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lecture16

# lecture16 - http/ocw.mit.edu MIT OpenCourseWare 2.830J...

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MIT OpenCourseWare ____________ http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: ________________ http://ocw.mit.edu/terms .

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2.830J/6.780J/ESD.63J 1 M anufacturing Control of Manufacturing Processes Subject 2.830/6.780/ESD.63 Spring 2008 Lecture #16 Process Robustness April 10, 2008
2.830J/6.780J/ESD.63J 2 M anufacturing Outline • Last Time – Optimization Basics – Empirical Response Surface Methods • Steepest Ascent - Hill Climbing Approach • Today – Process Robustness • Minimizing Sensitivity • Maximizing Process Capability – Variation Modeling • Noise Inputs as Random Factors – Taguchi Approach • Inner - Outer Arrays

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2.830J/6.780J/ESD.63J 3 M anufacturing What to Optimize? • Process Goals – Cost (Minimize) – Quality (Maximize Cpk or Minimize E(L)) – Rate (Maximize) – Flexibility (N/A for now)
2.830J/6.780J/ESD.63J 4 M anufacturing Simple Problem: Minimum Cost • Must Hit Target • Multiple Input Factors – Contours of constant output – Match to Target – Assume constant output variance • Choose Operating Point to – Minimize Cost (e.g. material usage; tool wear, etc) – Minimize Cycle Time x = T 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -4 -3 -2 -1 0 1 2 3 4 μ T USL LSL

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2.830J/6.780J/ESD.63J 5 M anufacturing Linear Model with Constraint -1 -0.2 0.6 -10 -5 0 5 10 15 Y X1 X2 -1 -1 +1 +1 0 Line of mean =5.0 Need Second Criterion to select unique x 1 and x 2 •cost •ra te ˆ y = 1 + 7 x 1 + 2 x 2 + 5 x 1 x 2 Target
2.830J/6.780J/ESD.63J 6 M anufacturing Quality: Minimum Variation • Minimize Sensitivity to Δα – Process Robustness • Maximize C pk • Minimize expected quality loss: E{L(x))} Δ Y = Y ∂α Δα + Y u Δ u

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2.830J/6.780J/ESD.63J 7 M anufacturing C pk = min ( USL − μ ) 3 σ , ( LSL − μ ) 3 C pk = min ( USL ˆ y ) 3 ˆ s , ( LSL ˆ y ) 3 ˆ s • Single variable that combines y and s • Could be discontinuous η j = min ( USL Measure using estimates of response of y and s : y j ) 3 s j , ( LSL y j ) 3 s j Or create a new response variable from the raw data Maximizing Cpk
2.830J/6.780J/ESD.63J 8 M anufacturing Variance Dependence on Operating Point • We often assume that σ 2 is constant throughout the operating space – Implicit in simple ANOVA, most regression fits

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lecture16 - http/ocw.mit.edu MIT OpenCourseWare 2.830J...

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