Process optimisation using Taguchi methods of ...

Introduction

Process optimisation using Taguchi methods of experimental design

Continuing customer satisfaction and economic viability in a competitive business environment can only be achieved through the continuous improvement of both product and process quality and capability at minimal cost. Experimental design (ED) based on Taguchi methdology is a powerful and effective approach to achieving this goal. The advantage of the Taguchi approach to experimental design is that it assists engineers with limited statistical skills to study and understand how several process parameters affect the process output using limited budget and resources (Antony and Kaye, 1999). Research has shown that the application of Taguchi methods in the UK manufacturing environment is limited and when applied it is often carried out by statisticians or external consultants. This often prohibits the engineering community within an organisation from learning why and how experimental design has been applied to a particular problem. Moreover the communication between engineers, managers and industrial statisticians needs to be improved so that everyone can learn the role and potential benefits of ED. In order to apply Taguchi methods effectively in industry, one may require planning, engineering, communication, statistical and teamwork skills (Antony, 1999). Moreover, the participation of the right people, the commitment of top management, an awareness of Taguchi methods, reasonable statistical skills, etc. are essential ingredients for the successful implementation of Taguchi methods in any organisation.

Jiju Antony Steve Warwood Kiran Fernandes and Hefin Rowlands The authors Jiju Antony, Steve Warwood and Kiran Fernandes are all based at the Warwick Manufacturing Group, International Manufacturing Centre, University of Warwick, Coventry, UK. Hefin Rowlands is based at the Department of Engineering, University of Wales College, Newport, UK. Keywords Taguchi methods, Design of experiments, Process control, Process efficiency Abstract Experimental design (ED) is a powerful technique which involves the process of planning and designing an experiment so that appropriate data can be collected and then analysed by statistical methods, resulting in objective and valid conclusions. It is an alternative to the traditional inefficient and unreliable one-factor-at-a-time approach to experimentation, where an experimenter generally varies one factor or process parameter at a time keeping all other factors at a constant level. This paper presents a step-by-step approach to the optimisation of a production process (of retaining a metal ring in a plastic body by a hot forming method) through the utilisation of Taguchi methods of experimental design. The experiment enabled the behaviour of the system to be understood by the engineering team in a short period of time and resulted in significantly improved performance (with the opportunity to design further experiments for possible greater improvements).

What is the role of Taguchi methods in total quality management? The ethos of total quality management (TQM) is ``continuous improvement'' of the quality of both products and processes. Improvement is generally as a result of proper management, which comes from good control of the process/ system. A key component of ``good control'' is the measurement of key characteristics of the process/system. It is difficult to improve the performance of a process unless the characteristics or attributes which are most crucial to customers are first identified and

Electronic access The research register for this journal is available at http://www.mcbup.com/research_registers The current issue and full text archive of this journal is available at http://www.emerald-library.com/ft Work Study Volume 50 . Number 2 . 2001 . pp. 51±57 # MCB University Press . ISSN 0043-8022

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Process optimisation using Taguchi methods of experimental design

Work Study Volume 50 . Number 2 . 2001 . 51±57

Jiju Antony, Steve Warwood, Kiran Fernandes and Hefin Rowlands

measured. Taguchi methodology is a powerful approach to understanding the process and then optimising the performance of the process using the statistical design of experiments. Taguchi methods provide a systematic approach to a better understanding of the process and assist industrial engineers to discover the key process parameters (or variables) which affect the critical process/ product characteristic(s). Taguchi's philosophy is more relevant in terms of working towards a target performance of product/process, which essentially reflects the continuous improvement attitude (Kolarik, 1995).

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Nature of the problem: Low welding strength of tin coated wires to a connector. Scale of the experiment. A total of 16 trials. Benefits gained. Capability of the process (Cpk) increased by more than 100 per cent. Annual savings were estimated to be more than £20,000.

