MIT OpenCourseWare http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303)Spring 2008For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.6.780 Quiz 2 study guide Hayden Taylor, 22 April 2008 Topic Notes References ADVANCED SPC Moving Averages Windowed Exponentially-weighted (EWMA) L9 Ss 6–16 Cumulative sum charts L9 Ss 17–24 Multivariate charts Chi-square Hotelling T2L9 Ss 38–45 L9 Ss 16–49 YIELD Definitions • Functional yield • Parametric yield Concept of critical area Murphy yield model Clustering Large α = little clustering Small α = lots of clustering L10 [Non-standard or device-specific situations] ANOVA Fixed effects model Degrees of freedom Lecture 11 FULL/FRACTIONAL FACTORIAL MODELS; DoE; REGRESSION • Contrasts • Sums of squares – they add up (why?) • Projection to estimate effects from fractional-factorial designs • Aliasing Lecture 12 Lecture 13 Lecture 14 Estimating residuals; dealing with replicates or a lack of them • When you have replicates of corner points • Using replicated center points • By discarding factors and using their SS (but need to be happy that discarded factor is insignificant e.g. 3-way interaction) • Residual distribution should be normal, homoskedastic PS6 Problem 1 PS7 Problem 2 ** PS6 Problem 4 ** plus Excel example From Lec 13 Identifying significant effects • Normal probability plots (care needed) • Using ANOVA (but need SSE estimate first) e.g PS7 Problem 2 Curvature testing • Estimate SSR (residuals); then: yF= grand mean of all factorial runsyC= grand mean of all center point runsSSQuadratic=nFnC(yF− yC)2nF+ nCMSQuadratic=SSQuadraticnc • Define F0 = MSquadratic/MSresidual Montgomery Ex 12-9; Excel example (from Lec 13)Lack-of-fit testing Possible when one or more effects has been disregarded. Curvature testing as a ‘special’ kind of lack-of-fit analysis, Lecture 15 Model fitting • From effects • Coefs directly from data (write down formulae) Lecture 12, 13 May and Spanos §8.1 Confidence intervals • Note formulae for variance of parameters M+S section 8.1 PROCESS ROBUSTNESS Lecture 16 NESTED VARIANCE • Formulae for contamination of variance • Subtleties of performing the analysis • Requirements: random sampling Drain Problem