12_13_A_Expdesig

12_13_A_Expdesig - Lecture Notes - OR 282 Quality Control...

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Lecture Notes - OR 282 Quality Control and Acceptance Sampling - Professor Thomas A. Mazzuchi - 1 EXPERIMENTAL DESIGN OVERVIEW What is DOE • a test or series of tests in which purposeful changes are made to input variables of a process so that we may observe corresponding changes in the output response Controlled Factors x . .. x 1p ÆÆ input PROCESS output y pp ÅÅ z . .. z 1q Uncontrolled Factors (noise) Objectives - Which variables are most influential on the response y? - Where to set x for y to be at nominal requirements µ - Where to set x for y to have minimal variance µ - Where to set x so that the effect of z on y is minimal µµ
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Lecture Notes - OR 282 Quality Control and Acceptance Sampling - Professor Thomas A. Mazzuchi - 2 U s e s - Process Development/Design - Process Trouble Shooting - Process Robustness Examples Process Product 1.Improved Yield 1. Contributions to Design 2. Reduced Variability and close 2. Material Alternatives conformance to nominal 3. Reduced Development Time 3. Analysis of Design Parameters 4. Reduced Costs •Note - DOE is as opposed to control charting active - DOE is offline as opposed to control charting - The assumption is that y (x , z ) (x , z ) œ µµ .5 % where ~N(0,1) (also true for multivariate case) % - z or portions of z may be controlled as part of the experiment
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Lecture Notes - OR 282 Quality Control and Acceptance Sampling - Professor Thomas A. Mazzuchi - 3 SINGLE FACTOR EXPERIMENTS Example: Tensile Strength of Grocery Bags • Current Situation - product = 10% hardwood pulp (H) - tensile strength = 15 psi (T) - process in control • Experimental Design: hypothesis is that T is an increasing function of H - Let H = 5, 10, 15, 20 % (economic range 5 H 20) ŸŸ - Test 6 samples (replications) at each level (n 6, i 1, . .., 4) i œœ - Test for strength randomly with four levels - Experoment design: Completely Randomized Single Factor Experimental Design with Replications (Balanced) - Observations Observations I n d e p V a r H 123456T o t a l s A v e r a g e 5 7 8 15 11 9 10 60 10.00 10 12 17 13 18 19 15 94 16.54 15 14 18 19 17 16 18 102 12.00 20 19 25 22 23 18 20 127 21.17 383 15.96
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Lecture Notes - OR 282 Quality Control and Acceptance Sampling - Professor Thomas A. Mazzuchi - 4 - Graphic Analysis
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Lecture Notes - OR 282 Quality Control and Acceptance Sampling - Professor Thomas A. Mazzuchi - 5 STATISTCIIAL ANALYSIS: ONE WAY ANALYSIS OF VARIANCE (ANOVA) Notation: y jth observation of factor level i, i 1, . ..,a œ ij and j 1, . .., n (same for each factor level œ Model y ij i ij i 1, . . . , a j 1, . . . , n .7% š œ œ overall mean . factor effect 7 i random error with N(0, ) iid %% 5 ij ij 2 µ Analysis Methods Fixed Effects Model: - factor levels are fixed, selected in advance - inference only about experimental , i 1,. .., a. 7 3 œ Random Effects Model or Compomemts of Variance Model: - factor levels selected at random - inference about all population of levels, are random variables. 7 3
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Lecture Notes - OR 282 Quality Control and Acceptance Sampling - Professor Thomas A. Mazzuchi - 6 Analysis for Fixed Effects Model ( specific for levels chosen) 7 i • Notation usually deviations from 0 7.
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This note was uploaded on 01/02/2010 for the course EMSE 282 taught by Professor Harris during the Spring '07 term at GWU.

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12_13_A_Expdesig - Lecture Notes - OR 282 Quality Control...

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