Taguchi method in Factorial experiment ppt

Design of Experiments

1. TAGUCHI METHOD IN FACTORIAL EXPERIMENTS Venugopal K Id No: PAMB 2157 M.Sc. (Agricultural Statistics)

2. Introduction Taguchi method Orthogonal array Methodology Merits and Demerits Applications Case studies and Conclusion Summary References Contents

3. Factorial Experiment: Factorial experiments are a type of experimental design that allows researchers to study the effects of multiple factors simultaneously. In a factorial experiment, every possible combination of the levels of the factors is tested. This approach provides comprehensive insights into the interactions between factors as well as their individual effects. = K factors, Z levels 3 factors, 2 levels and = 2 factors, 3 levels   3 Introduction

4. Full factorial Experiment: Full factorial design is one in which all possible combinations of the various factors at different levels are studied. Number of experiments (N)= Where, Z = number of levels, = number of factors E.g. - 3 factors, 2 levels each, N = = 8 runs.   4 Contd…

5. With increase in the number of factors and their levels, the number of experiments would be prohibitively large. For conducting so many experiments a number of batches of materials, different process conditions, etc. results in heterogeneity and the experimental results tend to become inaccurate (results in more experimental error). Hence care must be taken that variations in the experimental material, background conditions, etc. do not bias the conclusions to be drawn. To address these issues, statisticians have developed Fractional Replicate Designs (Fractional Factorial Designs). Contd.. 5 Krishnaiah and Shahabudeen (2012)

6. Fractional factorial experiment: This approach tests only a subset of the possible combinations, reducing the number of experiments while still providing valuable insights. In general, design is a fraction of a design using experiments . For example: design is a design using = =8 experiments. One among the fractional factorial designs is Taguchi design. These designs are orthogonal arrays allowing for a maximum number of main effects to be estimated from a minimum number of runs in the experiment while allowing for differences in the number of factor levels.   6 Contd .. Krishnaiah and Shahabudeen (2012)

7. Taguchi Method The Taguchi methods are statistical methods developed by Japanese scientist Genichi Taguchi in 1950. This method was developed based on orthogonal array experiments which gives much reduced variance for the experiment with optimum setting of control parameters. The principle of design of experiments along with optimization of control parameters to obtain best results is achieved in the Taguchi method. The Taguchi approach enables a comprehensive understanding of the individual and combined effects of various design parameters to be obtained from a minimum number of experimental trials . 7 Shyam and Rajeshwar (2012)

8. Contd … The aim of the Taguchi design method is to establish the parameter settings that render the product quality robust to unavoidable variations in external noise. ANOVA is a standard statistical technique to interpret the experimental results and is used extensively to identify the performance of the group of parameters under investigation. The purpose of ANOVA is to investigate the parameters, whose combination to total variation is significant. If a design parameter is found to be significant, it implies that this parameter plays a fundamental role in determining the optimal solution of the design problem. 8 Shyam and Rajeshwar (2012)

9. Contd … Objectives of Taguchi methods Minimize the variation in product response from mean response. To establish the best or optimal condition for the product or process. To establish the contribution of individual factors. To estimate the response under optimal condition. 9

10. Orthogonal arrays(OA) An orthogonal array is a matrix used in the design of experiments that allows for the study of multiple factors simultaneously with a balanced set of experiments In the Taguchi method, an orthogonal array is a systematic way of designing experiments to study a large number of variables with a minimal number of experiments. Orthogonal arrays are used to ensure that all levels of factors are considered equally, and interactions between factors can be studied efficiently. Each row in the array represents an experiment, and each column represents a factor. The entries in the array indicate the levels of the factors used in each experiment. 10 Krishnaiah and Shahabudeen (2012)

11. Contd … Properties of an orthogonal array: Each factor's levels are equally represented, and the array is balanced so that the effect of each factor can be separated and evaluated independently. It reduces the number of experiments required compared to a full factorial design, making the experimentation process more efficient and cost-effective. 11 Krishnaiah and Shahabudeen (2012)

12. Table 1: Standard orthogonal array   12 Trial No. Columns 1 2 3 4 5 6 7 1 1 1 1 1 1 1 1 2 1 1 1 2 2 2 2 3 1 2 2 1 1 2 2 4 1 2 2 2 2 1 1 5 2 1 2 1 2 1 2 6 2 1 2 2 1 2 1 7 2 2 1 1 2 2 1 8 2 2 1 2 1 1 2 Krishnaiah and Shahabudeen (2012)