Case 4: wave soldering process Process type. Wave soldering. . Nature of the problem. High solder defect rate (over 1,000ppm). . Scale of the experiment. A total of 32 trials. . Benefits gained. The number of defects on average reduced to less than 100ppm and as a result the annual estimated savings were confirmed to be more than £30,000 per annum. .

Key benefits of Taguchi methods in industry Taguchi methods have numerous applications in manufacturing companies, particularly in automotive, plastics, process, semiconductors and metal fabrication. The following section briefly demonstrates the benefits of Taguchi methods in various manufacturing sectors. Each case will encompass the nature of industry, the type of product/process, the objective of the experiment, the scale of the experiment and the resulting benefits.

Case 5: electronics and semi-conductors Process type. Wire bonding process. . Nature of the problem. Low wire pull strength which led to customer dissatisfaction. . Scale of the experiment. A total of 16 trials. . Benefits gained. The average pull strength has been increased by about 30 per cent after the experiment and the customer returns due to low strength have reduced from 20 per cent to nearly 2 per cent. Annual savings were estimated to be over £30,000. .

Case 1: plastics . Process type. Reinforced reaction injection moulding process. . Nature of the problem. High rejection rate of the product. . Scale of the experiment. Eight trials. . Benefits gained. Substantial reduction in rejection rate with an expected saving of more than £10,000 per month.

Case study The purpose of the study was to investigate the possibility of using lightweight plastics in a modern braking system. An experiment was performed based on Taguchi's orthogonal arrays (OAs) with the aim of optimising the production process of retaining a metal ring in a plastic body by a hot forming method. ED based on Taguchi methods was chosen due to the limited budget and also to acquire a quick response to the experimental investigation. The production process consists of a heated die, which is then forced down by air pressure onto a valve body forming a plastic lip into which a retaining ring was inserted. Figure 1 illustrates the production process. Although the process was fairly straightforward, the engineering team felt that the maximum pull-out strength was not being

Case 2: automotive Product type. Speed sensor for the antiskid braking system. . Nature of the problem. Excessive variability in the output voltage of the sensor and therefore the process was unstable and incapable. . Scale of the experiment. Eight trials. . Benefits gained. Increased stability and capability (Cpk) of the process. The annual savings were estimated to be over £100,000. .

Case 3: metal fabrication Process type. Welding.

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Process optimisation using Taguchi methods of experimental design

Work Study Volume 50 . Number 2 . 2001 . 51±57

Jiju Antony, Steve Warwood, Kiran Fernandes and Hefin Rowlands

Figure 1 A simple illustration of the production process

any industrial experiment (Miesel, 1991). A brainstorming session among senior design engineers, plastics engineers and operators identified a list of production parameters (control factors) which were thought to influence the pull-out strength. Table I illustrates the list of control factors. The control factor ``die temperature'' was studied at four levels and all other factors were kept at two levels for the experiment. The levels for each factor were selected by the design and plastics engineers based on their knowledge and experience of the production process.

achieved. In order to simulate the production process, a test rig was designed and a suitable metal insert made to the dimensions of the metal ring into which a tensometer could be screwed in order to measure the pull-out strength. The company had initially performed an experiment based on varying one-factor-ata-time. However the results obtained from this experimentation were neither repeatable nor predictable. This method did not seem to help in achieving the best pull strength and the supply of valve bodies available to the project was rapidly being consumed. At this stage, it was decided to design an experiment based on Taguchi methodology as it provides a systematic approach to the study of the effects of various production parameters in a limited number of experimental trials and hence limited budget and resources. The following steps are used for the experiment. Step 1: objective of the experiment The objective of the experiment was to maximise the pull-out strength with minimum variation in pull-out strength values. It is obvious that the optimum performance is determined by analysing both mean pull-out strength and also variation in pull-out strength. Therefore the objective was to identify those control factor settings which provided maximum pull-out strength with minimum variation.

