.2)
|
21
|
Tack Front Pocket, Fly & Crotch
|
Bar Tack
|
1
|
TRIA(0.31, 0.361, 0.45)
|
*Opn – Operation No., M/C – Machine, O/L – Overlock, Qty - Quantity |
4.4. Construction of Computer Model
A model of the assembly line for the selected garment (Kid’s Pant) was developed using a discrete event simulation software (Arena). The model, as illustrated in Fig. 4, was constructed based on the production process flow of the sewing line. Several Arena simulation modules, such as create, process, batch, record, assign, decide, dispose, etcetera, were used to make the model. The following assumptions were considered while developing the simulation model.
- Setup times of the machine were not taken into consideration because the setup processes were usually accomplished either at the beginning or at the end of the working time.
- Material transportation was not performed by assembly line operators.
- Each operator and helper were assigned to perform a single task on the assembly line.
- The production floor operated for 8 hours (480 minutes) daily, and there was no overtime.
- Reworks were done by the operators who made mistakes, and reworking time was considered operation failure time.
To determine the optimal replication number, we ran the model for n = 10 replications and found a sample mean µA = 739, a sample standard deviation s = 18.371, and the half-width of the 95% confidence interval turned out to be
t n−1 ,1−α/2 \(\frac{S}{\sqrt{n}}\) = 2.262\(\frac{18.371}{\sqrt{10}}\) = 2.262*5.809 = 13.14
It is probably obvious that the way to reduce the half-width of the confidence interval on the expected output is to increase the replication number [29]. To find the approximate required replication number, we need to set a specific half-width h and solve for n:
n =\({t}_{n-\text{1,1}-\alpha /2}^{2}\frac{{S}^{2}}{{n}^{2}}\)
n = \({z}_{1-\alpha /2}^{2}\frac{{S}^{2}}{{n}^{2}}\), replaced t distribution critical value by z, corresponding normal critical value.
An easier but slightly different approximation is
n \(\cong\) no\(\frac{{h}_{o}^{2}}{{h}^{2}}\)
Where n0 is the initial number of replications and h0 is the half-width we got from initial replications.
We set our desired half-width h = 3
n \(\cong\) 10 \(\frac{{13.14}^{2}}{{3}^{2}}\) \(\cong\) 192
Therefore, we considered 200 replications for the model.
The run length of the steady-state simulation model was determined to be 12 hours (8 hours daily production with a 4 hours warm-up period) [29].
4.4. Model Verification and Validation
Identifying whether a simulation model is a valid model or whether it accurately represents the actual system being examined is one of the most challenging tasks facing a simulation analyst. There are some techniques to verify and validate a simulation model [30].
The model was verified by running the simulation with different input parameters and checking whether the output was reasonable or not. We also traced and debugged the simulation model step by step.
A 95% confidence level hypothesis test is used to validate the model [31]. Here, the t-test hypothesis is used since it is often recommended for comparing data from small samples, typically fewer than 30.
The hypotheses are:
H0: µField = µArena
H1: µField \(\ne\) µArena
The test is if t0 < tα/2,nF + nA − 2, we would accept the null hypothesis H0, where,
t 0 = \(\frac{{\mu }_{F} - {\mu }_{A}}{{S}_{p }\sqrt{\frac{1}{{n}_{F}}} + \frac{1}{{n}_{A}}}\) \({S}_{P}^{2}\)=\(\frac{\left( {n}_{F} - 1\right){S}_{F}^{2} + ( {n}_{A} - 1){S}_{A}^{2}}{{n}_{F} + {n}_{A} - 2}\)
Where,
α - ‘significance level’- is the probability of rejecting the null hypothesis when the null hypothesis is true.
µ F is the mean throughput from the field
µ A is the mean production rate from the ARENA model
n F is the number of field samples
n A is the number of replications or runs of the model
\({S}_{F}^{2}\) is the variance of throughput from the field
\({S}_{A}^{2}\) is the variance of production rate from the ARENA model
\({S}_{P}^{2}\) = is the pooled mean-variance
In order to perform the hypothesis test, twenty days of data on the actual throughput of the assembly line was collected. The gathered data are summarized, and the results of the statistical parameter calculations are shown in Table 2.
Table 2
Actual system throughput and Simulation output data
Actual Throughput per 8 hours shift | Output Rate from Simulation |
---|
Sample data: | 730, 750, 770, 745, 690, 780, 720, 775, 790, 695, 765, 770, 750, 790, 785, 780, 720, 820, 775, 715 | Simulation output: | 720, 784, 681, 708, 737, 741, 765, 754, 747, 731, 702, 764, 718, 754, 703, 707, 786, 760, 765, 779 |
Sample size (nF) | 20 | No. of rep. (nA) | 20 |
Mean value (µF) | 755.75 | Mean value (µF) | 740.3 |
Variance (SF) | 1140.69 | Variance (SA) | 881.1 |
Std. deviation (SF) | 33.77 | Std. deviation (SA) | 29.68 |
From the abovementioned formulas, SP is calculated to be 31.79, which in turn, generates the t0 value of 1.54. From the t-table at a 95% confidence interval,
tα/2,nF + nA – 2 = t0.025,38 = 2.024
Since t0 < tα/2,nF + nA – 2, this suggests that the means are not significantly different from one another. As a result, the simulation model is reliable and accurately depicts the real system.