13. Contd… Table 2: Standard orthogonal array 13 Krishnaiah and Shahabudeen (2012)

14. Contd … Table 3: Comparison of number of experiments in full factorial & OA designs Number of factors Number of levels Number of experiments Full factorial Taguchi 3 2 8 4 7 2 128 8 15 2 32768 16 4 3 81 9 13 3 1594323 27 14 Krishnaiah and Shahabudeen (2012)

15. Contd … Taguchi method contains System design, Parameter design and Tolerance design procedures to achieve a robust process and result for the best product quality. 1 . System design: System design is the first step in the design of any product or process. This design at the conceptual levels involves creation, exploration and presentation of ideas. 15 Shyam and Rajeshwar (2012)

16. Contd… 2. Parameter design: Parameter design is the process of investigation leading to the establishment of optimal settings of the parameters, so that the product/process perform on target and is not influenced by the noise factors. Orthogonal experiments are used for this purpose. 16 Shyam and Rajeshwar (2012)

17. Contd … 3.Tolerance design: Tolerance design is the process of determining the tolerances around the nominal settings identified in parameter design process. Tolerances should be set such that the performance of the product/process is on target and at the same time they are achievable at minimum manufacturing cost. The optimal tolerances should be developed in order to minimize the total costs of manufacturing and quality. 17 Shyam and Rajeshwar (2012)

18. Eight steps in Taguchi methodology Step-1: Identify the performance characteristics and select process parameters to be evaluated. Step-2: Determine the number of levels for the process parameters and possible interactions between the process parameters. Step-3: Select the appropriate orthogonal array and assignment of process parameters to the orthogonal array Step-4 : Conduct the experiments based on the arrangement of the orthogonal array. Step-5 : Calculate the S/N ratio. 18 Shyam and Rajeshwar (2012)

19. 19 Step-6: Analyze the experimental results using the S/N ratio and ANOVA Step-7: Select the optimal levels of process parameters Step-8: Verify the optimal process parameters through the confirmation experiment. Contd …

20. Methodology used in Taguchi method SIGNAL-TO-NOISE RATIO (S/N) : In taguchi method, the term “signal” represents the desirable value (mean) for the output characteristic and the term “noise” represent the undesirable value (S.D) for the output characteristic. Where, M.S.D is the mean squared deviation for the output characteristic. There are three categories of quality characteristics namely: Lower the better. Higher the better. Nominal is the better .   20 Krishnaiah and Shahabudeen (2012)

21. Contd… 1. Smaller the better :- The quality characteristic is continuous and non negative. It can take any value between . The desired value (the target) is zero. (ex: surface roughness, tyre wear, etc.). The S/N ratio is given by Where, r = no. of replications = Total of response obtained at experment 2 . Nominal–the best :- In this the quality characteristic is continuous and non-negative. It can take any value from 0 to its target value is non-zero and finite.   21 Krishnaiah and Shahabudeen (2012)

22. Contd … The S/N ratio is given Where , 3. Larger–the better :- The quality characteristic is continuous and non negative. It can take any value from 0 to . The ideal target value of this type quality characteristic is (as larger as possible). Quality characteristics like strength values, fuel efficiency, etc. are examples of this type. The S/N ratio is given by   22 Krishnaiah and Shahabudeen (2012)

23. Merits It uses less number of treatment combination for study. It emphasizes a mean performance characteristic value close to the target value rather than a value within certain specification limits thus improving the product quality. By applying this method one can significantly reduce the time and resources required for experimental investigation. 23

24. Demerits Orthogonal array do not consider all factor combination, hence this should not be used where all relationship between all factors are needed. Taguchi deal with designing quality in rather than correcting for poor quality they applied most effectively at early stages of process development. 24

25. Applications Manufacturing processes: Taguchi methods are widely used in manufacturing industries to optimize production processes, reduce defects, and improve product quality. Chemical and pharmaceutical industries: Taguchi methods are employed in optimizing chemical processes and pharmaceutical manufacturing to enhance efficiency, reduce waste, and ensure product quality. 25

