doe (design of experiment)
DESCRIPTION
a presentation on DOETRANSCRIPT
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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.