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- 1. Robust Design ME 470 Systems Design Fall 2005
- 2. Why Bother? Customers will pay for increased quality! Customers will be loyal for increased quality!
- 3. Taguchi Case Study In 1980s, Ford outsourced the construction of a subassembly to several of its own plants and to a Japanese manufacturer. Both US and Japan plants produced parts that conformed to specification (zero defects) Warranty claims on US built products was far greater!!! The difference? Variation Japanese product was far more consistent!
- 4. Results from Less Variation Better performance Lower costs due to less scrap, less rework and less inventory! Lower warranty costs
- 5. Taguichi Loss Function Target Target Traditional Approach Taguichi Definition
- 6. Taguichi’s Loss Function Quality Level = total loss All products suffer some incurred by society due to loss the failure of the product The smaller the loss the to deliver the expected better performance + harmful Emphasis shifts from being side effects (including within a range to operating cost) achieving the target value
- 7. L( y) = k ( y − m) 2 (12.7) L(y) is the quality lost (often measured in$) y is value of the quality characteristic m is the target value for y k is the quality loss coefficient
- 8. Variations of the quadratic loss function Nominal is best (Figure 12.6) Smaller the better (Figure 12.6) Larger the better (Figure 12.6) An asymmetric relationship (we won’t worry about this)
- 9. Noise Output variability Input variability – Variational noise is the – Tolerances are design short term, unit to unit factor variability variation due to – Outer noise represents manufacturing processes variations in disturbance – Inner noise is the long- factors such as term change in product temperature, humidity, characteristics over time dust, etc
- 10. Signal to noise ratio Attempts to control the variation with respect to both the mean and the variation about the mean. Appropriate S/N ratios are given in equation 12.12, 12.13, and 12.14 for nominal is best, smaller is best, and larger is best. Be careful that you use the correct equation. The HIGHER the S/N ratio, the better!
- 11. Definition of Robust Design Robustness is defined as a condition in which the product or process will be minimally affected by sources of variation. A product can be robust: Against variation in raw materials Against variation in manufacturing conditions Against variation in manufacturing personnel Against variation in the end use environment ` Against variation in end-users Against wear-out or deterioration
- 12. Back to M&M’s® The making of M&M's® Milk Chocolates begins with milk chocolate centers, which are formed in a machine and then quot;tumbledquot; in order to obtain a smooth, rounded center. What follows is a process known as quot;panningquot;. Panning involves coating the chocolates by rotating them in a coating material in a revolving pan. Panning can be done using syrups and other materials such as chocolate, fats etc. The principle, briefly, is to coat the center with a layer of materials, which on evaporation leaves an even layer or shell of dry substance. The chocolate centers are color coated by rotating them in a revolving pan, while a sugar and corn syrup mixture is added. This process is repeated several times until M&M's® have a thin, smooth shell with the desired thickness. Then, the machine specially designed for the purpose gently imprints an 'm' on the surface of the fragile, crispy, colorful shell without cracking the shell.
- 13. What are Sources of Noise? Output variability Input variability
- 14. Parameter Design Taguchi recommends parameter design to get the best S/N ratio. If parameter design is not sufficient, then tolerance design may be used. Look for two types of design factors – control factors affect the S/N ratio, but not the mean – signal factors affect primarily the mean Taguchi creates a design parameter matrix and a noise matrix
- 15. Parameter Design The book has an excellent example in Section 12.6.1 If tolerance design is necessary, typically ANOVA is used to determine the relative contribution of each control parameter Some STATISTICIANS hate Taguchi!! But Taguchi is used by many companies!!
- 16. Design Resolution Full factorial vs. fractional factorial In our DOE experiment, we used a full factorial. This can become costly as the number of variables or levels increases. As a result, statisticians use fractional factorials. As you might suspect, you do not get as much information from a fractional factorial.
- 17. Fractional Factorials A Fractional Factorial Design is a factorial design in which all possible treatment combinations of the factors are NOT run. The runs are just a FRACTION of the full factorial matrix. The resulting design matrix will not be able to estimate some of the effects, often the interaction effects. Minitab and your statistics textbook will tell you the form necessary for fractional factorials.
