Design Space by Design of Experiments

Abstract

The quality of methods and products are usually influenced by several input factors. Research has recently focused on understanding the effects of multidimensional and interconnected input factors on the results of pharmaceutical products and analytical methods using Design of Experiment (DoE). Furthermore, it examines how DOE may be implemented, both for students and teachers, as well as highlighting historical perspectives on DOE. A good experimental design can help you make the most use of the available resources and make the analysis of the results easier. Collaborations between researchers and practitioners that are pushing the boundaries of experimental design are examined. It provides an overview of the principles and applications of the most common screening and response surface design, as well as creating mixtures designs.

Full text

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*Corresponding author: E-mail: ashwin.kuchekar@mitwpu.edu.in;
Journal of Pharmaceutical Research International
33(44A): 7-18, 2021; Article no.JPRI.73591
ISSN: 2456-9119
(Past name: British Journal of Pharmaceutical Research, Past ISSN: 2231-2919,
NLM ID: 101631759)
Design Space by Design of Experiments
Sushant Dangat1, Deep Patel1 and Ashwin Kuchekar1*
1School of Pharmacy, Dr. Vishwanath Karad MIT World Peace University, Paud Road, Kothrud,
Pune 411038, India.
Authors’ contributions
This work was carried out in collaboration among all authors. All authors read and approved the final
manuscript.
Article Information
DOI: 10.9734/JPRI/2021/v33i44A32584
Editor(s):
(1) Dr. Jongwha Chang, University of Texas, College of Pharmacy, USA.
Reviewers:
(1) Sumathi, Emory University, USA.
(2) Princy Agarwal, U. S. Ostwal Institute of Pharmacy, India.
Complete Peer review History: https://www.sdiarticle4.com/review-history/73591
Received 30 June 2021
Accepted 10 September 2021
Published 16 September 2021
ABSTRACT
The quality of methods and products are usually influenced by several input factors. Research has
recently focused on understanding the effects of multidimensional and interconnected input
factors on the results of pharmaceutical products and analytical methods using
Design of Experiment (DoE). Furthermore, it examines how DOE may be implemented, both for
students and teachers, as well as highlighting historical perspectives on DOE. A good experimental
design can help you make the most use of the available resources and make the analysis of the
results easier. Collaborations between researchers and practitioners that are pushing the
boundaries of experimental design are examined. It provides an overview of the principles and
applications of the most common screening and response surface design, as well as creating
mixtures designs.
Keywords: Design of experiments; design space; screening designs; factorial designs; response
surface plots.
Review Article

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1. INTRODUCTION
Experimental design is not a new concept. In the
1920s, Sir Ronald Fisher, a legendary
statistician, laid the foundation for modern
statistical research with his contributions to
statistics, which have been hailed as "a genius."
Research conducted has maintained a proactive
stance, which is at the core of the current
regulatory system that controls the development
of pharmaceutical products [1,2,3]. Walter A.
Shewhart, William E. Deming, and Joseph M.
Juran extended this work and advocated a
process-based culture for incorporating quality
into products. A five-step process called "Quality
by Design'' was coined by Juran to emphasize
the need to incorporate Quality into goods and
services; this process involves knowing the
customer, analyzing his needs, translating them
into product features, developing it, and
introducing them into operations. W.E. Deming
presented his systematic approach to wisdom,
using system thinking, understanding variation,
theory of knowledge, and psychology, about half
a century before Juran. According to him, quality
assurance should focus more on the process
than the results since "if you can't describe the
process, you're not doing it right" and "quality is
already in the product [4]." Control charts
featuring statistical process control were featured
in Schewhart's work on quality improvement.
Since the pharmaceutical industry relies heavily
on quality and process, it is likely the first sector
to adopt these concepts. Thus, regulatory bodies
asserted that quality cannot be built into products
(that is, made into it by design) early in the
millennium [5]. A Design of Experiments (DoE) is
used in research and industry contexts to
implement Quality by Design (QBD). It is
characterized as the primary system of
pharmaceutical development because, as a
legacy of Fisher's, it demands the application of
statistical thinking at the outset. Develop and
build quality levels in pharmaceutical products
has become increasingly popular. The
manufacturing process of pharmaceutical
products is the major source of quality problems
according to Juran. Studies and tests cannot
validate the safety and efficacy of a poorly
designed pharmaceutical product [6,7].
