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Proceedings of the 2016 International Conference on Industrial Engineering and Operations Management Kuala Lumpur, Malaysia, March 8-10, 2016

Empirical Analysis and Modeling of Learning Curve in The Apparel Manufacturing Industry

1Thilini Ranasinghe,2Chanaka D. Senanayake 1,2Department of Production Engineering

Faculty of Engineering, University of Peradeniya Sri Lanka

[email protected], [email protected]

3Kanthi Perera 3Department of Engineering Mathematics

Faculty of Engineering, University of Peradeniya Sri Lanka

[email protected]

Abstract— Apparel manufacturing is a labour intensive industry which is characterized by rapid product changes. Each time suchchangeover of product type occurs, it demands operator learning for the process to reach a steady-state. Higher the number of product type changes, higher the adverse impact of learning on the production performance. Purpose of this paper is to analyse and model this learning process in batch assembly (sewing) lines to improve the accuracy of forecasting, production planning and inventory control. For this purpose, empirical data of daily production efficiency is collected from a large scale apparel manufacturer in Sri Lanka over a period of 8 months. Product types or styles are categorized as “Repeat Styles” or “New Styles” based on whether the operators have prior experience in assembling the product type or not. Modelling of learning curves for above two categories of styles was carried out separately, using nonlinear regression analysis. This analysis indicates that the hyperbolic learning curve models are the best fitted learning curve for both style categories with different parameter estimates. Models were validated for both style categories using a separate set of daily efficiency data from same sewing lines.

Keywords— Manufacturing / Production; operator learning; learning curve; batch assembly; non-linear regression

I. INTRODUCTION

Anyone becomes better at performing a task for the second time than the first time. This is due to accumulation of familiarity and confidence by performing the task repetitively. Thereby, measures such as the time to complete and quality of outcome improves with the number of tasks completed. This phenomenon is called “Learning” or “Gaining Experience”. Quantifying the amount learning is essential to accurately predict the performance. Purpose of this paper is to understand the learning process in apparel manufacturing industry and identify the best fitting model in order to make accurate forecasts. “Learning Curve (LC)” is a mathematical representation of the learning process of a person who is exposed to a new repetitive task [1]. There is a point in time when the learning process ceases and the performance becomes steady at its maximum rate. This constant rate performance can be due to the performance limitations of the machines, capacity limitations of the operator or a combination of both. In the literature, this phenomenon is referred to as “Steady-state performance” or “Plateauing” [5].

Fig.1. Learning Curve

691© IEOM Society International


Performance measures related to the LC of an individual operator includes [1]: • time to produce a single unit• number of units produced per time interval• cost to produce a single unit• percentage of non-conforming units etc.

Learning curves are encountered in manufacturing systems that contain a higher degree of manual operations. There are various forms of LC in literature with varying complexities, which have been used to fit industrial data [5]. Among them log-linear, exponential and hyperbolic models are the best known [1]. “What is the best LC model to use in a particular industrial application?” is a legitimate question. The “Best Fitting LC” depends on the specifications of the application and the LC parameters should be determined from actual data [3]. Modeling the LC and its effects on manufacturing system performance has been the topic of many researches. Industrial segments used in such studies include: electronic, automotive, construction, software and chemical manufacturing among others [1]. Within the years 1936-1969, almost all the research work have focused military applications followed by cost related applications [8]. But Baloff [2] has analyzed the LC empirically in automobile assembly, apparel manufacturing and production of large musical instruments and concluded that the relevance of LC in labor intensive manufacturing extends beyond aerospace and defense industrial applications. Learning curve in semiconductor memory chips manufacturing has been examined empirically by Gruber [4]. Although the empirical analysis of the LC in apparel manufacturing has captured researchers’ interest it has been in a very limited scale. In his study, Baloff [2] has considered only three new styles produced in three different plants. As a result of the study he has concluded that the “LC analyses were useful to the apparel firm in determining the total cost of switching product lines between plants in the midst of their production seasons”; for effective production capacity planning. Apparently, to our knowledge there is no indication in the literature of experiments or analyses conducted on applicability of exponential and hyperbolic LC models on actual apparel manufacturing data.

