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Dr. Gary Blau, Sean Han Monday, Aug 13, 2007

Statistical Design ofExperiments

Evaluation of Chitosan Alginate Beads Using ExperimentalDesign: Formulation and In Vitro Characterization

RESPONSE SURFACEMETHODOLOGY;CCD

Eka Indra Setyawan, Nurniswati, Siti Aisiyah, Mutmainah, (UGM,2012).


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Methods


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Introduction

RSM is a collection of mathematicaland statistical techniques that areuseful for modeling and analysis in

applications where a response ofinterest is influenced by severalvariables and the objective is tooptimize the response.

Optimize maximize, minimize, orgetting to a target.

DOE CourseL.M.Lyle


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Monday, Aug 13, 2007Dr. Gary Blau, Sean Han

RESPONSE SURFACE MODEL

Models are simple polynomials

Include terms for interaction and

curvature

Coefficients are usually established byregression analysis with a computer

program

Insignificant terms are discarded


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TYPE OF 3D RESPONSESURFACES

Sample Maximum or Minimum

Stationary Ridge


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TYPE OF 3D RESPONSESURFACES

Rising Ridge

Saddle or Minimax


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TYPE OF CONTOUR RESPONSESURFACES

Sample Maximum or Minimum:

Stationary Ridge


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TYPE OF CONTOUR RESPONSESURFACE

Rising Ridge:

Saddle or Minimax:


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Preparation of beads


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Encapsulation efficiency


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Particle size


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Statistical analysis


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RESPONSE SURFACE MODELFOR TWO FACTORS

Response Surface Model for twofactors X1 and X2 and measuredresponse Y(Regardless of number oflevels):

Y = 0 constant

+ 1X1+ 2X2 main effects

+ 3X12

+ 4X22

curvature+ 5X1X2 interaction

+ error


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LACK OF FIT

Before deciding whether to build aresponse surface model, it is important toassess the adequacy of a linear model:

The lack of fit method presented below isgeneral and can be considered for anymodel:

Y = f(,Xi) + ,where f(,Xi) is an arbitrary function of thefactors and the statistical parameters.

N

0

i=1 1 1

Y= +

N N

i i ij i j

i j

X X X


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COMPONENTS OF ERROR

The error term in the model is comprised oftwo parts:1. modeling error, (lack of fit, LOF)

2. experimental error, (pure error, PE), which can

be calculated from replicate points

The lack of fit test helps us determine if themodeling error is significant different than

the pure error.

In the method compare LOF and PE by usingF ratios calculated from sum of squares.


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GRAPHICAL EXAMPLE OF LACKOF FIT IN ONE FACTOR


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CALCULATING THE F RATIO FORLACK OF FIT

The F ratio for the test is the ratio between theestimate of error due to lack of fit (LOF) and theestimate of error due to pure error (PE). Theestimates are obtained from the two componentswhich make up the total sum of squares for error

(SSE):

SSE = SSPE + SSLOF

where SSE = Total sum of squares for erroror Residual sum of squares

SSPE = Sum of squares due to pure error

SSLOF = Sum of squares due to lack to fit


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ESTIMATING THE PURE ERROR

Suppose we have n repeat points at someXj, then

where yi s arethe n different measuredvalue at Xj

Then the estimate of pure error is

MSPE = SSPE / ( n -2)

2

1

( )N

i

i

SSPE y y


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ESTIMATING THE ERROR DUE TOLOF

If there are m points available (m>>n),with grand mean ,

SSLOF = SSE SSPE

MSLOF = SSLOF / (m-n)

Fobs= MSLOF / MSPE with m-n and n-2

degree of freedom respectivelyIf Fobs >Fcal(DFLOF,DFPE,) (from tables),then there is a lack of fit.

Y

2 2

1 1

( ) ( )M N

k i

k i

SSLOF y y y y


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TYPES OF RSM DESIGN

Three Level Factorial Experiments

Central Composite Designs (CCD)

Box Behnken Designs


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CENTRAL COMPOSITE DESIGNS

2 Factor Central Composite Design

=

Factorial + Star points = CCD


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3 FACTOR CENTRAL COMPOSITEDESIGNS

+Factorial + Star points

=CCD


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CENTRAL COMPOSITE DESIGN

In a central composite design, each factorhas 5 levels

1. extreme high (star point)2. high3. center4. low5. extreme low (star point)

The hidden factorial or fractional factorial

experiment should be run first and analyzed

Depending on the results of a LOF test, thestar points should be run next


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VALUES OF


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PROCESS OPTIMIZATION

Response Surface Methodology (RSM)allowsthe researcher to approximate the behavior of aprocess in the vicinity of the optimum.

The challenge is to find the region within therange of the factors for which this RSM modelis a good approximation and then locate theoptimum.

A sequential approach of experimentationfollowed by analysis can be used to find theregion of interest.


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Result


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In vitro drug release


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Calculate LOF


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Effect of formulation variable on particlesize


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Effect of formulation on encapsulationefficiency


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Conclusion


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Terima kasih

Eka Indra Setyawan, Nurniswati, Siti Aisiyah,

Mutmainah

Monda A g 13 2007Dr Gar Bla Sean Han

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