The document discusses the steps for conducting a response surface methodology (RSM) experiment using central composite design (CCD). It involves determining independent and dependent variables, selecting an appropriate CCD, conducting the experiment runs according to the design, analyzing the data using statistical methods to develop a mathematical model and check its adequacy, and using the model to optimize responses. Key aspects of RSM and CCD covered include developing the design, analyzing results through ANOVA and regression, and checking model validity.
Approaches to Experimentation
What is Design of Experiments
Definition of DOE
Why DOE
History of DOE
Basic DOE Example
Factors, Levels, Responses
General Model of Process or System
Interaction, Randomization, Blocking, Replication
Experiment Design Process
Types of DOE
One factorial
Two factorial
Fractional factorial
Screening experiments
Calculation of Alias
DOE Selection Guide
Introduction to Design of Experiments by Teck Nam Ang (University of Malaya)Teck Nam Ang
This set of slides explains in a simple manner the purpose of experiment, various strategies of experiment, how to plan and design experiment, and the handling of experimental data.
Approaches to Experimentation
What is Design of Experiments
Definition of DOE
Why DOE
History of DOE
Basic DOE Example
Factors, Levels, Responses
General Model of Process or System
Interaction, Randomization, Blocking, Replication
Experiment Design Process
Types of DOE
One factorial
Two factorial
Fractional factorial
Screening experiments
Calculation of Alias
DOE Selection Guide
Introduction to Design of Experiments by Teck Nam Ang (University of Malaya)Teck Nam Ang
This set of slides explains in a simple manner the purpose of experiment, various strategies of experiment, how to plan and design experiment, and the handling of experimental data.
Experiments
A Quick History of Design of Experiments
Why We Use Experimental Designs
What is Design of Experiment
How Design of Experiment contributes
Terminology
Analysis Of Variation (ANOVA)
Basic Principle of Design of Experiments
Some Experimental Designs
Experimental design is a way to carefully plan experiments in advance so that results are both objective and valid. Ideally, an experimental design should:
• Describe how participants are allocated to experimental groups. A common method is completely randomized design, where participants are assigned to groups at random. A second method is randomized block design, where participants are divided into homogeneous blocks (for example, age groups) before being randomly assigned to groups.
• Minimize or eliminate confounding variables, which can offer alternative explanations for the experimental results.
• Allows making inferences about the relationship between independent variables and dependent variables.
• Reduce variability, to make it easier to find differences in treatment outcomes.
Types of Experimental Design
1. Between Subjects Design.
2. Completely Randomized Design.
3. Factorial Design.
4. Matched-Pairs Design.
5. Observational Study
• Longitudinal Research
• Cross Sectional Research
6. Pretest-Posttest Design.
7. Quasi-Experimental Design.
8. Randomized Block Design.
9. Randomized Controlled Trial
10. Within subjects Design.
DESIGN OF EXPERIMENTS (DOE)
DOE is invented by Sir Ronald Fisher in 1920’s and 1930’s.
The following designs of experiments will be usually followed:
Completely randomised design(CRD)
Randomised complete block design(RCBD)
Latin square design(LSD)
Factorial design or experiment
Confounding
Split and strip plot design
FACTORIAL DESIGN
When a several factors are investigated simultaneously in a single experiment such experiments are known as factorial experiments. Though it is not an experimental design, indeed any of the designs may be used for factorial experiments.
For example, the yield of a product depends on the particular type of synthetic substance used and also on the type of chemical used.
ADVANTAGES OF FACTORIAL DESIGN.
Factorial experiments are advantageous to study the combined effect of two or more factors simultaneously and analyze their interrelationships. Such factorial experiments are economic in nature and provide a lot of relevant information about the phenomenon under study. It also increases the efficiency of the experiment.
It is an advantageous because a wide range of factor combination are used. This will give us an idea to predict about what will happen when two or more factors are used in combination.