Consequently, QbD assumes that more analyses
will not improve quality. Another way to put it is
that the product's quality must be outstanding to
be built in. This approach to pharmaceutical
development starts with clearly defined goals and
focuses on product and process knowledge. It is
based on strong science and risk management of
high quality. Using QbD for pharmaceutical
production results in knowledge and
understanding. a) Achieving meaningful product
quality criteria b) Stabilizing processes and
reducing variability c) Improving pharmaceutical
development efficiency d) Improving cause-effect
analysis and regulatory flexibility. Worldwide,
most regulatory bodies have endorsed risk-
based approaches and comprehensive quality
assurance in pharmaceutical development.
There have been several publications discussing
how the QbD methods were used in the
development of analytical procedures. By
utilizing analytical quality management, robust
and cost-effective analytical procedures are
developed and refined. QbD implementation that
uses analytical methods provides more accurate
results while also reducing the probability of
failure. For centuries, pharmaceutical firms have
focused on enhancing one factor at a time
(OFAT). All variables are unchanged, apart from
one variable that is altered in a reasonable range
(or level). The OFAT method does not recognize
factor interactions, which could lead to
insufficient development and optimization. There
is a possibility that if you design experiments
properly, you can achieve superior results within
a few tests. DoE's collection of statistical
techniques includes screening and optimization
designs. In pharmaceutical and analytical QbD, a
DoE is the most important component [8,9]. As a
result, the current study discusses theoretical
and practical issues for using DoE in
pharmaceutical and analytical QbD.
2. RESEARCH
Among several publications, including more than
500 in 2005, as summarized by Singh et al., the
Marlow and Shangraw study is regarded as the
first publication on DoE application to the design
of pharmaceutical dosage forms. There are
currently 5200 results on Scopus for the
keywords "Design of Experiments" and
"pharmaceutical," covering the period from 1978-
2009. The adoption of these strategies is
becoming more common in books and articles
about statistics and quality, but the industry has
not made use of them as frequently as it should.
In 2006, we also surveyed manufacturers in the
Basque Country. Business experiments are used
by 94 percent of businesses, with the majority
following OFAT tactics, and only 20 percent
applying a predetermined statistical methodology
[10]. A methodology is also necessary, with 76
percent of respondents agreeing that the lack of
a defined approach is the most significant

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obstacle to DoE deployment. With the advent of
the International Council Harmonization (ICH) Q8
guideline, which provided a conducive
environment for the use of dose-equivalent
engineering, there has been significant progress
in research and industrial applications related to
this technology. Additionally, user-friendly
software has been available to ensure easy
design composition and analysis [11,12].
2.1 Definitions and Terminologies
Quality by Design (QbD) is defined as a
systematic approach to development that begins
with predefined objectives and emphasizes
product and process understanding and process
control, based on sound science and quality risk
management. It is a method that structures and
organizes information about the relationship
between process factors and output factors. Also
called "Design of Experiments" (DoE).
Essentially, it is the process of establishing how
inputs influence outputs that develops a process
knowledge.
Treatment - Various treatment combinations.
Treatment levels - Intensity of treatment during
the experiments
Treatment factors (variables) - A controlled
condition in an experiment.
Experimental unit - The subject upon whom
treatment will be applied and from which a
response will be measured. Also referred to as a
measurement of responses.
Responses - Results obtained after treatments
are applied to experimental units
Experimental design - Treatment level
assignment.
Analysis of variance (ANOVA) - Method for
identifying the causes of variability in responses.
Replication - Under identical experimental
conditions, observing the responses of multiple
experimental units.
Randomization - Choosing experimental units
not systematically.
Confounding - An experiment in which the effect
of one factor or treatment cannot be
distinguished from the effect of another factor or
treatment
Independent variables: Directly controlled by
formulation scientists
Dependent variables: Result variables
Factors: Qualitative and quantitative factors.