II. CASE OF APPAREL INDUSTRYApparel manufacturing accounts for nearly 70% of exports in Sri Lanka and by the year 2011, the employment given to the country by the apparel industry has been 276,551[6]. It is a labor intensive industry which is characterized by rapidly changing customer preferences and markets, thereby resulting in high product diversity. Apparel manufacturers usually implement batch production in the assembly phase of the product. Due to the high degree of diversity in product types (i.e. styles) assembled in multiple but similar sewing lines, the styles are categorized as “repeat styles” or “new styles” based on whether the operator has prior experience in assembling the same style or not, respectively. Repeat styles are product types that may have been re-introduced to the production line several times. Thus, the production behavior of those styles is familiar and more predictive than new styles. In batch production, unlike in continuous production systems, every time the batch or the product type changes, there is a disruption to the production and the effects of the LC become significant. Due to learning, the probability for the operator to reach steady state performance within a batch depends on the quantity of the batch. Higher the batch quantity, higher the probability of achieving steady state performance. For small batch quantities, the production may never reach the steady state. Thus, each style changeover results in a drop in process performance, such as production efficiency and product quality. Simultaneously, the number of changeovers is dependent on the quantity of each batch. Consequently, small batch quantities cause high number of product changeovers in the production line. Therefore, these changeovers result in a huge cumulative loss in production performance. This paper presents the initial step of a detailed study to model the learning process associated with batch assembly sewing lines in apparel manufacturing and quantifying the effects of learning on production performance.

III. METHODOLOGYAfter studying the literature and recorded data availability with the selected apparel manufacturer, “Percentage Daily Average Efficiency” of production lines was selected as the performance measure of interest. However, there are several assumptions had to be made.

i. There is no significant variation among the production lines selected due to factors including; skill level, traininggiven, machines available, styles assembled etc. This was required as there was insufficient data to analyse singleproduction line.

ii. The raw processing time (summation of all operation times for a particular style) does not affect the efficiencyalthough it directly affects production rate.

iii. A style that is re-introduced to a production line after 75 days from the previous production run is considered as anew style.

Hyperbolic and exponential LC models were fitted and evaluated to find out the best fitted LC curve model.



TABLE 1. HYPERBOLIC AND EXPONENTIAL LC MODELS

No Model Mathematical Equation Parameter Definitions

M1 2-ParameterHyperbolic Model y = k*x / (x + r)

y = Output rate k= Maximum performance level x = Operation time r = Learning rate

M2 3-ParameterHyperbolic Model

y = k*(x + p) / (x + p + r) p = Prior Experience Other parameter definitions remain the same.

M3 2-Parameter

Exponential Model y = k*(1- e-x/r) y= Output rate k= Maximum performance level x= Operation time r= Learning rate

M4 3-ParameterExponential Model

y= k*(1- e-(x + p)/r) p= Prior experience Other parameter definitions remain the same.

M5 Time Constant Model y = yc + yf * (1- e-t/τ)

y= Output rate yc= Initial performance level yf= Maximum performance level t= Operation time τ= Model time constant

Non-linear regression tool of MINITAB 17 was used for the analysis. Sum of Squared Errors (SSE) of each model was compared. Then the forecast accuracy measures Mean Squared Deviation (MSD), and Mean Absolute Percentage Error (MAPE) were calculated for each LC model. Then Akaike Information Criterion (AIC) was calculated and compared to decide on the quality of each LC model. Also the Bayesian Information Criterion (BIC) was calculated to aid the model selection decision. After selecting the best fitted 2 models, validation tests were done using a separate set of most recent sewing data from the same sewing lines to decide on which model resulted in the best forecast accuracy.

IV. RESULTS

A. Results for New StylesTABLE 2. NONLINEAR REGRESSION RESULTS AND MODEL ACCURACY MEASURES FOR NEW STYLES

Model Final SSE Parameter

Estimates 95% CI MSD MAPE AIC BIC

M1 2121.86 b1= 64.60 b2 = 0.98

(62.3092, 67.0226) ( 0.5860, 1.4971) 37.89 7.87% 207.54 211.59

M2 2108.28 b1 = 64.21 b2 = -0.29 b3 = 0.82

(61.7245, 67.0864) (-0.7911, 1.3134) ( 0.3278, 1.7468)

37.65 7.79% 209.18 215.26

M3 2179.29 b1 = 62.16 b2 = 2.06

(60.3130, 64.0284) ( 1.3869, 2.8570) 38.92 8.74% 209.04 213.09

M4 2464.55 b1 = 61.44

b2 =1.63E+19 b3= 3.82E+19

( 59.9795, 61.8575) (-4.97785E+35, *) (*, 9.38622E+39)