DISADVANTAGES
It is disadvantageous because the execution of the experiment and the statistical analysis becomes more complex when several treatments combinations or factors are involved simultaneously.
It is also disadvantageous in cases where may not be interested in certain treatment combinations but we are forced to include them in the experiment. This will lead to wastage of time and also the experimental material.
2(square) FACTORIAL EXPERIMENT
A special set of factorial experiment consist of experiments in which all factors have 2 levels such experiments are referred to generally as 2n factorials.
If there are four factors each at two levels the experiment is known as 2x2x2x2 or 24 factorial experiment. On the other hand if there are 2 factors each with 3 levels the experiment is known as 3x3 or 32 factorial experiment. In general if there are n factors each with p levels then it is known as pn factorial experiment.
The calculation of the sum of squares is as follows:
Correction factor (CF) = (𝐺𝑇)2/𝑛
GT = grand total
n = total no of observations
Total sum of squares = ∑▒〖𝑥2−𝐶𝐹〗
Replication sum of squares (RSS) = ((𝑅1)2+(𝑅2)2+…+(𝑅𝑛)2)/𝑛 - CF
Or
1/𝑛 ∑▒𝑅2−𝐶𝐹
2(Cube) FACTORIAL DESIGN
In this type of design, one independent variable has 2 levels, and the other independent variable has 3 levels.
Estimating the effect:
In a factorial design the main effect of an independent variable is its overall effect averaged across all other independent variable.
Effect of a factor A is the average of the runs where A is at the high level minus the average of the runs
LATIN SQUARE DESIGN RESEARCH DESIGN: DESCRIPTION OF LATIN SQUARE DESIGN, PROCEDURE, TABLES, LINEAR MODEL, ANALYSIS, ADVANTAGES AND DISADVANTAGES OF LATIN SQUARE DESIGN
Experiments
A Quick History of Design of Experiments
Why We Use Experimental Designs
What is Design of Experiment
How Design of Experiment contributes
Terminology
Analysis Of Variation (ANOVA)
Basic Principle of Design of Experiments
Some Experimental Designs
Experimental design is a way to carefully plan experiments in advance so that results are both objective and valid. Ideally, an experimental design should:
• Describe how participants are allocated to experimental groups. A common method is completely randomized design, where participants are assigned to groups at random. A second method is randomized block design, where participants are divided into homogeneous blocks (for example, age groups) before being randomly assigned to groups.
• Minimize or eliminate confounding variables, which can offer alternative explanations for the experimental results.
• Allows making inferences about the relationship between independent variables and dependent variables.
• Reduce variability, to make it easier to find differences in treatment outcomes.
Types of Experimental Design
1. Between Subjects Design.
2. Completely Randomized Design.
3. Factorial Design.
4. Matched-Pairs Design.
5. Observational Study
• Longitudinal Research
• Cross Sectional Research
6. Pretest-Posttest Design.
7. Quasi-Experimental Design.
8. Randomized Block Design.
9. Randomized Controlled Trial
10. Within subjects Design.
DESIGN OF EXPERIMENTS (DOE)
DOE is invented by Sir Ronald Fisher in 1920’s and 1930’s.
The following designs of experiments will be usually followed:
Completely randomised design(CRD)
Randomised complete block design(RCBD)
Latin square design(LSD)
Factorial design or experiment
Confounding
Split and strip plot design
FACTORIAL DESIGN
When a several factors are investigated simultaneously in a single experiment such experiments are known as factorial experiments. Though it is not an experimental design, indeed any of the designs may be used for factorial experiments.
For example, the yield of a product depends on the particular type of synthetic substance used and also on the type of chemical used.
ADVANTAGES OF FACTORIAL DESIGN.
Factorial experiments are advantageous to study the combined effect of two or more factors simultaneously and analyze their interrelationships. Such factorial experiments are economic in nature and provide a lot of relevant information about the phenomenon under study. It also increases the efficiency of the experiment.
It is an advantageous because a wide range of factor combination are used. This will give us an idea to predict about what will happen when two or more factors are used in combination.