- 18. Design Resolution Resolution V (Best) – Main effects are confounded with 4-way interactions – 2-way interactions are confounded with 3-way interactions Resolution IV – Main effects are confounded with 3-way interactions – 2-way interactions are confounded with other 2-way interactions Resolution III (many Taguchi arrays) – Main effects are confounded with 2-way interactions – 2-way interactions may be confounded with other 2-ways
- 19. Test Schedules Available in Text Figure 12. 9 (a) L9 experimental design for 4 control factors, each at three levels. Figure 12.9 (b) L4 experimental design for 3 factors each at 2 levels. Example 12.6 Three output temperatures, each at three levels. Use Figure 12.9 (a) and omit a column.
- 20. Procedure for Taguchi Determine Design Parameters (Inner array) Determine Noise factors (Outer array) Select the appropriate test matrix. Run the experiment Analyze the results
- 21. Taguchi Example of Robust Design Nerf Missilestorm Design Parameters – fin arrangement, – cavity size, – lubrication Noise Factors – skill of user Performance Characteristic Example modified from – firing distance Product Design; Techniques in Reverse Engineering and New Product Development
- 22. Form the inner array or the design parameter matrix Design parameters (2 ) High (1) Low d1 is the fin arrangement Angled fins Straight d2 is the lubrication Graphite powder None d3 is the cavity size 0 cm 3 cm Determine the Required Number of Experiments: One degree of freedom is associated with the overall mean. Next we add the degrees of freedom associated with each design parameter: (# of levels of design parameters)*(# of design parameters). For our case =3*(2-1) or 3. Therefore, we must run at least 1+3 tests. Test schedules may be found in different texts. We will only use the ones in our book or Minitab.
- 23. Test Matrix from 12.9 b Experiment 1 2 3 # 1 1 1 1 2 1 2 2 3 2 1 2 4 2 2 1
- 24. Design Parameter Matrix Trial d1 d2 d3 Randomized Order 1 1 1 1 3 2 1 2 2 2 3 2 1 2 4 4 2 2 1 1
- 25. Outer array, Noise Factor matrix Since there is only one Noise Factor in this experiment, we have a column matrix. n1 1 Unskilled Operator 2 Skilled Operator We will have to conduct 8 experiments. Each experiment will have to be conducted at both levels of the noise factor.
- 26. Results of Tests: Max Distance (m) Noise Noise Trial low (1) high(2) 1 9.30 8.31 2 9.83 10.11 3 8.26 6.99 4 8.23 9.19
- 27. Calculate S/N ratio for each row Because we want to maximize distance, we use Equation 12.14. 1 1 S / N = −10 * log( ∑ 2 ) n y i So for Trial 1, 1 1 1 S / N = −10 * log( ( 2 + 2 )) 2 9.3 8.31
- 28. Signal to Noise Ratios for Maximum Distance Tests Trial # S/N 1 18.85 2 19.97 3 17.55 4 18.76
- 29. Analysis of Results Calculate the average S/N for each factor at each of the three test levels. Average Average S/N of 1 & 2 Level d1 d2 d3 1 19.4 18.2 18.8 2 18.2 19.4 18.8 Average of Trials ___ & ___
- 30. Firgure 1: Comparison of S/N Ratio's for each Design Parameter 19.4 19.4 19.0 S/N Ratio 18.8 d1 18.8 d2 d3 18.2 18.2 18.0 0 1 2 3 Level Use Largest S/N – Pick d1 at Level 1
- 31. Let’s Do It in Minitab >Stat>DOE>Taguchi>Create Taguchi Design Select Display Available Designs
- 32. Select the L4 Design
- 33. Select factors
- 34. Enter Factor Names
- 35. Minitab generates runs that must be completed You must enter noise data directly
- 36. >Stat>DOE>Taguchi>Analyze Taguchi Design Select analysis Double Click on Unskilled Operator and Skilled Operator
- 37. Always check Options!!!! Minitab will assume a default value which may cause you to miss 10 points on the final.
- 38. Main Effects Plot (data means) for SN ratios Fin Arrangement Lubrication 19.6 19.2 18.8 Mean of SN ratios 18.4 18.0 1 2 1 2 Cavity Size 19.6 19.2 18.8 18.4 18.0 1 2 Signal-to-noise: Larger is better
- 39. Response Table for Signal to Noise Ratios Larger is better Cavity Level Fin Arrangement Lubrication Size 1 19.41 18.20 18.81 2 18.16 19.37 18.76 Delta 1.25 1.16 0.04 Rank 1 2 3
- 40. Homework: Due Monday, October 30 Individual Assignment 12.9 from Dieter by hand Modified 12.11 must be done using Minitab

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