Level: Value assigned to a factor
Responses surface plot: A plot of the
relationship between the independent factor and
the dependent factor in a 3-D
Interaction: It provides the net effect of two or
more variables without requiring additivity of their
effects
Effect: Amount of the change
Contour plot: An outline of one independent
variable plotted against another while keeping
the response constant
Contour lines: calculated contour lines over a
counterplot
Orthogonality: When no interaction occurs due
to the main factor of interest
Resolution: Measuring confounding
3. DESIGN OF EXPERIMENTS: STEPS TO
TAKE
The design of experiments must follow the
following steps to produce good findings.
i. Plan how to achieve your goal
ii. Determine the variables in the process
iii. Consider a design that allows for
experimentation
iv. Work on a design
v. Make sure the experimental assumptions
match the data
vi. The findings should be examined and
analyzed.
4. CONDUCTING EXPERIMENTS
ACCORDING TO A METHOD
4.1 Levels and Selections of Variables
A process variable includes both inputs and
outputs, such as factors and responses. This
type of experimental design is very popular since
it provides ample information for screening

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designs, is easy and cheap, and provides the
information needed to proceed to multilayer
response surface studies in the future as
needed. The choice here is based on the DoE's
goal, and it should ensure that the entire design
serves its purpose. Therefore, the type and level
of numeric and categorical factors are suitable
(i.e. the values within the design) [13,14,15]. In a
quantitative study, the independent variables
(factors) influence the response variable. It is
possible to identify components that may affect a
response variable using a fishbone diagram.
4.2 Design of Experimental Studies
When selecting an experimental design, consider
various aspects, such as the goals, the quantities
of components and interactions to be
investigated, the statistical validity, as well as the
effectiveness. To better understand experimental
design, two categories are available: a)
Designing for screening; b) Designing for
optimization. The type of experiment to be
conducted depends on two factors: what the
experiment's goals are and how many variables
are being examined. There are several types of
designs to choose from, including factorial, mixed
and process-based designs. All replication,
randomization, and blocking decisions should be
considered. The factor-response function can be
optimized, and the number of test samples can
be determined after a screening design identifies
significant factors [16].
5. HOW CAN EXPERIMENT DESIGN
BENEFIT YOU?
5.1 Treatment Comparison
This involves contrasting different levels of a
single element. Introducing statistics classes
typically explain a range of different statistical
studies applicable to this instance.
5.2 Variable Screening
As a result, fewer variables are used in an
experiment. Whenever there are too many
factors chosen to consider (more than 8) and
they cannot be reduced based on current
process information. Utilizing an innovative
design taking advantage of fewer runs, it
identifies as few variables as possible worth
investigating.
5.3 Variable Characterization
To quantify each variable's impact, this step must
be carried out. There are usually fewer variables
to consider when using this type of analysis.
Simple orthogonal designs are often chosen
because they facilitate the development of a risky
prediction model.
5.4 System Optimization
A process "ideal" requires determining how
processes should be run. Alternatively, the goal
is to determine the levels of each aspect that
allow the process to produce the best results. In
cases when the process is understood
sufficiently and the factors affecting its outcome
are minimal, the procedure is frequently carried
out. These cases, which allow for the estimation
of quadratic terms of second-order, are common.
Usually, non-linear zones exist near an optimum,
so this improves forecast accuracy.
5.5 System Robustness
By doing so, you need to determine what level of
the fundamental factors reduces the
unpredictability principally caused by the noise.
As a result, it's only employed in situations with
an exceptional level of crowd noise. On the other
hand, it necessitates special protocols known as
Robust Parameter Designs (RPD). By using this
interaction between the main (control) and
secondary (noise) components, these schemes
employ the advantages of dual-component
modeling [17].
6. CONCEPTS
To increase the efficacy of experiments in
industrial trials, three principles of experimental
design are employed: randomization, replication,
and blocking.
6.1 Randomization
In randomized experiments, noise factors
(unwanted variations) like temperature
fluctuations or fluctuations in power supply have
an equal chance of affecting all levels of a
parameter. All experimental materials are
allocated at random, as well as the order in
which they are conducted. This is critical for the
following three reasons:
a. The assumption that observations (or
errors) are independent random variables
is usually validated by randomization.
b. It makes it possible to "average out" any
additional factors; and

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c. There may be a learning process involved
or it may be important to have the
experiments conducted in the correct order
where the operation is repetitive.
Systematic bias can be eliminated with
randomization.
However, Randomization cannot eliminate the
variability resulting from uncontrollable variables,
although it can help to "average out" their
impacts. By blocking, we reduce or eliminate
'nuisance' variability, such as batch variances in
raw materials, that may influence the response to
an experiment but are of no direct significance. In
this way, the experimental error is smaller, and
the variability caused by these factors is
separated from the experimental error, allowing
for more precise conclusions.