DISADVANTAGES
It is disadvantageous because the execution of the experiment and the statistical analysis becomes more complex when several treatments combinations or factors are involved simultaneously.
It is also disadvantageous in cases where may not be interested in certain treatment combinations but we are forced to include them in the experiment. This will lead to wastage of time and also the experimental material.
2(square) FACTORIAL EXPERIMENT
A special set of factorial experiment consist of experiments in which all factors have 2 levels such experiments are referred to generally as 2n factorials.
If there are four factors each at two levels the experiment is known as 2x2x2x2 or 24 factorial experiment. On the other hand if there are 2 factors each with 3 levels the experiment is known as 3x3 or 32 factorial experiment. In general if there are n factors each with p levels then it is known as pn factorial experiment.
The calculation of the sum of squares is as follows:
Correction factor (CF) = (𝐺𝑇)2/𝑛
GT = grand total
n = total no of observations
Total sum of squares = ∑▒〖𝑥2−𝐶𝐹〗
Replication sum of squares (RSS) = ((𝑅1)2+(𝑅2)2+…+(𝑅𝑛)2)/𝑛 - CF
Or
1/𝑛 ∑▒𝑅2−𝐶𝐹
2(Cube) FACTORIAL DESIGN
In this type of design, one independent variable has 2 levels, and the other independent variable has 3 levels.
Estimating the effect:
In a factorial design the main effect of an independent variable is its overall effect averaged across all other independent variable.
Effect of a factor A is the average of the runs where A is at the high level minus the average of the runs
LATIN SQUARE DESIGN RESEARCH DESIGN: DESCRIPTION OF LATIN SQUARE DESIGN, PROCEDURE, TABLES, LINEAR MODEL, ANALYSIS, ADVANTAGES AND DISADVANTAGES OF LATIN SQUARE DESIGN
S1 - Process product optimization using design experiments and response surfa...CAChemE
An intensive practical course mainly for PhD-students on the use of designs of experiments (DOE) and response surface methodology (RSM) for optimization problems. The course covers relevant background, nomenclature and general theory of DOE and RSM modelling for factorial and optimisation designs in addition to practical exercises in Matlab. Due to time limitations, the course concentrates on linear and quadratic models on the k≤3 design dimension. This course is an ideal starting point for every experimental engineering wanting to work effectively, extract maximal information and predict the future behaviour of their system.
Mikko Mäkelä (DSc, Tech) is a postdoctoral fellow at the Swedish University of Agricultural Sciences in Umeå, Sweden and is currently visiting the Department of Chemical Engineering at the University of Alicante. He is working in close cooperation with Paul Geladi, Professor of Chemometrics, and using DOE and RSM for process optimization mainly for the valorization of industrial wastes in laboratory and pilot scales.”
Design Of Experiments (DOE) Applied To Pharmaceutical and Analytical QbD.SALMA RASHID SHAIKH
According to ICH Q8 Quality should be built into the product.
Design of Experiments (DoE) generate knowledge about a product or process and established a Mathematical relationship of dependent variables and independent variables.
The most common screening designs, such as two-level full factorial, fractionate factorial, and Plackett- Burman designs.
Optimization designs, such as three-level full factorial, central composite designs (CCD), and Box-Behnken designs.
Analysis of variance (ANOVA) used in multiple regression analysis to evaluate regression significance, residual error, and lack-of-fit adjustment.
Determination coefficients (R2, R2 -adj, and R2 -pred) is also evaluated.
Quality By Design:
QbD is “a systematic approach to pharmaceutical development that begins with predefined objectives and emphasizes product and process understanding and process control, based on sound science and quality risk management”
Goals Of Pharmaceutical QbD:
To achieve meaningful product quality specifications
To increase process capability and reduce product variability
To increase pharmaceutical development and manufacturing efficiencies and
To enhance cause-effect analysis and regulatory flexibility.
