2. Taguchi’s Definition of Quality –or lack thereof “ The loss a product causes society after it is shipped ” Loss due to 1)Variability in function 2) Harmful side effects

3. Noise –Sources of Functional Variation (1)Inner or deterioration noise (2) Outer or environmental noise (3) Variational or piece to piece variation caused during manufacture

4. Examples Refrigerator temperature control inner noise – leakage & mechanical wear of compressor parts outer noise – use conditions, frequency of opening, what stored, ambient temp., voltage variation etc. variational noise – fits, variation in friction coefficient etc. Automobile Brakes inner noise – wear of drums and pads, leakage of fluid outer noise – road conditions, speed of car, weight etc. variational noise – tightness of door, amount of refrigerant, imperfection in compressor parts etc.

5. Process Input Output y Controllable input factors Uncontrollable input factors

6. Activity/Noise Source Inner Noise Outer Noise Variational Noise ManufacturingXXO Process DesignXXO Product DesignOOO X – No Countermeasure Possible O – Countermeasure Possible Activities Where Counter Measures to Noise are Possible

7. Robust Parameter Design Experiments

11. Simulated Noise factor H represents position in the kiln - = in the center, + = near kiln walls where temperature is higher Total of 2 7-4 = 8×2 1 = 16 measurements

13. Total of 9×8=72 tests

14. Output R T resistance at which the relay turns on

15. Levels for noise factors ±2.04% of nominal setting Example: when control factor A is 2.67 low level of noise factor A is (1.0-0.0204)×2.67=2.62 high level of noise factor A is (1.0+0.0204) )×2.67=2.72

16. )

17. Noise Factor Array when =

20. H = - (inner kiln position), H = + (outer kiln position) response = number of defective per 100 tiles

23. Effects on the mean Positive Effect

25. Effects on the log e (var) Positive Effect

27. Conclusion: increasing the content of lime from 1% to 5% reduces the average percentage of defective tiles, and reduces the variability in percentage of defective tiles caused by the temperature gradient in the kiln.

37. RunABCDEFGHy 1 111 0.161 21 11 0.171 31 1 1 0.120 4111 0.060 5 11 1 0.212 611 1 0.748 711 1 0.433 811111110.263 9 111 10.489 101 1110.422 111 1 110.201 12111 10.284 13 11 110.833 1411 1 11.571 1511 1 10.927 16111111111.571 Data written in a single array format

38. No replicates of whole plots, therefore analysis is conducted by making separate normal plots of whole-plot effects and sub-plot effects as described in Sections 8.4 and 8.5.

44. Response Modeling with Multiple Noise Factors

46. Standardize orthogonal contrasts by dividing by the square root of the Number of replicates of each level of the factor in the design. This makes the (X 'X) a 72×72 Identity matrix

49. Fit a model to the largest effects identified on the normal plot

50. Interpretation of Results

54. (3 3 ×2)=2

55. 1/6 fraction

60. Adjustment Factor

61. Single Array Experiment to Improve an Injection Molding Process Excessive part shrinkage was causing assembly problems Control Factors (could be easily varied): A: mold temperature B: screw speed C: holding time D: gate size Noise Factors (normally difficult to control): E: cycle time F: moisture content G: holding pressure

64. Shrinkage is minimized when mold temperature is at the low level, there are no significant control by noise interactions to exploit.

65. Too much variability in % Shrinkage at low screw speed. This will still cause problems in assembly.

66. Box plots show C: holding time is a dispersion effect. Choosing the low level of holding time reduces variability in % shrinkage.