DOE (Design of Experiment)

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DOE (Design of Experiment) Made By: ISHA JAIN NIDHI GAHLOT Division of MPAE

description

a presentation on DOE

Transcript of DOE (Design of Experiment)

Page 1: DOE (Design of Experiment)

DOE (Design of Experiment)

Made By:ISHA JAIN

NIDHI GAHLOTDivision of MPAE

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Some Typical Applications of Experimental Design

• Characterising: also known as “screening”. To determine which factors affect the output.

• Optimising: to determine the region in the important factors that leads to the best possible response.

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Strategy of Experimentation

• One factor at a time approach: keep all other factors constant and change any one (say A). This gives “main effect A ONLY”.

• Factorial: gives main effects as well as interaction.

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Basic Principles of ExperimentationBasic principles What do they mean? Why do we do them?

replication Repetition of basic experiment. NOT same as repeated measurements

•Improves validity of DOE•Reflects variability b/w runs

randomisation Allocation of experimental material and order of runs in random

Assists in averaging out the effects of extraneous factors

blocking A design technique to improve precision with which comparisons among factors on interest are made

Reduces effect of nuisance factors

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What is Factorial Design?• factors• levels• x y = (no. of levels) (no. of factors) • Main effect• Interaction

let us consider simplest factorial design possible.22 full factorial

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Regression Model• Refers to the equation establishing

quantitative relationship b/w factors of interest (A & B) and response (y)

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Types of Plots Obtained from DOE

• Interaction Plots• Normal Probability Plots/ Half Normal Plots

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Interaction Plots

• One factor interaction plot• Two factor interaction plot

Let us study “two factor interaction plot”

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Two factor interaction plot• Plots that help us realise interaction AB.• A significant interaction will often “mask” the

significance of main effects.

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Normal Probability Plots

• The effects that are negligible are normally distributed, with mean zero & variance ^2 & will tend to fall along a straight line on this plot, whereas significant effects will have non zero means and hence will not lie along a straight line.

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Normal Probability Plots Vs Half Normal Plots

Take only +ve half of bell shaped curves!

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Analysis of Variance Table (ANOVA)

Source of variation

Sum of squares

Degrees of freedom

Mean square

F - Value P - Value

A SSA (a-1) MSA FA PA

B SSB (b-1) MSB FB PB

AB SSAB (a-1)(b-1) MSAB FC PC

Error SSE ab(n-1) MSE 1

Total SST abn-1

•A “P value” less than 0.005 implies variation is significant•A “P value” more than 0.005 implies variation is NOT significant

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When no. of factors increase…• 23 = 8

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Fractional Factorial Designs

• When do we use fractional factorial?Too many no. of runsCharacterising/ screening• Properties of fractional factorial?Sparsity of effectsProjective property*Sequential experimentation*

*later

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The One Half Fraction on 2k Design

• Consider 23= 8half of 8= 4for fractional factorial, we will perform 4 runsONLY.

2(3-1) Design way of representing one half fractional factorial on 23

Which 4 runs to choose and which 4 runs to reject?

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Which 4 runs to choose and which 4 runs to reject?

combination I A B C AB AC BC ABC

a + + - - - - + +b + - + - - + - +

c + - - + + - - +

abc + + + + + + + +

ab + + + - + - - -

ac + + - + - + - -

bc + - + + - - + -

1 + - - - + + + -

Hence. 2 relations are possible.I= ABC or I= -ABCHence. 2 one half fractional factorials can be obtained from one one full factorial.

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• I = ABC• Known as “principle fraction”

lA A + BC

lB B + AC

lc C + AB

• I= -ABC• Known as “alternate fraction”

lA’ A - BC

lB’ B - AC

lc’ C - AB

Add to obtain A, B and C.Subtract to obtain AB, BC and AC.

Sequential experimentation

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Projection Property

A one half fractional factorial design for 23 factorial can be perceived as 22 full factorial design.