26. Contd … Agriculture: Crop yield optimization: Taguchi method used to optimize factors affecting crop yield, such as planting density, irrigation levels, fertilizer application, and other environmental conditions. By systematically studying the impact of these factors, agricultural practices can be adjusted to maximize productivity. Crop quality improvement: Taguchi methods can be applied to optimize factors influencing the quality of crops, including nutrient levels, soil composition, and harvesting techniques. This can lead to improvements in crop taste, appearance, and nutritional content. 26

27. CASE STUDY 1 Optimization of cutting parameters for turning operations based on Taguchi method Yang and Tarng ( 1998 )

28. 28 Turning is a very important machining process in which a single-point cutting tool removes material from the surface of a rotating cylindrical workpiece. In a turning operation, it is an important task to select cutting parameters for achieving high cutting performance. Usually the desired cutting parameters are determined based on experience or by use of a handbook. Since turning operations are accomplished using a cutting tool, the high forces and temperature during machining create a very harsh environment for the cutting tool. Therefore tool life is an important index to evaluate cutting performance in turning operations. Yang and Tarng ( 1998 ) Contd …

29. 29 Contd … In this study three important cutting parameters with three levels are chosen as shown below (Table 4). Table 4 : Cutting parameters and their levels Symbol Cutting parameter Level 1 Level 2 Level 3 A Cutting speed (m ) 135 210 285 B Feed rate (mm 0.08 0.2 0.32 C Depth of cut (mm) 0.6 1.1 1.6 Symbol Cutting parameter Level 1 Level 2 Level 3 A 135 210 285 B 0.08 0.2 0.32 C Depth of cut (mm) 0.6 1.1 1.6 Yang and Tarng ( 1998 )

30. 30 Contd … Table 5 : E xperimental layout using an L9 orthogonal array Experiment No. Cutting parameter level Cutting speed (m ) Feed rate (mm Depth of cut (mm) 1 1 1 1 2 1 2 2 3 1 3 3 4 2 1 3 5 2 2 1 6 2 3 2 7 3 1 2 8 3 2 3 9 3 3 1 Experiment No. Cutting parameter level Depth of cut (mm) 1 1 1 1 2 1 2 2 3 1 3 3 4 2 1 3 5 2 2 1 6 2 3 2 7 3 1 2 8 3 2 3 9 3 3 1 Yang and Tarng ( 1998 )

31. 31 Analysis of the S/N ratio S/N ratio was used to measure the quality characteristic deviating from the desired value. In this study, they testing optimum cutting parameters for the tool life. Hence higher-the-better quality characteristic for tool life must be taken. For higher-the-better quality characteristic the S/N ratio is calculated as Where m = number of test, = value of tool life in the test   Yang and Tarng ( 1998 )

32. 32 Contd … Table 6: Experimental results for tool life and S/N ratio Experimental No. Cutting speed (m ) Feed rate (mm Depth of cut (mm) Tool life (s) S/N ratio (dB) 1 135 0.08 0.6 2645 68.45 2 135 0.20 1.1 2060 66.28 3 135 0.32 1.6 1733 64.78 4 210 0.08 1.6 1310 62.35 5 210 0.20 0.6 1198 61.57 6 210 0.32 1.1 734 57.31 7 285 0.08 1.1 854 58.63 8 285 0.20 1.6 765 57.67 9 285 0.32 0.6 216 46.69 Experimental No. Depth of cut (mm) Tool life (s) S/N ratio (dB) 1 135 0.08 0.6 2645 68.45 2 135 0.20 1.1 2060 66.28 3 135 0.32 1.6 1733 64.78 4 210 0.08 1.6 1310 62.35 5 210 0.20 0.6 1198 61.57 6 210 0.32 1.1 734 57.31 7 285 0.08 1.1 854 58.63 8 285 0.20 1.6 765 57.67 9 285 0.32 0.6 216 46.69

33. 33 Contd … Since the experimental design is orthogonal, hence it is possible to separate out the effect of each cutting parameter at different levels. Table 7:The mean S/N ratio for each level of all the factors Cutting parameter Mean S/N ratio Level 1 Level 2 Level 3 Cutting speed 66.50 60.41 54.33 Feed rate 63.14 61.84 56.26 Depth of cut 58.90 60.74 61.60 Yang and Tarng ( 1998 )