44.01 9.41% 217.93 224.00

M5 2006.91 b1 = 25.09 b2 = 37.64 b3 = 3.85

( 2.1364, 39.2317) (23.5711, 60.1204) ( 1.9776, 6.8347)

35.84 7.84% 206.42 212.50

There is no significant difference in MSD, MAPE, AIC and BIC values among the 5 models and residual plots (Refer to Appendix A). Both exponential models (M3 and M4) were rejected because they showed steep learning curve, which then achieved the steady-state performance very early. The 3-parameter hyperbolic model (M2) was rejected due to negative parameter estimate for the prior experience level. The time constant model (M5) provided the minimum SSE, MSD and AIC as shown in Table 2. But the length of the 95% confidence intervals of estimated parameters was large. Lastly, the 2- parameter hyperbolic model (M1) showed narrow confidence intervals for parameter estimates compared to model M5. Considering above factors and the graphical output (i.e. fitted curve) of the models (Refer to Appendix A), 2-parameter



hyperbolic (M1) and time constant (M5) models were selected for the validation test for new styles. Daily efficiency data of eight (08) recent new styles were used to examine the validity of the models. Mean Forecast Error (MFE) and Mean Absolute Deviation (MAD) were calculated and compared to select the best fitted LC model for new styles (Refer to Appendix A).

TABLE 3. VALIDATION RESULTS SUMMARY FOR NEW STYLES

Style No Minimum MFE Minimum MAD

1 M1- 2 parameter Hyperbolic M5 – Time Constant model

2 M1- 2 parameter Hyperbolic M1- 2 parameter Hyperbolic



5 M5 – Time Constant model M1- 2 parameter Hyperbolic

6 M5 – Time Constant model M5 – Time Constant model


8 M5 – Time Constant model M1- 2 parameter Hyperbolic

M1 showed minimum MFE and MAD in four (04) cases while M5 showed both minimum MFE and MAD only once. Therefore, the forecast accuracy of “2 Parameter Hyperbolic model” (M1) is higher than Time constant model (M5).

B. Results for Repeat StylesTABLE 4. NONLINEAR REGRESSION RESULTS AND MODEL ACCURACY MEASURES FOR REPEAT STYLES

Model Final SSE Parameter

Estimates 95% CI MSD MAPE AIC BIC

M1 5139.37 b1= 74.77 b2 = 0.71

(73.2493, 76.3486) ( 0.3972, 1.1102) 44.69 6.85% 440.97 446.46

M2 4623.52 b1 = 78.90 b2 = 10.88

b3 = 4.2652

(75.4893, 88.0949) ( 2.0400, 56.5599) ( 1.4264, 21.9473)

40.20 6.16% 430.81 439.04

M3 6000.56 b1 = 73.07 b2 = 1.04

(71.6905, 74.4481) ( 0.5423, 1.6873) 52.18 7.74% 458.79 464.28

M4 5980.31 b1 = 73.0

b2 =8.57E+17 b3= -4.9E+18

(71.78, 74.34) (-1.66183E+32, *)

(-1.15621E+52, 5.73977E+35)

52.00 7.70% 460.40 468.63

M5 4650.23 b1 = 59.42 b2 = 16.72 b3 = 24.38

(52.1987, 64.8802) (*, 23.1157)

(11.4358, 68.7105) 40.44 6.19% 431.47 439.70

Repeat styles did not show significant difference in MSD, MAPE, AIC and BIC values among the 5 models and residual plots (Refer to Appendix B) similar to new styles. 3-parameter hyperbolic model (M2) and time constant model (M5) showed minimum SSE values, but M5 resulted parameter estimates with wide confidence intervals as given in the Table 4. Both M2 and M5 models were tested for validity using daily efficiency data for seven (07) recent repeat styles. The same test procedure as new styles was followed. (Refer to Appendix B).



TABLE 5. VALIDATION RESULTS FOR REPEAT STYLES

Style No Minimum MFE Minimum MAD

1 M2 – 3 Parameter Hyperbolic M2 – 3 Parameter Hyperbolic


3 M5 – Time Constant model M2 – 3 Parameter Hyperbolic





M2 showed minimum MFE and MAD in four (4) cases whereas M5 showed only one. Therefore, the forecast accuracy of “3-Parameter Hyperbolic model”(M2) is higher than Time constant model(M5).