6.2 Replication
To estimate experimental errors and main and
interaction effects more precisely, it includes
repeating an experiment, all, or part of it, in
random order. Rather than performing an
experiment once and getting several
measurements, replication involves repeating it
under the same conditions. A probability density
function can be utilized to explain the differences
between two sample sizes, which may be used
as a measure of statistical significance. Because
the variance of the sample means is less than
that of the individual observations, replication
allows the researcher to acquire a more precise
estimate of the influence of a factor in the
experiment. Repetition of measurements
however leads to an increase in variability, which
is a consequence of the inherent variability of the
measuring system or gauge [18].
6.3 Blocking
To spread out the effect of changes in blocking
factors, such as batch size, machine type, and
time of day, it is the practice of grouping similar
testing runs into blocks (or groups). All
experiments should be managed to avoid
confounding (confusions over which changes in
the output are a result of changes in the block or
factor levels).
7. DESIGN OF EXPERIMENTS
Historically, DoE has been an instrument that
has contributed to improving product quality and
reliability. Different industries are increasingly
using DoE for their decisions, whether for new
products or process improvements.
Administration, marketing, hospitals,
pharmaceuticals, the food industry, energy and
architecture, and chromatography, among other
applications, are among its uses. Models both
physically and computer-based can be simulated
using DoE. An experiment's design, analysis,
and interpretation are part of a study's DoE. This
type of applied statistics is often used to examine
how changing the input variables (X’s) affects
measuring the response variable (Y) in a system,
process, or product. Using the DoE technique,
variables are initially screened to determine
those that have significant impacts on results
(excipient kind, proportion, disintegration time
(DT), etc.) [19]. Optimizing the procedures
involves determining which are the best settings
for each of the essential variables [20]. This
research involves investigating how changes in
mixture composition affect the mixture's
attributes using mixture designs. Chemical,
physical, and manufacturing stability are
fundamental to product development and
manufacturing. To ensure product safety and
efficacy, different quality criteria must be fulfilled
[21]. To ensure a targeted formulation effort, a
target product profile (TPP) must be identified. In
TPP (appearance), one frequently finds
information about the formulation, methods of
administration, maximum and minimum doses,
and characteristics of pharmaceutical elegance.
Formulation scientists are assisted by the TPP in
developing formulation strategies as well as
directed and efficient efforts. Developing a
formulation requires many investigations after the
TPP is clearly defined. DoE can be very useful to
formulation scientists during all phases of the
formulation process since it helps them make
informed decisions. There are many important
steps in this process, including product
optimization, excipient compatibility, formulation
and scale-up, and process characterization. A
DoE may be generated and analyzed rapidly
using appropriate statistical software. Statistical
packages for this purpose can be found as both
freeware and commercial software. Minitab,
Statistica, Statistical Package for the Social
Sciences (SPSS), Statistical Analysis
System(SAS), Design-Expert, STATGRAPHICS,
Prisma, and other well-known commercial
packages are examples [22].
Several commercial software packages offer an
intuitive interface and excellent output visuals,
such as Minitab and STATISTICA. Using the. R
(R is a free software environment for statistical
computing and graphics) platform, Action

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produces graphics using Excel and the R
platform. Furthermore, Microsoft Excel can be
used to quickly perform DoE design and analysis
by utilizing the procedure and formulas provided
in the next paragraph. Knowing how to use
ANOVA and linear regression as statistical
approaches is essential to do any DoE as
mentioned above [23].
7.1 Advantages
Compared with OFAT, DoE exhibit numerous
advantages. A method to design experiments
that maximize process knowledge while
minimizing resource use is the experimental
design strategy. As much as possible, provide
accurate information. Find out how factors
interact. Analyze each factor individually to
determine its relative significance. Predicting how
a process will behave within a design space [24].
OFAT is superior to DoE on several counts.
Utilize the least number of resources possible
with experimental design methodologies. Data
should be provided as accurately and efficiently
as possible. Investigate their interactions. Rank
each variable according to its relative
importance. Within the design space, allow for
the prediction of process behavior. (CPPs)
Critical Process Parameters and (CQAs) Critical
Quality Attributes should be linked in a strong,
casual manner. Pharmaceutical products must
be optimized simultaneously as they include
multiple CQA’s. Improve product or process
resilience, i.e., make it less susceptible to
uncontrollable factors and external events.