In general, a factorial experiment involves several variables.
One variable is the response variable, which is sometimes called the outcome variable or the dependent variable.
The other variables are called factors.
Formulation and development is a process of selection of component and processing.
Now days computer tools used in the formulation and development of pharmaceutical product.
Various technique, such as design of experiment are implemented for optimization of formulation and processing parameter.
Many times finding the correct answer is not simple and straight forward in such cases use of computer tools (optimization procedure) for best compromise is the smarter way to solve problem.
Week 4 Lecture 12 Significance Earlier we discussed co.docxcockekeshia
Week 4 Lecture 12
Significance
Earlier we discussed correlations without going into how we can identify statistically
significant values. Our approach to this uses the t-test. Unfortunately, Excel does not
automatically produce this form of the t-test, but setting it up within an Excel cell is fairly easy.
And, with some slight algebra, we can determine the minimum value that is statistically
significant for any table of correlations all of which have the same number of pairs (for example,
a Correlation table for our data set would use 50 pairs of values, since we have 50 members in
our sample).
The t-test formula for a correlation (r) is t = r * sqrt(n-2)/sqrt(1-r2); the associated degrees
of freedom are n-2 (number of pairs – 2) (Lind, Marchel, & Wathen, 2008). For some this might
look a bit off-putting, but remember that we can translate this into Excel cells and functions and
have Excel do the arithmetic for us.
Excel Example
If we go back to our correlation table for salary, midpoint, Age, Perf Rat, Service, and
Raise, we have:
Using Excel to create the formula and cell numbers for our key values allows us to
quickly create a result. The T.dist.2t gives us a p-value easily.
The formula to use in finding the minimum correlation value that is statistically
significant is r = sqrt(t^2/(t^2 + n-2)). We would find the appropriate t value by using the
t.inv.2T(alpha, df) with alpha = 0.05 and df = n-2 or 48. Plugging these values into the gives us
a t-value of 2.0106 or 2.011(rounded).
Putting 2.011 and 48 (n-2) into our formula gives us a r value of 0.278; therefore, in a
correlation table based on 50 pairs, any correlation greater or equal to 0.278 would be
statistically significant.
Technical Point. If you are interested in how we obtained the formula for determining
the minimum r value, the approach is shown below. If you are not interested in the math, you
can safely skip this paragraph.
t = r* sqrt(n-2)/sqrt(1-r2)
Multiplying gives us t *sqrt (1- r2) = r2* (n-2)
Squaring gives us: t2 * (1- r2) = r2* (n-2)
Multiplying out gives us: t2– t2* r2 = n r2-2* r2
Adding gives us: t2= n* r2-2*r2+ t2 *r2
Factoring gives us t2= r2 *(n -2+ t2)
Dividing gives us t2 / (n -2+ t2) = r2
Taking the square root gives us r = sqrt (t2 / (n -2+ t2)
Effect Size Measures
As we have discussed, there is a difference between statistical and practical
significance. Virtually any statistic can become statistically significant if the sample is large
enough. In practical terms, a correlation of .30 and below is generally considered too weak to be
of any practical significance. Additionally, the effect size measure for Pearson’s correlation is
simply the absolute value of the correlation; the outcome has the same general interpretation as
Cohen’s D for the t-test (0.8 is strong, and 0.2 is quite weak, for example) (Tanner & Youssef-
Morgan, 2013).
Spearman’s Rank Correlation
Another typ.
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Online aptitude test management system project report.pdfKamal Acharya
The purpose of on-line aptitude test system is to take online test in an efficient manner and no time wasting for checking the paper. The main objective of on-line aptitude test system is to efficiently evaluate the candidate thoroughly through a fully automated system that not only saves lot of time but also gives fast results. For students they give papers according to their convenience and time and there is no need of using extra thing like paper, pen etc. This can be used in educational institutions as well as in corporate world. Can be used anywhere any time as it is a web based application (user Location doesn’t matter). No restriction that examiner has to be present when the candidate takes the test.