V. DISCUSSION The results of the analysis appear to confirm that the hyperbolic learning curve models are the best fitted for the batch assembly sewing lines in apparel manufacturing industry

TABLE 6. BEST FITTED LC MODELS

Style Category LC model Equation

New 2 parameter Hyperbolic Y = 64.60 * X / (X + 0.98)

Repeat 3 Parameter Hyperbolic Y = 78.90 * (X + 10.88) / (X + 10.88 + 4.27)

X is the day of production of the particular style and Y is the daily average efficiency% of the sewing line.

Fig.2. Fitted LC models



As explained previously in the paper, since repeat styles may have been re-introduced to the production line several times, the production behavior of those styles are familiar and more predictive than new styles. This explanation is supported further by the results of the analysis. For new styles 2-parameter hyperbolic model was sufficient, where the two parameters represent the maximum performance level and the learning rate. Learning curve of repeat styles was best represented by a 3-parameter hyperbolic behavior, which includes a parameter to represent the prior experience level in the model equation. The fitted models as showed in Fig.2, provide clear evidence to the fact that learning period and rate for new styles are higher than repeat styles. Also the steady- state performance level is much lower for new styles.

VI. CONCLUSION

The objective of this paper was to empirically analyze and model the learning curve in the apparel manufacturing industry. The empirical analysis showed that the learning curve in batch assembly sewing lines tends to be hyperbolic. For new styles the best fitting curve was “2-parameter hyperbolic” and for repeat styles it was a “3-parameter hyperbolic”. Learning curve model for repeat styles incorporate prior experience level additionally to the new styles’ LC model. The same empirical analysis could be improved by building the models using hourly average efficiency data instead of daily data. We hope to extend the same analysis in future by using hourly efficiency data.

REFERENCES

[1] Anzanello, M. and Fogliatto, F., (2011), “Learning curve models and applications: Literature review and research directions”, International Journal of Industrial Ergonomics, 41, pp.573-583.

[2] Baloff, N., (1971), “Extension of the Learning Curve — Some Empirical Results”, Journal of Operations Research Society, 22(4), pp.329-340.

[3] Dar-EI,E.M.,(2000), “Human learning: From learning curves to learning organizations”, Kluver Academic Publishers, Massachusetts. [4] Gruber, H., (1992), “The learning curve in the production of semiconductor memory chips”, Applied Economics, (24), pp.885 - 894. [5] Jaber, M.,(2010),“Learning and Forgetting Models and Their Applications”, In: A. Badiru., Handbook of Industrial and Systems

Engineering, 2nd edition. Boca Raton: CRC Press, Taylor and Francis Group, pp.535 - 566. [6] LMD, Apparel Industry,2014, Stiching Its Way to Stardom. Available from: < lmd.lk/apparel-industry/>. [09.11.2015]. [7] Womer, K. and Patterson, W., (1983), “Estimation and Testing of Learning Curves”, Journal of Business & Economic Statistics, 1(4),

pp.265-272. [8] Yelle, L., (1979), “The Learning Curve: Historical Review And Comprehensive Survey”, Decision Sciences, 10(2), pp.302-328.


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BIOGRAPHY Thilini Ranasinghe is a fulltime graduate research student who is currently reading for her M.Phil. in Department of Production Engineering, Faculty of Engineering, University of Peradeniya, Sri Lanka. She has obtained her BSc degree specialized in Production Engineering from the same faculty.

C.D. Senanayake is a Senior Lecturer and Head of the department of Production Engineering, Faculty of Engineering,University of Peradeniya. He has obtained his BSc in Production Engineering from the Faculty of Engineering, University ofPeradeniya. He obtained his PhD from the National University of Singapore in 2012 and his research involved thedevelopment of analytical tools for evaluating the performance of manufacturing systems. His teaching and research interestsinclude topics in production planning and control, and performance evaluation of manufacturing systems.

Kanthi Perera is a Senior Lecturer in the Department of Engineering Mathematics, Faculty of Engineering, University of Peradeniya. She has obtained BSc Special degree in Mathematics from University of Sri Jayawardenapura, Sri Lanka and M.A. and Ph.D. in Mathematical Statistics from State University of New York, Albany, USA. She has been the Head of theDepartment of Engineering Mathematics from 2001-2004 and the Coordinator of the M.Sc. program in Applied Statistics(from May 2008- April 2015) and a member of the Board of Study in statistics and Computer Science at the PostgraduateInstitute of Science, University of Peradeniya. Dr. Perera is a life member of the Institute of Applied Statistics Sri Lanka.Her research interests are estimation, regression analysis and probability theory.


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