34. 34 Results and discussions The purpose of the analysis of variance (ANOVA) is to investigate which design parameter significantly affecting the quality characteristic. Table 8: ANOVA Source of variation df Sum of squares Mean square F Contribution(%) Cutting speed 2 222.17 111.08 12.36 66.98 Feed rate 2 80.19 40.09 4.46 24.17 Depth of cutting 2 11.38 5.69 0.63 3.43 Error 2 17.97 8.98 - - Total 8 331.71 - - - Yang and Tarng ( 1998 )

35. 35 Contd … Cutting Speed has the highest F-ratio ( 12.39 ), indicating it has the most significant impact on the S/N ratio. Feed Rate has a moderate impact with an F-ratio of 4.47 . Depth of Cut has the least impact with an F-ratio of 0.63. Based on S/N ratio and ANOVA analysis, the optimal cutting parameters for tool life are the cutting speed at level 1 , the feed rate at level 1 and the depth of cut level 3. Yang and Tarng ( 1998 )

36. 36 Contd … Confirmation test Once the optimal level of the design parameters has been selected, the final step is to predict and verify the improvement of the quality characteristic using the optimal level of the design parameters. Table 9: Results of the confirmation experiment for tool life Yang and Tarng ( 1998 ) Initial cutting parameters Optimal cutting parameters Prediction Experiment Factor combinations A 2 B 2 C 2 A 1 B 1 C 3 A 1 B 1 C 3 Tool life (s) 1059 2890 2604 S/N ratio (dB) 60.50 69.22 68.31

37. 37 Conclusion The Taguchi method provides a systematic and efficient methodology for the design optimization of the cutting parameters with far less effect than would be required for most optimization techniques. It has been shown that tool life can be improved significantly for turning operations. The confirmation is conducted to verify the optimal cutting parameters.

38. CASE STUDY 2 Taguchi design optimization of cutting parameters for surface roughness in turning INCONEL. Deva Raj et.al. (2016)

39. The work piece considered for the experiment was Inconel 718 and cemented carbide insert with TiCn – Al 2 O 3 coating was used as cutting tool. Turning tests were carried out on a computer numerically controlled (CNC) lathe machine under wet condition using iso vg68 cutting fluid. Three cutting parameters (speed, feed rate and depth of cut) were considered with three levels for each cutting parameter (Table10) . Three experimental factors and three levels for each factor are considered. So, orthogonal array was taken and the experimental combinations were shown in Table 11 .   39 Deva Raj et.al. (2016) Contd …

40. Contd … 40 Levels of the experimental factors   Factors (Cutting parameters)   Factors   Speed, N (rpm) Feed rate, f (mm/rev) Depth of cut, d (mm) 1 300 0.05 0.1 2 400 0.10 0.3 3 500 0.15 0.5 Table 10 : Experimental factors and their levels Deva Raj et.al. (2016)

41. Contd … 41 Deva Raj et.al. (2016) Run no. Cutting parameters Speed N (rpm) Feed rate f (mm/rev) Depth of cut d (mm) 1 1(300) 1(0.05) 1(0.1) 2 1(300) 2(0.10) 2(0.3) 3 1(300) 3(0.15) 3(0.5) 4 2(400) 1(0.05) 2(0.3) 5 2(400) 2(0.10) 3(0.5) 6 2(400) 3(0.15) 1(0.1) 7 3(500) 1(0.05) 3(0.5) 8 3(500) 2(0.10) 1(0.1) 9 3(500) 3(0.15) 2(0.3) Table 11 : orthogonal array  

42. Evaluation of signal-to-noise ratio To determine the effect each variable has on the output, the signal-to-noise (S/ N ) ratio needs to be calculated for each experiment conducted(Table 12). To obtain optimal machining performance smaller-the better performance is considered as the characteristic for surface hardness. The sn ratio formulae are given below: s/n s where, y = average of the observed data r = number of replications.   42 Deva Raj et.al. (2016)

43. Contd … 43 Run no. Cutting parameters Output response S/N ratio (dB) Speed ‘N’ (rpm) Feed rate ‘f’ (mm/rev ) Depth of cut ‘d’ (mm) SR (μm) 1 300 0.05 0.1 1.23 -1.7981 2 300 0.10 0.3 1.26 -2.0074 3 300 0.15 0.5 1.24 -1.8684 4 400 0.05 0.3 1.25 -1.9382 5 400 0.10 0.5 1.30 -2.2788 6 400 0.15 0.1 1.25 -1.9382 7 500 0.05 0.5 1.35 -2.6066 8 500 0.10 0.1 1.67 -4.4543 9 500 0.15 0.3 1.22 -1.7272 Table 12: Machining conditions and responses Deva Raj et.al. (2016)

