lecture11

# lecture11 - 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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1 MIT 2.830/6.780/ESD.63 Control of Manufacturing Processes Introduction to Analysis of Variance: a tool for assessing input-output relationships
2 Have focused so far on interpreting output Equipment Material E ( t ) “controls” Geometry and properties “outputs” Y

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3 Review of tools for interpreting outputs Tool # outputs # samples # inputs Levels per input ? ? ? ? (2?) ? (2?) ? (2?) t, F tests 1 2 control charts, cusum, EWMA etc 1m a n y χ 2 , T 2 charts 2m a n y Also talked about yield modeling and process capability, but need ways of modeling and thus improving processes
4 Injection molding data IM Run data 2.015 2.020 2.025 2.030 2.035 2.040 2.045 2.050 2.055 2.060 111111111111111222222222222222333333333333333444444444444444 Levels changes v - low t - low v - high t - low v - low t - high v - high t - high diameter (in)

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5 Want to start relating input(s) to output(s) Δ Y = Y ∂α Δα + Y u Δ u Y ( α ) process parameters Equipment Material E ( t ) “controls” Geometry and properties “outputs” Y “inputs” α
6 What is our goal? Developing a process model – Relating inputs and disturbances to outputs – Determining significance of the input effect • Does it really matter? Process optimization – Max (Cpk) or Min (QLF) – Models for mean shifting – Models for variance reduction

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7 Empirical Modeling • What is the objective? • What is the output? • What are the input(s)? • What do we want to vary? • What model form should we use? Y = Φ ( α , u ) is not specific! • How many data can we take?
8 First step: determining which inputs matter Tool # inputs Levels per input # samples # outputs t, F tests ? ? (2?) 2 1 control charts, cusum ? ? (2?) many 1 χ 2 , T 2 charts ? ? (2?) many 2 Analysis of variance 1 2 2 1

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9 Agenda 1. Comparison of treatments (one variable) Fixed effects model Analysis of Variance (ANOVA) technique Example 2. Multivariate analysis of variance Model forms MANOVA technique
10 Comparison of Treatments Sample A Sample B Sample C Population A Population B Population C • Consider multiple conditions (treatments, settings for some variable) – There is an overall mean μ

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lecture11 - http/ocw.mit.edu MIT OpenCourseWare 2.830J...

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