Every time when lecturers/professors need to conduct examinations they have to sit down think about the questions and then create a whole new set of questions for each and every exam. In some cases the professor may want to give an open book online exam that is the student can take the exam any time anywhere, but the student might have to answer the questions in a limited time period. The professor may want to change the sequence of questions for every student. The problem that a student has is whenever a date for the exam is declared the student has to take it and there is no way he can take it at some other time. This project will create an interface for the examiner to create and store questions in a repository. It will also create an interface for the student to take examinations at his convenience and the questions and/or exams may be timed. Thereby creating an application which can be used by examiners and examinee’s simultaneously.
Examination System is very useful for Teachers/Professors. As in the teaching profession, you are responsible for writing question papers. In the conventional method, you write the question paper on paper, keep question papers separate from answers and all this information you have to keep in a locker to avoid unauthorized access. Using the Examination System you can create a question paper and everything will be written to a single exam file in encrypted format. You can set the General and Administrator password to avoid unauthorized access to your question paper. Every time you start the examination, the program shuffles all the questions and selects them randomly from the database, which reduces the chances of memorizing the questions.
ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
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4. What response variables are to be measured, how they will be
measured, and in what sequence?
Which factor are most important and therefore will be included in the
experiment, and which are least important and can these factor be
omitted? With the important factors, can the desired effects be
detected?
What extraneous or disturbing factors must be controlled or at least
have their effects minimized?
What is the experimental unit, that is to say, what is the piece of
experimental material from which a response value is measured? How
are the experimental units to be replicated, if at all?
The choice of the factors and level determined the type, size and
experimental region. The no. of level at each factor as well as the no. of
replicated experiment units represent the total no. of experiment.
5. Box-Wilson central
composite designed
(CCD)
INDEPENDENT VARIABLE
-how many?
-what are the range? DEPENDENT
VARIABLE/RESPONSE
-conversion, yields, selectivity?
e.g.: full 34 factorial designs (four
factors each at three levels),
eight star point and two center
point
6. Variables are things that we measure, control, or
manipulate in research.
Independent Variables are those that are manipulated.
They are processing conditions that are presumed to
influence the values of the response variable.
Similar words: regressor or explanatory variables, factors.
Dependent Variables are those that are only measured
whose value is assumed to be affected by changing
the levels of the factors, and whose values we are
most interested in optimizing.
Similar words: response variables, outcomes.
7. The most common design (for the 2nd degree
model) is Central Composite Design (CCD)
Central Composite Design consists of:
(a). 2k vertices of a k-dimensional “cube” (2-level full
factorial design) coded as ±1
(b). 2k vertices of a k-dimensional “star” coded as ±
(c). n0≥1 “center” point replicates coded as 0
8. Factors Symbol
Range and Levels
-1 0 +1
Molar ratio methanol: oil X1 20:1 30:1 40:1
Catalyst loading, wt% X2 2 3 4
Reaction Time, min X3 120 180 240
Reaction Temperature X4 90 120 150
16. Select all → right click→
copy with headers
STEP 1
Paste on spreadsheetSTEP 2
17. Right click on the
column→edit
STEP 1
click file→saveSTEP 2
click file→printSTEP 3
18. Run
s
Manipulated Variables Responses
X1 X2 X3
Operating
temperature,T(oC)
Levelb Molar Ratio
(meOH: oil)
Level
b
Reaction
time,t (h)
Levelb Yield, Y1
(%)
1 50 -1 3 -1 2 -1 91.90
2 50 -1 3 -1 4 +1 84.60
3 50 -1 10 +1 2 -1 65.15
4 50 -1 10 +1 4 +1 95.95
5 70 +1 3 -1 2 -1 63.90
6 70 +1 3 -1 4 +1 94.95
7 70 +1 10 +1 2 -1 87.60
•DOE is a collection of encoded settings of the process variables. Each process variable is
called an experimental factor
•Each combination of settings for the process variable is called a run
•A response variable is a measure of process performance.