Step 3: selection of most suitable response for the experiment A ``response'' is an output performance characteristic of a product or process favoured are those most critical to customers; these often reflect the quality of the finished product (Antony, 1997). It is important to choose responses that can be measured quantitatively and with stability and equally important to make sure that the input control factors do have some effect on the selected response. Selection of qualitative response for experimental design is not a good practice. The authors recommend the choice of quantitative response(s) over qualitative output. For the present case study, it was decided to measure pull-out strength in kilo newtons (KN). Step 4: choice of orthogonal array (OA) design Orthogonal arrays are simple and useful tools for planning and designing industrial experiments (Ross, 1988). They have the balanced property that every factor level occurs the same number of times for every level of all other factors in the experiment. Matrix experiments using OAs play a crucial role in seeing whether interactions are large compared to the main effects. Taguchi considers the ability to detect the presence of interactions to be the primary reason for using OAs. Extra care must be taken prior to Table I List of control factors for the Taguchi experiment Level Control factor Die temperature (A) (ëC) Hold time (B) (sec.) Batch no. (C) Maximum force (D) (KN) Force application rate (E) (KN/sec.)

Step 2: identification of the control factors and their levels The identification of production parameters (or control factors) is crucial for the success of 53

1

2

3

4

180 5 1 6 5

200 15 2 7 1

220 ± ± ± ±

240 ± ± ± ±

Process optimisation using Taguchi methods of experimental design

Work Study Volume 50 . Number 2 . 2001 . 51±57

Jiju Antony, Steve Warwood, Kiran Fernandes and Hefin Rowlands

selecting the required scale of the experiment from standard OAs (Logothetis, 1992, Antony, 1999a). The selection of OA depends on the number of factors to be studied, the number of interactions (if any) to be studied and, of course, time and cost constraints. A ``rule of thumb'' is to make sure that the number of degrees of freedom associated with the experiment is always greater than or equal to the number of degrees of freedom required for studying the main and interaction effects. Here, ``degrees of freedom'' is the number of fair and independent comparisons that can be made from a number of levels. For example, the number of degrees of freedom associated with a factor at two levels is 1 as only one comparison can be made from the mean performance at level 1 and 2 respectively. For the experiment, we had to study one factor at four levels, four factors at two levels and also the interaction between hold time (B) and force application rate (E) was of interest to the team. Therefore the degrees of freedom required for studying all the effects is equal to 8. The closest number of experimental trials (from the standard OAs) which will meet this objective is an L16 OA (Taguchi and Konishi, 1987). However the standard L16 OA contains 15 two level factor columns. In other words, this array is used to accommodate only two level factor columns. Hence it was essential to modify the standard L16 OA in order to study the four level factor. As a four level factor consumes 3 degrees of freedom, it was decided to combine columns 2, 4 and 6 of the standard array. The modified OA is shown in Table II.

Step 6: statistical analysis and interpretation of experimental results Having completed an experiment, it is always a good idea to arrange a short meeting with all the people involved in the execution of the experiment. Unusual occurrences and discrepancies can be discussed (in detail) during this period. If the team has planned, designed and performed the experiment correctly, then statistical analysis will provide the experimenters with statistically valid and reliable conclusions. For more details on how to analyse and interpret the results (i.e. theory and a step-by-step example), see the paper entitled ``How to analyse and interpret Taguchi experiments'' published in Quality World (Antony, 1999b). For the present case study, the first step was to analyse the signalto-noise (S/N) ratio, which measures the functional robustness of product or process performance in the presence of undesirable external disturbances (Kapur and Chen, 1988). In this case, as we needed to maximise the pull-out strength with minimum variation, the S/N ratio for ``larger-the-better'' response (sometimes called quality characteristic) was selected. The higher the S/N ratio, the better the product performance will be. The S/N ratio for larger-the-better response is given by the following equation: 9 8P n i> > > 2 = < yi > S=N ratio ˆ 10 log iˆ1 …1† > n > > > ; : Using the above equation, the S/N ratio corresponding to each trial condition was computed. The Appendix presents the S/N ratio values for the experiment. Having obtained the S/N ratio values, the next step was to calculate the average S/N ratio at each level of each factor. For interaction effect, it is important to analyse the S/N ratio corresponding to each factor level combination. Table III provides the average S/N ratio values for all the factors and the interaction between hold time (B) and force application rate (E). In order to determine which of the factor/ interaction effects are statistically significant, a powerful statistical technique called analysis of variance (ANOVA) was used. Using ANOVA, one is able to identify the active and inactive factor/interaction effects with statistical confidence (Logothetis, 1994). As the S/N ratio is a single performance statistic, it is