44. Contd … Since the experimental design is orthogonal, it is then possible to separate out the effect of each cutting parameter at different levels . 44 Levels   Factors   Speed ‘N’ (rpm) Feed rate ‘f’ (mm/rev) Depth of cut ‘d’ (mm) 1 -1.8913 -2.1143 -2.7302 2 -2.0517 -2.9135 -1.8909 3 -2.9294 -1.8446 -2.2513 Table 13: Response table for S/N ratios Deva Raj et.al. (2016)

45. Results and discussions Analysis of variance: Table 14: Results of ANOVA 45 Machining parameter df Sum of square (SS) Mean sum of squares(MSS) F Contribution (%) N 2 1.8735 0.9367 1.77 32.03 f 2 1.8540 0.9270 1.75 31.70 d 2 1.0635 0.8317 1.00 18.18 Error (e) 2 1.0572 0.5286 - - Total (T) 8 5.8483 - - - Deva Raj et.al. (2016)

46. Contd … The Speed factor has the highest F-ratio ( 1.77 ), indicating it may have the most significant impact on the response variable among the three factors. The Feed Rate and Depth of Cut factors have similar F-ratios ( 1.75 and 1.00 respectively), suggesting their impact on the response variable may be comparable. Based on S/N ratio and ANOVA analysis, the optimal combination for minimizing the surface roughness is 300 rpm speed, 0.10 mm/rev feed rate and 0.3 mm depth of cut 46 Deva Raj et.al. (2016)

47. Contd … Confirmation test : For the optimal combination, n 1 f 3 d 2 , a confirmation experiment was performed for 300 rpm speed, 0.15 mm/rev feed rate and 0.3 depth of cut. Table 4: Results of confirmation test 47 Reference value Optimal cutting condition Prediction Experiment Factor combinations N 1 f 1 d 1 N 1 f 3 d 2 N 1 f 3 d 2 Surface hardness 1.23 1.19 1.20 S/N ratio -1.7981 -1.5109 -1.5836 Deva Raj et.al. (2016)

48. Conclusion The effectiveness of this approach was verified by the confirmation test and analysis of variance (ANOVA). The Experimen tal S/N ratio value of surface roughness is -1.5836 which was in close proximity with the predicted value -1.5109 . The results show that using the optimal parameter settings ( n 1 f 3 d 2 ) causes a lower surface roughness. The predicted and the experimental S/ N ratios and surface roughness were measured of the optimal combination, and the results were in close proximity. 48 Deva Raj et.al. (2016)

49. Summary In the industrial context as the number of factor increases, factors combination increases there by increasing the heterogeneity, this reduces the precision of the experiment. By using this method we can considerably reduce the number of factor combination in the experiment thereby increase the precision. T he Taguchi design is a powerful tool for improving quality and efficiency in industrial processes. Its focus on robustness and simplicity makes it particularly useful for practical applications where consistent performance and cost savings are critical. 49

50. References DEVA RAJ, SRINIVAS ,C., MASTAN RAO, P. AND SUNEEL, D., 2016, Taguchi design optimization of cutting parameters for surface r oughness in turning Inconel. Int. R es. J. E ng. Tech., 3 (5):2556-2560. KRISHNAIAH, K. AND SHAHABUDEEN, P., 2012, Applied Design of Experiments and Taguchi Methods. PHI learning private limited , New Delhi, pp.:198-233. SHYAM, K.K. AND RAJESHWAR, S., 2012, An overview on Taguchi method . Int. J. Eng. Math. Sci ., 1 :11-18. 50

51. Contd … SHRADDHA GAONKAR, NIMISHA KARANJAVKAR AND SHANKAR KADAM, 2016, Taguchi method. Int. J. Sci . Res. Sci . Eng. Technol ., 2 (2):842-845. YALDAGARD., MORTAZAVI AND TABATABAIE., 2008, Applications of ultrasonic waves as a priming techniques for accelerating and enhancing the germination of barley seed optimization of method by Taguchi approach., J. Inst. Brew . , 114 (1):14-21. YANG, W. H. AND TARNG, Y. S., 1998, Design optimization of cutting parameters for turning operations based on the Taguchi method. J. Materials processing tech ., 84 :122-129. 51

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