•Each value of response is called an observation.
19.
20. Remember save the spreadsheet
(note: spreadsheet is an important in statistica)
Open spreadsheet and insert the result STEP 1
25. Analysis of the central composite (response surface) experiment windows opened.
(note: this windows is an important for analysis since it display all information needed.
26. Y = βo + β1X1 + β2X2 + β3X3 + β12X1X2 + β13X1X3 +β23X2X3 +
β11X1
2 + β22X2
2 +β33X3
2
Y : predicted response
o : intercept coefficient (offset)
1 , 2 and 3 : linear terms
11 , 22 and 33 : quadratic terms
12 , 13 and 23 : interaction terms
X1 , X2 and X3 : uncoded independent
variables
The full quadratic models of conversion and ester yield were
established by using the method of least squares:
28. The adequacy of the fitted model is checked by ANOVA
(Analysis of Variance) using Fisher F-test
The fit quality of the model can also be checked from
their Coefficient of Correlation (R) and Coefficient of
Determination (R2)
The significance of the model parameters is assessed by
p-value and t-value.
Coefficient of Determination (R2) reveals a proportion of
total variation of the observed values of activity (Yi)
about the mean explained by the fitted model
R2=SSR/SST
Coefficient of Correlation (R) reveals an acceptability
about the correlation between the experimental and
predicted values from the model.
29. The F-value is a measurement of variance of data about the mean
based on the ratio of mean square (MS) of group variance due to
error.
F-value = MS regression/MSresidual = (SSR/DFregression)/ (SSE/DFresidual)
F table =F(p−1,N−p,α)
p−1 :DFregression
N−p:DFresidual
α-value: level of significant
Null hypothesis: all the regression coefficient is zero.
the calculated F-value should be greater than the tabulated F-
value to reject the null hypothesis,
30. Sources
Sum of
Squares(SS)
Degree of
Freedom(d.f)
Mean Squares
(MS)
F-value F0.05
Regression
(SSR)
2807.32 14 200.52 3.39 >2.74
Residual 649.87 11 59.08
Total (SST) 3457.29 25
Click ANOVA table tabSTEP
R2>0.75
(Haaland, 1989)
SST
Residual
SSR= SST-residual
DF
DFSSR= DFSST-DF residual
32. T-Value:
Measure how large the coefficient is in relationship to its standard
error
T-value = coefficient/ standard error
P-value
is an observed significance level of the hypothesis test or the
probability of observing an F-statistic as large or larger than one we
observed.
The small values of p-value the null hypothesis is not true.
Interpretation?
- If a p-value is ≤ 0.01, then the Ho can be rejected at a 1% significance level
“convincing” evidence that the HA is true.
- If a p-value is 0.01<p-value≤0.05, then the Ho can be rejected at a 5% significance
level “strong” evidence in favor of the HA.
- If a p-value is 0.05<p-value≤0.10, then the Ho can be rejected at a 10% significance
level. it is in a “gray area/moderate”
- If a p-value is >0.10, then the Ho cannot be rejected. “weak” or ”no” evidence in
support of the HA.
46. • Response Surface Methodology is a powerful
method for design of experimentation, analysis of
experimental data, and optimization.
• Advantage:
– design of experiment, statistical analysis, optimization,
and profile of analysis in one step
– Produce empirical mathematical model
• Disadvantage: only single-response optimization
47. Montgomery, D. C. 1997. Design and Analysis of
Experiment. Fifth Edition. Wiley, Inc., New York, USA.
Brown, S. R. and Melemend, L. E. 1990. Experimental
Design and Analysis Quantitative Application in the
Social Science. Sage Publication, California. 74.
Cornell J.A. 1990. How to Apply Response Surface
Methodology. America Society For Quality Control:
Statistic Devision . US.
Haaland, P. D. 1989. Experimental Design in
Biotechnology. Marcel Dekker Inc., New York.