Step 5: preparation of experimental layout and run In this step, the main task is to design the experimental layout and assign the factors to appropriate columns of the chosen OA. Table II illustrates the experimental layout. The actual values are replaced by coded levels (i.e. level 1 and level 2) for each two level factors and (level 1, level 2, level 3 and level 4) for the four level factor (see Table II). The experiment was conducted according to the above experimental layout. The response values corresponding to each trial condition are shown in Table II. The trials were monitored to find any discrepancies while running the experiment. The experimental trial was repeated three times in order to have adequate degrees of freedom for the error term. 54

Process optimisation using Taguchi methods of experimental design

Work Study Volume 50 . Number 2 . 2001 . 51±57

Jiju Antony, Steve Warwood, Kiran Fernandes and Hefin Rowlands

Table II Experimental layout used for the study Run

B

A

C

D

E

BE

y1

y2

y3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2

1 1 2 2 3 3 4 4 1 1 2 2 3 3 4 4

1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1

1 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1

1 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2

2.18 2.68 2.46 2.92 2.83 3.61 3.31 4.02 3.08 3.07 3.35 3.46 3.42 3.56 4.33 4.77

2.10 2.65 2.57 2.59 2.74 3.22 3.40 3.98 3.14 2.97 3.15 3.21 3.81 3.70 4.90 4.70

2.14 2.67 2.52 2.76 2.79 3.42 3.36 4.00 3.11 3.02 3.25 3.34 3.62 3.63 4.62 4.74

Table III Average S/N ratio values Factor interaction effect

Factors B1 B2 A1 A2 A3 A4 C1 C2 D1 D2 E1 E2 Interaction effect B1 E1 B1 E2 B2 E1 B2 E2

objective, the ANOVA on the mean pull-out strength was conducted. The results of the ANOVA are shown in Table V. Table V shows that factors A, B, C and D have significant effect (at both the 5 per cent and 1 per cent significance levels) on the mean pull-out strength. Factor E will also have a significant effect on the mean pull-out strength at the 5 per cent significance level. Interaction between B and E was not significant at both the 5 per cent and 1 per cent significance levels.

Average S/N ratio 9.25 11.15 8.64 9.37 10.47 12.33 9.81 10.59 9.85 10.56 10.26 10.14

Determination of optimal condition

9.33 9.18 11.20 11.11

advisable to pool the insignificant effects to obtain a reasonable estimate of error variance. According to Roy (1990), one should pool the effects (either factor or interaction effects) with low sum of squares in magnitude. Here control factors C, D, E and interaction between B and E have been considered for pooling and the results of the ANOVA on the S/N ratio are shown in Table IV. Having identified the most dominant factor/ interaction effects which influence the S/N ratio, the next step was to identify the most important effects which influence the mean pull-out strength. In order to achieve this 55

The optimal condition is the optimal factor settings which yield the optimum performance. In this case, it is the factor settings which provide the highest pull-out strength with minimum variation. The optimal condition is obtained by identifying the levels of significant control factors which yield the highest S/N ratio and maximum mean pull-out strength. As both factors A and B have significant impact on the S/N ratio, it was important to determine the optimal levels of these factors. The optimal settings based on the S/N ratio are: A4 B2. Similarly, the optimal settings based on the mean pull-out strength are: A4 B2 C2 D2 E1. It is obvious that there is no trade-off in the factor levels. Therefore the final optimal condition is given by: A4 B2 C2 D2 E1

