LECTURE 17 - ENGR 4045U Quality Control Lecture 17 1...

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ENGR 4045U Quality Control Lecture 17 1
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Schedule Week 8 Part V: Process Design and Improvement with Designed Experiments. Chapter 13: Factorial and Fractional Experiments for Process Design and Improvements. Week 9 Chapter 13: ANOVA, Design of Experiments. Week 10 Midterm-2 2
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Schedule Week 11 Chapter 14: Process Optimization and Designed Experiments. Part VI: Acceptance Sampling. Chapter 15: Lot-by-Lot Acceptance Sampling for Attributes. Week 12 Chapter 16: Other Acceptance Sampling Techniques. Week 13 ISO & Six Sigma Discussions & Review 3
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Process Optimization and Designed Experiments Use the response surface approach to optimizing processes Apply steepest ascent method Analyze second-order response surface model Determine optimum operating conditions for a process Set up and conduct an experiment using a central composite design Understand the difference between controllable process variables and noise variables Understand process robustness study Understand evolutionary operation (EVOP) and its use to maintain a process that is subject to dirt near its optimum operating conditions 4
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Response Surface Methods and Designs RSM is a mathematical and statistical technique that are used to optimize response by analyzing input variables that affect the response variable Initially used for chemical industry To find the levels of reaction temperature (x1) and reaction time (x2) to maximize the yield (y) of the process, E(y) is the response surface. 5 ) , ( ) ( ) ( 2 1 2 1 x x f y E x x f y
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Response Surface Plot E(y) vs. x1, and x2 as contour plot in three dimensional response surface In most of RSM problems, the relationship between the response [y] and independent variables [x1,x2] are unknown. The first step is to find approximation for the relationship between y and x1, x2 6 ) 2 .... ( ) ( .......... ... 1 1 2 1 0 1 1 0 Order nd x x x x y Order First x x y j k i i ij k i i ii k i i i k k
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RSM From current point, move in the response surface closer to the optimum point. 7
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Steepest Ascent The initial estimate of the optimum operating condition is usually far from the actual optimum The method of steepest ascent is a procedure for moving sequentially along the path of steepest ascent: in the direction of maximum increase in the response 8 k i i i x y 1 0
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Steepest Ascent The path of steepest ascent will be the line
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