Application of Taguchi Method of Experimental Design

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The Emerald Research Register for this journal is available at www.emeraldinsight.com/researchregister The current issue and full text archive of this journal is available at www.emeraldinsight.com/1741-0401.htm Applications of Taguchi approach to statistical design of experiments in Czech Republican industries Jiju Antony, V. Somasundarum and Craig Fergusson Division of Management, Caledonian Business School, Glasgow Caledonian University, Glasgow, UK, and Taguchi approach to statistical design 447 Received December 2003 Revised May 2004 Accepted May 2004 Pavel Blecharz VSB-TU The Faculty of Economics, University of Ostrava, Sokolska, Czech Republic Keywords Taguchi methods, Statistical methods, Czech Republic, Organizational effectiveness Abstract Dr Genichi Taguchi is a Japanese engineer and quality consultant who has promoted the use of statistical design of experiments for improving process/product quality at minimal costs. Taguchi has developed a practical and strategic approach for designing quality into products and processes at the product planning, design and development stages, which is often referred to as off-line quality control. Although many companies in Europe and the USA have used the Taguchi approach to statistical design of experiments with success, very few applications of this method are realised in countries such as the Czech Republic. This paper reports the applications of experimental design advocated by Taguchi in two manufacturing companies in the Czech Republic. The results of the study are stimulating and will lead to wider applications of this methodology for tackling process and quality-related problems in the Czech Republican industries in the near future. Introduction Statistical design of experiments (SDOE) plays a powerful role in many organisations today in terms of improving process efficiency, product quality and process capability; and reducing process variability, costs of poor quality such as scrap, rework and other failure costs. This powerful technique has proven to be one of the most effective and reliable weapons in the twenty-first century arsenal of globally competitive organisations. It was initially developed by R.A. Fisher at Rothamsted Agricultural Station, London, England (Fisher, 1935). However, the person who is seen to have most influenced the development of SDOEs (SDOE) in the industrial world is Dr Genichi Taguchi. Dr Taguchi has been very successful in integrating statistical methods into the powerful engineering processes for achieving greater process stability, capability and yield. Taguchi emphasised the importance of designing quality into products and processes right from the design stage through to the entire product development cycle (Taguchi, 1987). A number of successful applications of the Taguchi approach to SDOEs have been reported by many American and European manufacturers (Phadke, 1989; Quinlan, 1985; Taguchi and Yokohama, 1993; Rowlands et al., 2000; Antony et al., 1999). The SDOE methodology developed and promoted by Taguchi has accentuated the importance of making products’ functional performance or process performance insensitive to various sources of noise conditions (e.g. ambient temperature changes, International Journal of Productivity and Performance Management Vol. 53 No. 5, 2004 pp. 447-457 q Emerald Group Publishing Limited 1741-0401 DOI 10.1108/17410400410545914 IJPPM 53,5 448 relative humidity fluctuations, equipment or machine performance degradation, tool wear, product-to-product variation, etc.). This is also known as robust parameter design (RPD). RPD is essentially a part of Taguchi’s SDOE. Despite the successful applications of the Taguchi approach to SDOE, a wider use of the approach and its associated techniques is only possible by gaining a better understanding of the method (i.e. where, when and how to use) and its analysis. The successes and failings of the Taguchi approach to SDOE have been widely discussed (Nair, 1992; Pignatiello and Ramberg, 1991; Bendell et al., 1989; Box et al., 1988; Kumar et al., 2000). Taguchi’s main successes have been to demonstrate the importance of designing quality into products and processes at early stages of the product development process, making processes robust against undesirable nuisance factors without actually eliminating them completely from the process, simplifying the use of SDOE as a powerful tool for industrial engineers, and so on. On the other hand, Taguchi’s main weaknesses have been the use of linear graphs for assigning factors and interactions to various columns of the orthogonal array (OA), the use of signal-to-noise ratio (SNR) as a performance indicator of robustness, lack of use of sequential and adaptive approach to experimentation, lack of importance on interactions among the process or design parameters, and so on. Taguchi case studies This paper presents two case studies generated