Process optimisation using Taguchi methods of experimental design

Work Study Volume 50 . Number 2 . 2001 . 51±57

Jiju Antony, Steve Warwood, Kiran Fernandes and Hefin Rowlands

Table IV Results of pooled ANOVA on S/N ratio Source of variation B A Pooled error Total

Degree of freedom

Sum of squares

Mean square

F-ratio

Per cent contribution

1 3 11 15

14.48 30.89 5.26 50.63

14.48 10.30 0.48 3.38

30.25** 21.51** ± ±

27.65 58.17 14.18 100

Notes: From F-tables: F0.01,1,11 = 9.65, F0.05,1,11 = 4.84, F0.01,3,11 = 6.22 and F0.05,3,11 = 3.59 ** Implies that both factor effects A and B are statistically significant at the 5 per cent and 1 per cent significance levels Table V Results of ANOVA on the mean pull-out strength Source of variation B A C D E BE Error Total

Degree of freedom

Sum of squares

Mean square

F-ratio

Per cent contribution

1 3 1 1 1 1 39 47

6.04 14.47 0.88 0.68 0.08 0.03 0.92 23.11

6.04 4.82 0.88 0.68 0.08 0.03 0.024 0.49

251.67** 200.83** 44.00** 28.33** 3.33* 1.25 ± ±

26.06 62.32 3.72 2.86 0.23 0.0087 4.81 100

Notes: From F-tables F0.01,1,39  7.31, F0.05,1,39  4.07, F0.01,3,39  4.31 and F0.05,1,39  2.84 ** Implies that both factor effects A, B, C and D are statistically significant at the 5 per cent and 1 per cent significance levels * Implies that factor E is statistically significant at the 5 per cent significance level

Estimation of predicted mean response at the optimal condition

(1 ± confidence level). For Taguchi experiments, we may choose 1 per cent, 5 per cent or 10 per cent. Here ``'' measures the risk of saying that a factor is significant when in fact it is not. ``n'' is the number of degrees of freedom for the error term and ``ne '' is the effective number of degrees of freedom and is given by the equation:

In this case, the procedure is based on the additivity (non-interaction) of the factor effects. If one factor can be added to another to predict the response, then good additivity of factor effects exists (Phadke, 1989). Two factors are said to be additive if there is no interaction between them. The predicted mean pull-out strength (at the optimal condition is given by: 4 T  ‡ …A  † ‡ …B 2 T † ^ ˆT …2† 2 T  † ‡ …D 2 T  † ‡ …E 1 T † ‡ …C

ne ˆ

ˆ 4:83

…4†

where ``T '' is the total number of observations in the experiment, ``M'' is the degree of freedom for the overall mean (which is always equal to unity) and ``S'' is the degrees of freedom for the significant factor/interaction effects. T 48 For the present study, ne ˆ M‡S ˆ …1‡5† ˆ 8:0 e = error variance = mean square due to error = 0.024 (from Table V) and F0.01,1,39  4.07. Substituting the values into equation 3, we obtain, r 0:024 : 4:07 CL99% ˆ  8 ˆ 0:11KN

 = where ^ = predicted mean response and T overall mean of all observations in the data ^ ˆ 4:18‡3:66‡3:45‡3:43‡3:35 4

T M‡S

…3:31†

The predicted mean pull-out strength at the 99 per cent confidence limits is given by: r e
F;1;n CL99% ˆ  …3† ne where: e = error variance, ``'' is the significance level and is equal to 56