Identify outliers inside the established
experimental matrices to ensure their protection
[25].
On the other hand, OFAT methods identify local
sub-optimal zones by modifying one aspect at a
time. It cannot study multiple factors at once or
look at their interconnections, as this antiquated
technique requires a lot of time. QbD applications
cannot use OFAT due to its flaws. A key
advantage of the DoE technique over OFAT
experiments is how it clarifies the interaction
between input elements. Input elements' effects
on output are assessed by plotting interaction
effects.
By using this method, an existing design can be
enhanced while reducing the number of
experimental trials, analyzing, and optimizing the
complex interaction between independent
variables, and reducing the total amount of data.
Therefore, compared to traditional experimental
work, this statistical method is more practical
because it incorporates interactions between
variables and, therefore, displays the cumulative
effects of the variables. In addition, several types
of response surface design, such as the Central
Composite, Box-Behnken, and Hybrid designs
are sometimes useful in practice [10].
8. TYPES OF DoE AND DESIGN SPACE
8.1 Implementing Design Spaces:
Challenges and Barriers
The challenges and obstacles associated with
implementing Design Space include fear of
revenge when expressing all the information and
data collected. In terms of design, the "current
state" of things is well understood by the
industry, which must be associated with higher
quality assurance criteria and stricter risk
management. There is also the possibility of
higher initial development expenses and a longer
development period. Planned experiments are
part of the experimentation strategy. As a result,
the best method is typically used because it
relies on guesswork to select input pieces.
Although this may seem to be an excellent
solution, it has no scientific basis and there is no
way of knowing if it is the best. As another option
for adjusting one variable at a time, the OFAT
method is employed [26,27]. A level can be
quantitative (e.g., temperature or voltage) or
qualitative (e.g., coolant presence) (such as
temperature). When a level changes in a factor, it
generates a change in response. On the other
hand, the OFAT approach can reveal only one
causal effect, and the causal effects of multiple
factors are generally not additive, indicating that
they interact. This is called interaction when one
component's effect on another component's
reaction differs on different levels. A single
element is changed in the OFAT approach
without affecting all the other elements. A
scientific study involves simultaneously varying
multiple variables to detect the main effect and
the interaction effect of the response variable. If
factors have discrete values (levels), then the
number of levels will define the experimental
design. Full factorial experiments involve
experimenting with all scenarios of component
levels available. As opposed to the full factorial
design, fractional factorial experiments only use
a portion of the runs in the design [28,29].
8.1.1 Screening designs
In addition to determining which ingredients to
include in follow-up studies, these designs are

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used to quantify the gradient impact of individual
components.
8.1.1.1 Taguchi designs
For the analysis of parameter space, Taguchi
uses fractional factorial arrays calculated from a
DoE, also known as orthogonal arrays. Since
Taguchi believes it is unnecessary to consider
interactions between two design variables
directly, he invented a method of tabulated
designs that requires fewer experiments than a
full factorial design. It is advantageous to be able
to work in discrete variables. Taguchi ignores
parameter interactions, which is a disadvantage.
Using these pillars, we established a whole
approach that simplifies the implementation of
DoE in enterprises. Our goal is to offer
businesses a straightforward engineering
process that doesn't ignore the issue's
complexity or statistics [30]. It is a great
advantage that today's software is capable of
aiding users in setting up and conducting
investigations [31,32].
8.1.1.2 Plackett Burman design
Regardless of the level of N runs, k=N-1 factors
can be analyzed at each level of N, where N
represents a multiple of four. Screening tests are
typically done with resolution III designs. Due to
the muddled nature of the alias structure, each
significant influence is accompanied by partial
effects of several two-factor interactions [33]. To
determine the effect of both components on
lactase production, Plackett-Burman statistics
are commonly used. The 'n+1' test screens "n"
variables in the two-factorial (i.e., 1 and +1)
design for variables relevant to the production.
Plackett-Burman matrices were used to examine
all 11 characteristics in this study. Using high
(+1) and low (1) measurements of each variable,
the primary effect was determined [34]. Plackett-
Burman configuration is a useful tool for
screening process parameters' effects on yields
when using a response surface methodology.