from two automotive manufacturers in the Czech Republic. Although the Taguchi approach to SDOE has been successful in many European manufacturers, research has shown that the application of this powerful technique in the Czech Republican manufacturing industries is very limited. Some noticeable reasons for this gap are: . lack of awareness of general quality management principles; . lack of awareness of the importance of industrial experimentation and the benefits gained out of it; . inadequate education on applied industrial statistics at academic institutions; . managerial intransigence that home-grown solutions (generally one-factor-at-a-time approach) are sufficient for process optimisation problems; . inadequate skills and expertise in advanced statistical methods for problem solving; . poor attitude towards quality improvement and process optimisation strategies; and . lack of resources to initiate pilot studies. In order to assist with the application of the Taguchi approach to SDOE, the following steps were employed. More information on the methodology can be obtained from Antony and Kaye (1999). (1) Define the objective of the experiment (or nature of the problem). (2) Define the response or quality characteristic of interest. (3) Identification of process or design parameters which influence the response or quality characteristic. (4) Define the levels of the process or design parameters and the feasible ranges. (5) Selection of appropriate orthogonal array from standard orthogonal array designs. (6) Execute the experiment and record data on pre-prepared design matrix (or experimental layout). (7) Perform statistical analysis of data. (8) Determination of optimum condition. (9) Predict response at optimal settings and establish confidence interval. (10) Confirmation and implementation of new settings. The following two case studies were carried out by strictly following the above steps. The first case study is about the application of Taguchi SDOE for the development of a new ignition coil for an automotive vehicle. The performance of the ignition coil is measured by “burn time” (i.e. time in which the electric arc lasts on ignition coil). Although extensive tests were carried out using the traditional approach to experimentation (one-factor-at-a-time), the current achieved performance (i.e. 1.7ms) fell far short of the desired performance specified by customers (i.e. 1.9ms). In order to tackle the problem, the company decided to employ Taguchi’s approach to SDOE due to the following reasons: . Few engineers within the company were already trained on Taguchi’s approach to SDOE. . The purpose of the experiment was to obtain results in a short period of time with minimum budget and resources. . The experiment involved a large number of design parameters (14) and it was important to screen the most important design parameters which influence the “burn time”. The following objectives were set for the experiment by a team of people from quality, design, production, maintenance, process and operators: . Which of the design parameters and their interactions have major influence on “mean burn time”? . Which of the design parameters affect variability in “burn time”? . determine the best settings to achieve a target value of 1.9ms for “burn time”. Through an extensive brainstorming session with the team, it was decided to study 14 design parameters at two levels. The experimentation team was interested to analyse one interaction among the design parameters. The degrees of freedom required for studying 14 main effects and one interaction effect is 15. The most appropriate OA design to meet this requirement is a 16-trial experiment (L16 OA). Table I illustrates the list of design parameters and their ranges chosen for the experiment. The experiment was performed using the above uncoded design matrix. Each trial condition was replicated three times to capture variation due to noise parameters, which are hard or expensive to control during the experiment, but have significant impact on the product’s functional performance variability (Schmidt and Launsby, 1992). The results of the experiment are shown in Table II. The first step in the analysis was to compute the SNR corresponding to each trial condition. SNR is a measure of the performance variability of products/processes in the presence of noise factors (Antony et al., 1999). The idea is to maximise the SNR and Taguchi approach to statistical design 449 IJPPM 53,5 Design parameter Length of core Core material Magnet material Number of magnets Number of turns on secondary coil Type of secondary coil Length of sheet covering (mm) Length of primary coil (mm) Thickness of sheet covering (mm) Core connection Core temp. processing Number of core sheets Core-magnet gap (mm) Material of sheet covering Label A B C D E F G H I J K L M N Level 1 60 Material 1 Current 1 19,000 Tree 74 66 0.35 Not welding Annealing 1 0 Material X Level 2 67 Material 2 Better 2 23,000 Section 92 61 0.55 Welding Not annealing 