LECTURE 20

LECTURE 20 - ENGR 4045U Quality Control Lecture 20 1...

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ENGR 4045U Quality Control Lecture 20 1
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Schedule Week 11 Chapter 14: Process Optimization and Designed Experiments. Week 12 Part VI: Acceptance Sampling. Chapter 15: Lot-by-Lot Acceptance Sampling for Attributes. Week 13 Chapter 16: Other Acceptance Sampling Techniques. 2
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Response Surface to Process Robustness For x1, x2 controllable factors and z as noise In response model, 11 or 21 should be 0 to have robust design problem Noise are random variables, that are expressed in coded units: zero, variance 2(z), and for several noise variables, covariance is 0 3
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Response Surface to Process Robustness A model for the mean response by taking the expected value of y A model for the variance response y 4 2 2 2 22 1 11 1 2 ) ( ) ( x x y V z z
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Response Surface to Process Robustness The mean and variance models involve only the controllable variables (easy to achieve target value) The variance model includes only controllable variables, but with the interaction regression coefficients between controllable and noise variables, it will reflect the impact of noise into the response The variance model is quadratic function of the controllable variables 5
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Example 14.3 Robust Design 6
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Example 14.3 Robust Design Study factors 2^4 in experiment Assume factor A (temperature) is hard to control, so it is noise variable z1, while controllable variables: x1 (pressure), x2 (concentration), x3 (stirring rate) Design 2^4 experiment (A, B, C, D), to maximize the filtration rate (response) 7
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Example 14.3 Robust Design The mean and variance models: Assume low and high of temperature (noise) of standard deviation in either sides: 8 51 . 19 , 1 2 z
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Example 14.3 Robust Design Plot the contour of the response, when noise is 0 (temperature) 9
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Example 14.3 Robust Design The mean filtration rate increases as concentration and stirring rate increase 10
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Example 14.3 Robust Design Overlay plot of the contours of mean filtration rate and square root of variance as function of concentration and stirring rate Set concentration at high level and stirring rate near the middle level 11
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Example 14.4 Robust Manufacturing 12
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Example 14.4 Robust Manufacturing A process robust study was conducted in a semiconductor manufacturing plant involving two controllable variables x1, x2 and a single noise factor z 13
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Example 14.4 Robust Manufacturing The objective is to find operating conditions that give a mean response between 90 and 100, while making the variability due to noise is minimum 14 The least square fit
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Example 14.4 Robust Manufacturing 15
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