Using this method in conjunction with an
optimization study can significantly reduce the
number of experiments required in the following
optimization study [35,36].
The QbD approach was used by Kuchekar et al.,
to develop polymeric micelles containing
capecitabine. Plackett Burman screening design
was used to identify the significant formulation
and process variables like HP β-CD,
ultrasonication time, and drug concentration. The
factors were confirmed using the p-value less
than 0.05 to evaluate robustness. The. Finally
based on the findings the design space was
confirmed. The Plackett Burman screening
design was performed using STATGRAPHICS
XVI [33].
8.1.2 Factorial design
With factorial designs, a predetermined matrix of
factors is used to alter process parameters
simultaneously and deliberately. They are
distinguished from mixed designs by their ability
to alter each aspect separately. Several factors
can be used in a factorial experiment. An
experiment with only one component is a simple
comparative experiment. In these cases, we
analyzed the data using a t-test or an ANOVA
[37]. Studies with more components have more
possible combinations as well. A 2-level design
with 8 variables has 256 combinations, which
makes constructing and analyzing them
challenging. An experiment requiring multiple
factors requires a lot of resources, supplies, and
time. A second challenge with multiple factorial
designs is maintaining experimental conditions
across many trials. To avoid the issues
associated with multiple factor factorial designs,
they may be designed as Full Factorial Design 2k
or Fractional Factorial Design 2kp, depending on
the circumstances [38]. This example employs a
full factorial that consists of 2 levels, k factors,
and p fractions. Factorial therapies are based on
a combination of factors.
8.1.3 Full factorial design
They show all possibilities of combining the
levels of each element with those of the others.
Multiplying the number of levels of each factor by
the number of levels of each factor determines
the number of experimental runs. It is especially
valuable to experiment with two levels of
components (2k) as it is extremely efficient. Full
factorial designs with two levels offer the greatest
power for screening experiments since they allow
one to study the principal effects of the input
variables and their interactions on the output
responses [39,40]. There are 2k experiments
needed for full factorial designs with two levels,
where k is the number of factors to be
investigated. In this study, two levels of factoring
are used. An experimental design with two levels
always places all input elements at the same
level.
Kuchekar et al. developed diltiazem
hydrochloride chronotherapeutic tablets using 32

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full factorial designs with dependent variables
selected as t10%, t25%, t75%, and t90% of the
cumulative drug. The concentrations of
independent variables, xanthan gum, and
concentration sodium alginate were varied to
check the impact on the selected responses. The
study concluded that the drug release pattern
changed by the selection of independent
variables. DESIGN EXPERT was used to
perform the 32 full factorial designs [41].
8.1.4 Fractional factorial design
Usually, 12 or 1=4 are the fractional factorial
designs, which are a subset of full factorial
designs. The screening method is frequently
used when there are more than 4 or 5
components. They are unable to decipher major
effects and interactions due to confounding or
aliasing. A design's "resolution" refers to its
ability to assess effects and interactions without
being confounded. Major effects do not alias to
other main effects in Resolution III designs, but
they may alias with two-factor interactions, some
of which may alias to each other. The presence
of two-factor interactions that adversely affect the
answer can be misleading [42]. A major effect in
Resolution IV does not alias into another main
effect or a two-factor interaction, but instead, it
may alias into a three-factor interaction.
Interactions between two factors are also
aliased. Due to their clear principal effects, they
are a good choice for screening. Compared to
full factorial designs, Resolution V (or higher)
designs are less expensive and take up less
space. There is no aliasing of principal effects or
interactions between two factors. To refer to
these latter interactions, you could use the term
"three-factor interactions.". If interactions
between three factors (or higher) are not
significant or unlikely, both main effects can be
estimated. With decreasing design resolution, it
becomes increasingly difficult to understand the
results [43]. For factors with just two levels
apiece, even a full factorial can have a very large
number of runs. To minimize the number
of runs, it is possible to select a fraction of the
whole factorial, such as half or a fourth.
Fractional factorial designs are the same as 2k-p
factorial designs. What they are, however, is the
1/2p fraction of a 2k factorial experiment.
Factorial fractionation can cause confounding.
Therefore, because the resolution measures
how confused the design is, it is a very important
factor. The ease of use and high inductive
power of factorial designs make them useful
[44,45].