3 0.1 Material Y 450 Table I. List of design parameters used for the experiment Run 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 A 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 B 1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 A£B 1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1 C 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 D 1 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1 E 1 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 F 1 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2 G 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 H 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 I 1 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1 J 1 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2 K 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 L 1 2 2 1 1 2 2 1 2 1 1 2 2 1 1 2 M 1 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2 N 1 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1 Burn time (ms) 1.23, 1.47, 1.89, 1.93, 1.58, 1.53, 1.49, 1.55, 1.57, 1.50, 1.92, 1.85, 1.92, 1.94, 1.53, 1.59, 1.21, 1.42, 1.98, 1.84, 1.60, 1.54, 1.51, 1.58, 1.61, 1.51, 1.94, 1.89, 1.99, 1.96, 1.49, 1.58, 1.24 1.41 1.93 1.87 1.60 1.60 1.53 1.56 1.64 1.60 1.98 1.90 1.99 1.97 1.53 1.60 Table II. Results of the Taguchi experiment thereby minimise the effect of random noise factors which have significant impact on the process performance. SNR for nominal-the-best quality characteristic (here it is burn time) is calculated using the following equations (Roy, 2001): SNR ¼ ÿ10 log MSD where: n X ð1Þ ðyi ÿ mÞ2 n : ð2Þ MSD ¼ i Here, MSD (mean squared deviation) is a measure of deviation of a product’s performance characteristic (y) from its desired target value (m). Based on the above equations, SNR is calculated corresponding to each design point. Table III presents the SNR values for all 16 trial conditions. Having obtained the SNR values, the next step was to obtain the mean SNR at low and high levels of each design parameter. The main effects plot for the SNR is shown in Figure 1. The main effect plot clearly indicates that design parameters A, B, C, D and E have the biggest influence on the SNR. In order to determine the statistical significance of the effects, it was decided to perform ANOVA (analysis of variance) for the SNR. Pooling strategy was employed (Roy, 2001) to create adequate degrees of freedom for Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 SNR (dB) 3.433 6.599 25.025 26.021 10.261 9.233 8.167 9.447 10.591 8.695 25.071 29.586 22.163 24.629 8.313 10.168 Taguchi approach to statistical design 451 Table III. SNR values Figure 1. Main effects plot for the SNR IJPPM 53,5 452 the error term so that sound conclusions about the significance of effects of design parameters can be drawn. ANOVA was performed with the idea of sub-dividing the total variation of data into useful and meaningful components of variation due to main effects (i.e. effects of design parameters). The pooled ANOVA table is shown in Table IV. The table shows that the most influential design parameters are E, C and A, which account for more than 80 per cent of total variation in data. Table IV indicates that design parameters C and E are statistically significant at both 5 per cent and 1 per cent significance levels, whereas design parameters A, B and D are statistically significant at only 5 per cent significance level. This, in essence, shows that design parameters A, B, C, D and E have significant effect on “burn time”. Determination of optimal condition The optimal settings are those which provide the best performance based on the data obtained from the experiment. In this case, we need to select the settings of significant design parameters which yield maximum SNR. Based on Figure 1, the optimal condition is determined as: Design parameter A ¼ Length of core – level 2 (67mm). Design parameter B ¼ Core material – level 1 (Material 1). Design parameter C ¼ Magnet material – level 2 (better). Design parameter D ¼ Number of magnets – level 2 (2). Design parameter E ¼ Number of turns in secondary coil – level 2 (23,000). Predicted SNR at optimal condition       SNRpredicted ¼ T þ ðA2 ÿ TÞ þ ðB1 ÿ TÞ þ ðC 2 ÿ TÞ þ ðD2 ÿ TÞ þ ðE 2 ÿ TÞ ¯ where T is the average SNR. ¼ 14.838 + (17.569 – 14.838) + (17.381 – 14.838) + (18.223 – 14.838) + (17.223 – 14.838) + (22.060 – 14.838) ¼ 33.104dB Degrees of freedom 1 1 1 1 1 10 15 Pure sum of squares 95.974 74.691 146.805 63.616 763.131 – – Percentage contribution (r) 7.690* 5.984* 11.763** 5.097* 61.148** 8.318 100.00 ð3Þ Design parameter A B C D E Error Total Table IV. Pooled ANOVA table Sum of squares 102.893 81.61 153.724 70.534 770.049 69.185 1247 Mean square 102.893 81.61 153.724 70.534 770.049 6.919 – F-ratio 14.872 11.976 22.219 10.195 111.305 – – Notes: F0.05, 1, 10 = 4.965, F0.01, 1, 10 = 10.044; * indicates that the design parameter is statistically significant at only 5 per cent significance level; ** indicates that the design parameter is statistically