In this ppt the viewer will able to know about designing of experiments. How experimental design helps to improve the quality & purity of the products. In this example, our experimental design is a planned experiment that is used to determine how reactor temperature and residence time affect purity so we can find the optimum operating conditions. Experimental design is needed to rectify the error in materials, methods & machines. Portion explained: 1. Introduction to the problem 2. EXPERIMENTAL DESIGN TERMINOLOGY 3. EXPERIMENTAL DESIGN DATA 4. EFFECTS AND MAIN EFFECTS 5. INTERACTIONS BETWEEN FACTORS 6. ARE THE EFFECTS, MAIN EFFECTS AND INTERACTIONS SIGNIFICANT?

1. Experimental Design Techniques
BY
Dr. Jitendra Patel
Associate Professor
AIPS, Hyderabad, India.

2. Stirred Batch Reactor.

3. INTRODUCTION TO THE PROBLEM
• Suppose your process involves a stirred batch reactor. Your
product is a chemical and the purity of that chemical is
critical to customers. You would like to improve the
chemical's purity.
• There are two process variables that you think impact the
purity: the reactor temperature and the residence time of
the chemical in the reactor. How do you find out the
following?
1. Do the reactor temperature and/or residence time impact
the average purity
2. If so, by how much? For example, if I change the reactor
temperature 5 degrees, what is the impact on the average
purity?
3. Do the reactor temperature and/or residence time impact
the variation in the purity?
4. If so, by how much? For example, if I increase the residence
time in the reactor by 10 minutes, do the purity results
have more variation?

4. • Experimental design techniques can help you
quickly find out the answers to these questions.
• Some people still approach experiments doing
the "one factor at a time" approach.
• If you use this approach, you would change
reactor temperature while holding residence time
constant.
• Once you found the optimal purity, you would
then hold the reactor temperature at that level
and change residence time.
• The one factor approach is not efficient and does
not account for interaction between reactor
temperature and residence time .
• Let’s begin by introducing the terminology
associated with experimental design.

5. EXPERIMENTAL DESIGN TERMINOLOGY
• An experimental design is a planned experiment to determine,
using a minimum number of experimental runs, what factors have a
significant effect on
1. A product response and/or
2. Variability in the product response and
3. How large the effect is in order to find the optimum set of
operating conditions.
• A factor is a variable over which there is direct control. It is the
independent variable in statistical terms. In this example, we have
two factors: the reactor temperature and the residence.
• The level of a factor refers to the value of the factor used in an
experimental run. The levels of residence time are 30 minutes and
90 minutes. The levels of temperature are 50°C and 90°C.
• Qualitative factors are factors whose levels can not be arranged in
magnitude of order. Examples include different shifts or different
operators in a plant. Quantitative factors are factors whose levels
can be arranged in order of magnitude. Reactor temperature and
residence time are examples of quantitative factors.

6. • Fixed factors are factors whose levels in an experiment are set
at particular values. Both factors in our example are fixed.
• There are also random factors. Random factors are factors
whose levels in an experimental run are only randomly
chosen samples from a population of levels that could be
included.
• For example, a raw material may contain an impurity that may
affect your process. Although you do not have direct control
over the impurity, you can randomly select two different
samples of the raw material. The impurity is then a random
factor.
• A response is a variable whose value depends upon the levels
of the factors. It is the dependent variable in statistical terms.
In this example, purity is the response.
• A discrete response is one that does not produce a numerical
value. This type of response produces attributes data: yes/no
or counting. A continuous response does produce a numerical
value. Purity is a continuous response.
•

7. EXPERIMENTAL DESIGN DATA
• Two factors, reactor temperature and residence time, are
thought to impact the product purity obtained in a
chemical reaction. A planned experiment to investigate this
could take the form shown below.
• A treatment or treatment combination is represented by
one cell. For example, in cell 1, the treatment is
temperature = 50°C and residence time = 30 minutes. A
treatment represents the levels of all factors used in a
given experimental run. For this experimental design, there
are four treatments (r0t0, r0t1, r1t0, and r1t1).

8. • Each treatment combination is run three times. This is
called replication of the treatment. In total, we have 12
experimental runs. Suppose we have conducted these
experimental runs in random order. The results are shown below.
The table also shows the average as well as the range (maximum -
minimum) for each treatment combination.

9. • Experimental error is represented by the difference in
experimental runs with the same factor levels.
• For example, the run number 1 was replicated three
times.
• The differences (74, 78, and 73) in the purity for these
two run is caused by experimental error.
• Experimental error is not a very good term for this. It is
actually measuring the process variation.
• This process variation will be used to determine if a
factor has a significant effect on a response.
• If the differences seen in the response variable due to
different levels of the factor can be explained by
normal process variation, we will conclude that the
factor does not affect the response.
• However, if the differences can not be explained by
normal process variation, we will conclude that the
factor does affect the response.

10. EFFECTS AND MAIN EFFECTS
• The concepts of effects, main effects and
interactions are introduced below. The two
factor design above can be drawn as shown
below.

11. • An effect is defined as the average response when a factor is
at its high level minus the average response when a factor is
at its low level with all other factors held constant. There are
four effects that can be determined in this example. The
effect of temperature when residence time is at its low level
(30) can be determined as shown in the figure below.

13. • A main effect is defined as the difference between the results when a
factor is at its high level and when a factor is at its low level. For
example, the main effect of temperature is the average of the results
when temperature is at its high level minus the average of the results
when temperature is at its low level. The figure below uses a plus sign (+)
to indicate the high level of a factor and a minus sign (-) is used to indicate
a low level of a factor. As you can see, the main effect of temperature is
the average of the runs 2 and 4 minus the average of runs 1 and 3.

14. INTERACTIONS BETWEEN FACTORS
• The main effect describes how a factor influences a product
response. This influence, however, sometimes depends on
the levels of the other factors. This is called interaction.
• For example, the effect of temperature on purity may vary
when residence time is at its low level from when residence
time is at its high level.
• There are three possible types of interactions. These are
easy to see if you plot the response variable (Y) versus the
two factors.
• The figure below is an example of no interaction. Factor A is
on the x axis; the response variable on the Y axis. The two
lines represent the results for Y when Factor B is at its high
level (blue) and when Factor B is at its low level (red).
• The two lines are essentially parallel. This means there is no
interaction between the factors.

16. ARE THE EFFECTS, MAIN EFFECTS AND
INTERACTIONS SIGNIFICANT?
• Experimental design techniques are used to determine the main
effects and interactions. We have determined the following so far:
• Main Effect of Temperature = 1.5
• Main Effect of Residence Time = 11.5
• Interaction between Temperature and Residence Time = 10.5
• Are these numbers significant? If a factor does not have an effect on
a product response, one would expect the main effect or
interaction to be zero. Of course, with normal process variation, the
main effect or interaction will not be zero. For a main effect or
interaction to be statistically significant, it must be significantly
different from zero. Next month's newsletter will describe how to
determine if these main effects or interaction are statistically
significant.

17. Conclusion
• In this example, our experimental design is a
planned experiment that is used to determine
how reactor temperature and residence time
affect purity so we can find the optimum
operating conditions. Experimental design is
needed to rectify the error in materials,
methods & machines.

18. Thank You