8.1.5 Response surface methodology
An empirical model is developed by utilizing
response surface methodology (RSM).
Experiments designed meticulously have the
goal of maximizing an output variable (response)
influenced by numerous independent variables
(input variables) [46]. The experimental analysis
consists of a series of tests, known as Runs, that
are used to test the effects of modifications to
input variables on output responses. Before
moving on to numerical experiment modeling,
RSM was initially designed to model
experimental response [47]. The difference is in
the type of error caused by the response. While
measurement error can produce inaccurate
results in physical experiments, numerical noise
occurs in computational experiments as the
result of inaccuracies in iterative processes,
round-off errors, or discrete representations of
continuous physical phenomena. It is supposed
that RSM generates random errors [48].
8.1.5.1 Centre composite design
Central composite designs (CCDs) are among
the most popular as they require fewer
experiments and use five levels of each input
component compared to complete factorial
designs with three levels. These aspects of the
design are the factorial points of the design, the
axial points of the design, and the center point.
An axial (or star) point is necessary to estimate
second-order effects based on an axiomatic
design (the cube's corners). Response surface
approaches are the most common [49]. Alpha
value 1.0, as measured by a face-centered
central composite design, can alter the number
of levels for each factor in a typical design. There
are only three levels in each aspect of face-
centered design. A quadratic model is estimated
by using this architecture, which does not
depend on missing data [11,50]. CCDs
composed of composite factorial data (CCD)
include point factorial data, axial data, and center
data [51.52].
8.1.5.2 Box Behnken design
As a kind of multilevel fractional factorial design,
Box-Behnken can simulate first and second-
order response surfaces. Three-level full factorial
designs are less efficient than these, especially if
there are many input variables. Design that
utilizes three levels per element and fewer trials
per element than the central composite design,
called Box Behnken Design (BBD) [53,54]. Axial

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15
points and corners of the design space are
eliminated (or extreme factor combinations are
bypassed) to address many of the shortcomings
of central composite designs. In addition, this
design is completely rotatable, so all its
equidistant sites from the design center will
display the same prediction variance. With this
design, fewer experiments are conducted for an
equal number of factors than those with a
composite central design. Due to these factors,
BBD outperforms central composite designs [55].
It is a second-order, incomplete three-part
factorial, rotatable, and not like conventional
fractions. BBD is a result of combining blocks
with factorials. In q factor block designs of size
two, find an incomplete block design for q
treatments [56,57,58,59].
Pawar et al. [60] studied the evaluation of Gellan
Gum, sodium bicarbonate, and calcium chloride
concentration, three independent variables, using
a Box Behnken factorial design to determine the
floating lag time and t50 (time required for 50%
drug release). The BBD was performed using
SYSTAT 13 and was subjected to multiple
regression analysis.
8.1.6 Mixture designs
8.1.6.1 Simplex lattice
One of the widely used designs. In this design,
factors with the same ranges are considered. To
generate the design, it imposes an equal
distance grid over the design area. To detect its
absence, this design needs to be improved.
8.1.6.2 Simplex centroid
In addition to a simplex-lattice design, a simplex-
centroid design may be used. It is applicable if all
components have the same range of values
(between 0 and 1) and no constraints limit the
design area. Every run has a center point
containing equal amounts of all ingredients
[61,62].
9. CONCLUSION
Finally, statistical thinking and knowledge
management are useful tools in pharmaceutical
development because they support operational
excellence within the QbD framework. It is
projected that DoE's use trend will slow down in
the short term for existing scientific domains, but
it will expand very quickly to other areas of
science. Factorial trials help develop or enhance
systems, processes, and products by making
decisions that are informed and accurate. Design
an experiment, conduct it, collect the data, and
analyze the results. It has become more popular
in recent years to optimize formulations. The
optimization would become a much more popular
development tool. In all phases of product
development, from pre-formulation through
clinical trials and beyond, DoE is a significant tool
for formulation scientists. A quality breakthrough
requires persistence, patience, perseverance,
and a thirst for knowledge in computer and
statistical fields. Optimizing products reduce the
number of trials, reducing the cost and time
spent on product development.
CONSENT
It is not applicable.
ETHICAL APPROVAL
It is not applicable.
COMPETING INTERESTS
Authors have declared that no competing
interests exist.
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