significant at both 5 per cent and 1 per cent significance levels Confidence interval for the predicted SNR The confidence interval is the variation of the estimated result at the optimum condition. The confidence interval for the predicted SNR at the optimum condition is given by: CI ¼ ^ Fða; 1; n2 Þ*MSE Ne ð4Þ Taguchi approach to statistical design 453 where: MSE ¼ error variance ¼ 6.919 (from ANOVA table). F(a, 1, n2) ¼ tabled value of F with 1 degree of freedom for the numerator and n2 degrees of freedom for the error term: Ne ¼ N 1 þ ne ð5Þ where N ¼ total number of SNR values and y e is the number of degrees of freedom used in the estimate of the SNR: N e ¼ 16=5 ¼ 3:33: Substituting the values into equation (3), we get, CI¼ ^ 3.212. Therefore, the predicted SNR at the optimal condition is 33.104 ^ 3.33 at the 95 per cent confidence level (or 5 per cent significance level). Having determined the CI for the SNR, it was then suggested that confirmatory runs were performed. The results from the confirmatory runs were satisfactory. The mean burn time from the confirmatory runs was very close to the target value (1.9ms). The design capability (Ppk) was estimated to be well over 2.0. The company has managed to meet the above specified target value for burn time with minimum variation around it. This has resulted in increased customer satisfaction, improved market share and increased awareness of the power of the Taguchi approach to SDOE in product design and development process. The results of the study have encouraged the team members of experimentation to deploy the applications of SDOE in other core processes where low capability and poor yield were two major quality problems. The second case study illustrates the application of Taguchi SDOE to the development process of a new alternator model used widely in the automotive industry. The objective of the experiment here was to reduce the noise developed by the alternator under usage conditions. In other words, the purpose of an experiment in this case was to determine the most important design parameters which influence noise developed by the alternator. Previous studies have shown that no interactions were important and hence the objective of the experiment was to study only the main effect of design parameters. The customer requirement for the noise is defined by curve of maximum sufferable noise (Figure 2). Further to a thorough brainstorming exercise with a number of people from design department, manufacturing, quality and technicians, 11 design parameters were identified. As part of an initial investigation into the design process, it was decided to study each design parameter at two levels. Table V illustrates the list of design parameters and their levels for the experiment. As the team was only interested in evaluating the main effect of these design parameters, the most appropriate OA design to meet this requirement is a 12-trial experiment (L12 OA). IJPPM 53,5 454 Figure 2. Noise of alternator (before experiment) The experiment was carried out using the L12 OA. The results of the experiment along with SNR are illustrated in Table VI. As the objective of the experiment was to minimise the noise, SNR for smaller-the-better quality characteristic was selected. Each trial condition was replicated three times to capture variability due to uncontrollable Design parameter Chamfer of star Chamfer of bottom Thickness of plate (mm) Jointing of plates Relief of cover Edge of pole (degrees) Perforated isolation Vacuum impregnation Rubberizing Collar above stator Thickness of cover (mm) Label A B C D E F G H I J K Level 1 Smaller Yes 1 Welding Current 45 Yes Yes Yes Yes Standard Level 2 Bigger No 0.5 Riveting 4 points 0 No No No No +0.4 Table V. List of design parameters and their levels used for the experiment Run 1 2 3 4 5 6 7 8 9 10 11 12 A 1 1 1 1 1 1 2 2 2 2 2 2 B 1 1 1 2 2 2 1 1 1 2 2 2 C 1 1 2 1 2 2 2 2 1 2 1 1 D 1 1 2 2 1 2 2 1 2 1 2 1 E 1 1 2 2 2 1 1 2 2 1 1 2 F 1 2 1 1 2 2 1 2 2 1 2 1 G 1 2 1 2 1 2 2 2 1 1 1 2 H 1 2 1 2 2 1 2 1 2 2 1 1 I 1 2 2 1 1 2 1 1 2 2 1 2 J 1 2 2 1 2 1 2 1 1 1 2 2 K 1 2 2 2 1 1 1 2 1 2 2 1 Y1 485.17 167.69 98.11 76.10 84.21 58.48 439.27 173.07 95.08 192.58 337.32 226.37 Y2 127.25 14.25 43.54 252.84 87.05 93.25 367.24 405.87 156.68 393.68 204.55 102.45 Y3 79.33 45.01 68.60 75.27 188.68 62.20 331.28 154.73 201.26 490.85 500.54 530.46 SNR 2 49.34 2 40.05 2 37.33 2 43.99 2 42.24 2 37.27 2 51.64 2 48.63 2 43.93 2 51.59 2 51.32 2 50.58 Table VI. Results of the experiment with SNR values parameters. SNR was calculated using equation (1). The MSD for smaller-the-better quality characteristic is given by: n X y2 i ; where i varies from 1 to 3: ð6Þ Taguchi approach to statistical design 455 MSD ¼ i¼1 n Sample calculation For trial 1, MSD ¼ {(485.17)2 + (127.25)2 + (79.33)2}/3 ¼ 85,958.58 SNR ¼ 2 10 log (MSD) ¼ 2 49.343dB Figure 3 shows the main effects plot for the SNR. The main effects plot indicates that design parameters A, D, F, and I have significant impact on