indra tugas
TRANSCRIPT
-
7/31/2019 indra tugas
1/38
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).
-
7/31/2019 indra tugas
2/38
-
7/31/2019 indra tugas
3/38
Methods
-
7/31/2019 indra tugas
4/38
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
-
7/31/2019 indra tugas
5/38
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
-
7/31/2019 indra tugas
6/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
TYPE OF 3D RESPONSESURFACES
Sample Maximum or Minimum
Stationary Ridge
-
7/31/2019 indra tugas
7/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
TYPE OF 3D RESPONSESURFACES
Rising Ridge
Saddle or Minimax
-
7/31/2019 indra tugas
8/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
TYPE OF CONTOUR RESPONSESURFACES
Sample Maximum or Minimum:
Stationary Ridge
-
7/31/2019 indra tugas
9/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
TYPE OF CONTOUR RESPONSESURFACE
Rising Ridge:
Saddle or Minimax:
-
7/31/2019 indra tugas
10/38
Preparation of beads
-
7/31/2019 indra tugas
11/38
Encapsulation efficiency
-
7/31/2019 indra tugas
12/38
Particle size
-
7/31/2019 indra tugas
13/38
-
7/31/2019 indra tugas
14/38
Statistical analysis
-
7/31/2019 indra tugas
15/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
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
-
7/31/2019 indra tugas
16/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
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
-
7/31/2019 indra tugas
17/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
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.
-
7/31/2019 indra tugas
18/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
GRAPHICAL EXAMPLE OF LACKOF FIT IN ONE FACTOR
-
7/31/2019 indra tugas
19/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
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
-
7/31/2019 indra tugas
20/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
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
-
7/31/2019 indra tugas
21/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
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
-
7/31/2019 indra tugas
22/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
TYPES OF RSM DESIGN
Three Level Factorial Experiments
Central Composite Designs (CCD)
Box Behnken Designs
-
7/31/2019 indra tugas
23/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
CENTRAL COMPOSITE DESIGNS
2 Factor Central Composite Design
=
Factorial + Star points = CCD
-
7/31/2019 indra tugas
24/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
3 FACTOR CENTRAL COMPOSITEDESIGNS
+Factorial + Star points
=CCD
-
7/31/2019 indra tugas
25/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
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
-
7/31/2019 indra tugas
26/38
-
7/31/2019 indra tugas
27/38
-
7/31/2019 indra tugas
28/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
VALUES OF
-
7/31/2019 indra tugas
29/38
Monday, Aug 13, 2007Dr. Gary Blau, Sean Han
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.
-
7/31/2019 indra tugas
30/38
Result
-
7/31/2019 indra tugas
31/38
In vitro drug release
-
7/31/2019 indra tugas
32/38
Calculate LOF
-
7/31/2019 indra tugas
33/38
-
7/31/2019 indra tugas
34/38
Effect of formulation variable on particlesize
-
7/31/2019 indra tugas
35/38
Effect of formulation on encapsulationefficiency
-
7/31/2019 indra tugas
36/38
-
7/31/2019 indra tugas
37/38
Conclusion
-
7/31/2019 indra tugas
38/38
Terima kasih
Eka Indra Setyawan, Nurniswati, Siti Aisiyah,
Mutmainah
Monda A g 13 2007Dr Gar Bla Sean Han