Taguchi and Response Surfaces

Taguchi and Response Surfaces - Taguchi Methods and ‘...

Info iconThis preview shows pages 1–19. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 16
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 18
Background image of page 19
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Taguchi Methods and ‘ Response Surface ' Alternatives Once in control, goal is to produce uniformly near a target. I ° Mean on target ° Reduce variation Three possible situations: - Smaller is better 0 Larger is better ° On target is best On target is best. Taguchi considered deviation from target to be loss to society. Taguohi models this as: 120’) =K(Y—T)2 Y 2 Quality Control ' T 2 Target value On average, loss is proportional to: ‘ E(Y —- T)2 = Varfl’) + (Bier?)2 where B iaS : difference of mean and Target 5 For smaller is better, Taguehi has less as: L(Y) = Y2 _ i.e. on average E(Y 2). So Target is 0. For larger is better, Taguchi considers loss as: MY) =1/y2 0f E(1/y2). First step in Taguchi ' Method is parameter % I design. Parameters are inputs known or suspected to affect the quality characteristic. Goal: Design in quality, don’t sample to catch poor output. 8 Parameters are divided into two groups: ° Control variables- parameters which can be controlled in the process. ° Noise variables— parameters which vary and are usually not controlled (sometimes hard or expensive to control). Levels are chosen for each of the control variables. Levels are chosen 1 and temporarily fixed for each of the - noise variables. Control variables are placed into inner array. Example: [\JNHMNNHh—d :Nl—tNr—tNr—twv—‘l Eight design points, each row one design point 11 Noise variables are ' placed in outer array Example: ' 2 l 2 2 Generally the levels span What is experienced in production conditions. 12 The structure of each array is typically ° Factorial design ° Fractional factorial design (sometimes referred to as - “orthogonal array”.) The arrays are then crossed and observa— tions collected. 13 Goal of analysis: Minimize _ E(Y -— N by choice of best control variable settings. Taguohi suggests look at “signal to noise” ratio. % Bigger is better. Then adjust mean. 14 Criticisms: -° Crossing inner and outer arrays can lead to unwieldy designs. ° Use of signal to noise ratios very ad-hoc and hard to generalize (various versions). '15 Alternatives proposed include ReSponse Surface Methodology ' (RSM). * Goals: - Model the response Y as a function of control and noise variables. - Use information on distribution of noise variables to model mean and variance. l6 Simple example: I Y = Lamina thickness X I : Viscosity (control variable) _ X 2 :— Ambient humidity (noise variable) . Fitted model: Y = 60+B‘1X1+B\12X1X2 Select X to minimize loss. 17' E(f)=6O+BIXI ‘ +6 X -E(X2) 12 1 Var()7) 2(612X1r -Var(X2) 2 +6 (Conditional mean and variance, conditional 0n ~ parameter estimates). 18 More complex example: XPX2 —C0ntr01 X3 —N0ise 17:50 +61X1+BA2X2 + B23X2 'X3 E®Zfio+61X1+62X2+323X2+623X2 '(EX3) Vam=(fi23X2)-Vaz(X3)+o Can set X2 set X1 to control mean. to minimizevariance 19' ...
View Full Document

This note was uploaded on 02/20/2012 for the course STAT 513 taught by Professor Na during the Spring '11 term at Purdue.

Page1 / 19

Taguchi and Response Surfaces - Taguchi Methods and ‘...

This preview shows document pages 1 - 19. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online