noise. ANOVA was then performed to determine the statistical significance of effects of parameters. The results of pooled NOVA are shown in Table VII. The pooled ANOVA table shows that design parameters A, D, F and I account for up to 90 per cent of variation. The contribution of error or noise is about 10 per cent, which was quite satisfactory to the experimentation team. Determination of optimal condition The optimal condition is determined by selecting the best levels of most influential design parameters which have a significant impact on the output performance or quality characteristic(s) which is/are critical in the eyes of the customer. Here, the optimal condition for A, D, F and I are obtained as (equation 7): Design parameter A ¼ Chamfer of star – level 1 (smaller). Design parameter D ¼ Jointing of plates – level 2 (riveting). Figure 3. Main effects plot for the SNR IJPPM 53,5 Design parameter A D F I Pooled error Total Degrees of freedom 1 1 1 1 7 11 Sum of squares 187.74 24.00 36.94 58.10 36.382 343.16 Mean square 187.74 24.00 36.94 58.10 5.197 – F-ratio 36.12** 4.62 7.11* 11.18* – – Pure sum of squares 186.77 23.04 35.97 57.13 – – Percentage contribution (r) 55.20 6.81 10.63 16.89 10.47 100.00 456 Table VII. Pooled ANOVA table Note: F0.05,1,7 = 5.59, F0.01, 1,7 = 12.25; ** indicates that the design parameter is statistically significant at both 5 per cent and 1 per cent significance levels; * indicates that the design parameter is statistically significant at only 5 per cent significance level Design parameter F ¼ Edge of pole – level 2 (0 degrees). Design parameter I ¼ Rubberizing – level 2 (no).      SNRpredicted ¼ T þ ðA1 ÿ TÞ þ ðD2 ÿ TÞ þ ðF 2 ÿ TÞ þ ðI 2 ÿ TÞ ¼ 245:66 þ ð241:704 þ 45:66Þ þ ð244:245 þ 45:66Þ þ ð243:905 þ 45:66Þ þ ð243:459 þ 45:66Þ ¼ 236:33 From the predicted SNR value, the noise (i.e. response or quality characteristic) was generated. The predicted noise at the optimal condition was 65.53. In other words, at the optimal condition, the total sum of squares of plus (positive) deviations from curve of customer requirement is 65.53 in the speed range of 1,600-10,000 RPM. The noise before experiment was estimated to be 205.84. A significant reduction in noise was observed after the experiment (refer to Figure 4). The next phase of this study is to further analyse the effect of factors such as angle of chamfer (different angles), tail of the star (cut or no cut), type of chamfer (single or double) etc. on the performance of star. Conclusion The Taguchi approach to SDOE has intensive applications in the engineering design and development environment. Although many companies in Europe and the USA ð7Þ Figure 4. Noise of alternator (after experiment) have used the Taguchi approach to SDOE with success, very few applications of this method are realised or reported in the Czech Republic. This paper presents two applications of the Taguchi approach to SDOE in the Czech Republican industries. Both case studies were primarily focused on the use of scientific experiments in the new product development process. Both experiments were successful in terms of meeting the objectives set out by the team from both organisations. The results of the study have made an increased awareness of the application of SDOE to the engineering fraternity in both organisations. For wider application of such powerful techniques, the first step is to promote the Taguchi approach of experimental design through local industry networking, seminars and workshops. The initial events should be primarily targeted for executive leaders, senior managers and directors of various business units from various organisations. This should be followed by more detailed training on such methods from well experienced Taguchi practitioners or consultants who have a lot of hands-on experience. References Antony, J. and Kaye, M. (1999), Experimental Quality: A Strategic Approach to Achieve and Improve Quality, Kluwer Academic Publishers, Norwall, MA. Antony, J., Hughes, M. and Kaye, M. 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(1991), “Top ten triumphs and tragedies of Genichi Taguchi”, Quality Engineering, Vol. 4 No. 2, pp. 211-25. Quinlan, J. (1985), “Process improvement by the application of Taguchi methods”, paper presented at the Transactions of the Third Symposium on Taguchi Methods, Dearborn, MI, pp. 11-16. Rowlands, H., Antony, J. and Knowles, G. (2000), “An application of experimental design for process optimisation”, The TQM Magazine, Vol. 12 No. 2, pp. 78-83. Roy, R. (2001), Design of Experiments Using the Taguchi Approach, Wiley, New York, NY. Schmidt, S.R. and Launsby, R.G. (1992), Understanding Industrial Designed Experiments, Air Academy Press, Colorado Springs, CO. Taguchi, G. (1987), System of Experimental Design, Vols 1 and 2, ASI, Dearborn, MI. Taguchi, G. and Yokohama, Y. (1993), Taguchi Methods – Design of Experiments, ASI Press, Dearborn, MI. Taguchi approach to statistical design 457


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