Process optimisation using Taguchi methods of experimental design

Work Study Volume 50 . Number 2 . 2001 . 51±57

Jiju Antony, Steve Warwood, Kiran Fernandes and Hefin Rowlands

Step 7: confirmation run/trial A confirmation run/trial is necessary in order to verify the results from the analysis (Antony and Kaye, 1995). This is to demonstrate that the factors and levels chosen for the experiment do provide the desired results. For the case study, a set of confirmation trials were carried out and the average pull-out strength was calculated. It was observed that the average pull-out strength was close to the prediction and fell within the confidence limits. This shows a significant improvement (more than 35 per cent) on the pull-out strength compared to the average pull-out strength before experimentation. Moreover a significant reduction in variability of pull-out strength values was also achieved from the experiment.

References Antony, J. (1997), ``Experiments in quality'', Journal of Manufacturing Engineer, Vol. 76 No. 6, pp. 272-5. Antony, J. (1999a), ``Ten useful and practical tips for making your industrial experiments successful'', The TQM Magazine, Vol. 11 No. 4, pp. 252-6. Antony, J. (1999b), ``How to analyse and interpret Taguchi experiments'', Quality World, (Technical paper), February, pp. 42-9. Antony, J. and Kaye, M. (1999), Experimental Quality ± A Strategic Approach to Achieve and Improve Quality, Kluwer Academic Publishers, Dordrecht, November. Antony, J. and Kaye, M.M. (1995), ``A methodology for Taguchi design of experiments for continuous quality improvement'', Quality World Technical Supplement, September, pp. 98-102. Kapur, K.C. and Chen, G. (1988), ``Signal-to-noise ratio development for quality engineering'', Quality and Reliability Engineering International, Vol. 4, pp. 133-41. Kolarik, W.J. (1995), Creating Quality: Concepts, Systems, Strategies and Tools, McGraw-Hill, Maidenhead. Logothetis, N. (1992), Managing for Total Quality ± From Deming to Taguchi and SPC, Prentice-Hall, Englewood Cliffs, NJ. Logothetis, N. (1994), Managing for Total Quality, Prentice-Hall, Englewood Cliffs, NJ. Miesel, R.M. (1991), ``A planning guide for more successful experiments'', ASQC Annual Congress Transactions, pp. 174-9. Phadke, M.S. (1989), Quality Engineering Using Robust Design, Prentice-Hall Publishers, Englewood Cliffs, NJ. Ross, J. (1988), Taguchi Techniques for Quality Engineering, McGraw-Hill Publishers, Maidenhead. Roy, R.K. (1990), A Primer on the Taguchi Method, VNR Publishers, Princeton, NJ. Taguchi, G. and Konishi, S. (1987), Standard Orthogonal Arrays and Linear Graphs, ASI Press, MI.

Conclusions and further work This paper has demonstrated an application of experimental design based on Taguchi methods for process optimisation. The study has shown a significant improvement in pullout strength and thereby encouraged the engineering team within the company to attempt continuous improvement through further experimentation. The paper also illustrated a systematic approach to carrying out industrial experiments based on Taguchi methods. It is important to bear in mind that the successful application of Taguchi methods of experimental design requires planning, engineering, statistical, communication and teamwork skills. The real benefits are achievable when the method is used in conjunction with other tools and techniques such as statistical process control. As the pullout strength increases with an increase in die temperature, hold time and maximum force, it was decided to perform a three level experiment with the aim of achieving greater optimisation. The Taguchi method of experimental design was an immediate replacement of the traditional ``one-factor-at-a-time'' experiment, which did not provide any insight into the behaviour of the system and the best levels identified were rather far from optimum. The results of improved and more consistent pull-out force will reduce the number of rejects and thereby produce a more reliable and robust product.

Appendix Table AI Table for S/N ratio values

57

Run

S/N ratio

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

6.61 8.52 8.01 8.78 8.90 10.64 10.52 12.04 9.85 9.60 10.23 10.45 11.14 11.19 13.25 13.51