Evolutionary Operation

Operational Excellence
Evolutionary Operation
Introduction
3/4/2017 Ronald Morgan Shewchuk 1
• The experimental designs we have explored thus far may be considered
revolutionary in nature.
• We purposely chose high and low levels for the input factors that were expected to
make a large change in the output response variable.
• This allowed us to observe changes in the output variable that were not due to
random noise and which permitted mapping of the total response surface.
• Incurring a “bad” result in the output response variable is not considered Faustian
but rather, a natural part of the discovery process.
• There are situations, however, where a reduction in the response variable,
throughput or quality level cannot be tolerated.
• Process improvements in these situations are best deployed through the technique
of Evolutionary Operation.
• Evolutionary Operation (EVOP) was developed by George Box and first published in
his 1957 article Evolutionary Operation: A Method for Increasing Industrial
Productivity in the Journal of Applied Statistics.

Introduction
• As with many experimental designs, EVOP pre-dates the advent of personal
computers.
• The underlying statistic fundamentals of EVOP have been established for many
years.
• Personal computers, with their associated software programs, simply facilitate the
analysis of the underlying statistics.
• Dr. Box developed a simple worksheet method by which two-level full factorial
experiments with center points are conducted in phases as part of routine
production operations.
• The objective is to nudge the operating parameters along the pathway of steepest
ascent of the response variable without any interruption to the process or any
increase in defective product.
• This nudging process may be visualized as in Figure 9.23 where the boxes
represent individual 22 full factorial experiments.

Figure 9.23 Successive 22 Full Factorial Experiments Conducted in EVOP
A
B
0.80.70.60.50.40.30.20.10.0
1.75
1.50
1.25
1.00
0.75
0.50
>
–
–
–
–
–
< 70
70 75
75 80
80 85
85 90
90 95
95
Yield
Contour Plot of Yield vs A, B
95
90
85
80
75
70

Introduction
• Of course, we do not know the surface topography of the response variable, if we
did it would be elementary to dial-in the optimum factor settings.
• Thus, we set the center point of our first experiment at the current operating
conditions and measure the response variable at the high and low tolerances of
the two input factors.
• We must conduct a sufficient number of replicates to ensure that our conclusions
about the direction of steepest ascent are statistically significant and not the result
of random process noise.
• This is not a problem since replicates result in good production lots which we need
to meet market demand.
• Replication is continued within successive cycles until a new optimum corner point
has been validated.
• This milestone represents the conclusion of the first phase of the EVOP.
• The second phase of the EVOP thus begins with its center point at the optimum
corner point identified in phase one.

Introduction
• The process is continued until the response variable is maximized.
• It is important to recognize that the topography of a response variable is not etched
in stone.
• The response variable surface is influenced by noise factors such as variations in
supplied raw materials, ambient environment, uncontrolled process conditions, etc.
• Consequently, practitioners of EVOP have found it useful to perpetually continue
Evolutionary Operation experiments to account for these noise variables which
move the response variable maxima.
• It is typical for EVOPs to be limited to two factors although the technique can easily
be extrapolated to three or more factors.
• In the latter case, it is best to use a statistical software package to analyze the EVOP
phase results to reduce the chance of transcription errors.
• We will demonstrate the use of Evolutionary Operation to optimize the process of
producing biodiesel in Case Study XVI. The analysis of this case study will be
facilitated by the 22 EVOP Worksheet as shown in Figure 9.24.

Figure 9.24 22 EVOP Worksheet
EVOP 2
2
Worksheet
Process:
+1 d b
Cycle n: 1
Factor B 0 z
Phase:
-1 a c
Response:
f(5,n): - -
-1 0 +1
Factor A
Treatment Combination z a b c d
1. Previous Sum Previous Sum of Std Dev
2. Previous Average Previous Avg Std Dev
3. New observation New Std Dev = Range·f(5,n)
4. Difference (2 - 3) Difference Range
5. New sum (1 + 3) New Sum of Std Dev
6. New average: (5 / n) New Avg Std Dev
Date
Time
Effects: Error Limits: n = cycle number
A = (b + c - a - d)/2 = For Averages and New Effects: 2 s-bar / SQRT(n) =
For Change in Center Effect: 1.78 s-bar / SQRT(n) =
B = (b + d - a - c)/2 =
Statistical Significance:
AB = (a + b - c - d)/2 =
For Averages: Difference (2 - 3) > 2 s-bar / SQRT(n)
Effect of Change in Center*: For New Effects: A, B, AB > 2 s-bar / SQRT(n)
For  (zero & Effect):  (zero & Effect) > 1.78 s-bar / SQRT(n)
(a + b + c + d - 4z)/5 =
 (zero and Max(Effect)) =
Cycle # f(5,n)
Max Point = 1 - -
2 0.30
 (zero and Min(Effect)) = 3 0.35
4 0.37
Min Point = 5 0.38
6 0.39
* If negative, center is near maximum 7 0.40
* If positive, center is near minimum 8 0.41
9 0.41
Manual Entry Field 10 0.42
11 0.42
Calculated Field 12 0.43
Calculation of Averages
Calculation of Std Deviation
Table of f(5,n)

Case Study XVI: Optimization of Biodiesel Production Yield by EVOP
Kuwat Pramana is beaming with pride. His small Indonesian start-up company is successfully producing biodiesel from the
transesterification of palm oil. It has been a long, hard road building the reaction, purification and filling plant followed by
the process equipment commissioning and yield ramp. Over several months, Kuwat and his operators have been able to
sustain production yields of 89%. Kuwat can now begin paying back the loan which he received from the Economic
Development Administration in Jakarta to build his facility.
Indonesia has an abundant supply of crude palm kernel oil, the primary raw material used in the transesterification reaction.
The price of palm oil is driven by demand from the food and cosmetics industries. Kuwat has calculated that he must
operate at yields above 88% to ensure that his operation remains profitable. The higher the yield, the quicker he can repay
his loan and reduce his interest expenses.
The transesterification process consists of reacting the crude palm kernel oil with methanol in the presence of a base
catalyst, sodium hydroxide. Glycerine is produced as a by-product of the reaction. Reactant purity, mixing time, reaction
temperature, catalyst type, catalyst concentration, and mass ratio of methanol to oil have been identified as key factors
affecting biodiesel yield. Kuwat has decided to hold all factors constant and use the technique of Evolutionary Operation to
optimize production yield through incremental changes in methanol to oil mass ratio (factor A) and sodium hydroxide
catalyst concentration (factor B) within the reactor. Phase 1 through phase 3 experiments are captured in the EVOP 22
Worksheets of Figures 9.25 through 9.35.

We begin at phase 1, cycle 1 using a new 22 EVOP worksheet. The names of the factors to be optimized are entered in cells
F14 and B7 for factor A and factor B respectively. The biodiesel process is currently operating at a methanol to oil ratio of
0.32 and a catalyst concentration of 0.92 wt % NaOH. These values are entered as the zero point of phase one in cells F11
and D6 respectively. Kuwat does not wish to “upset the apple cart” so he decides with his team that the maximum change in
MeOH : Oil Mass Ratio will be 0.02 units and the maximum change in wt% NaOH will be 0.03%. The high (+1) and low (-1)
values of the factors are entered in the appropriate cells in the worksheet. We now have a game plan to conduct phase one
experiments. The first experiment is conducted at the current factor conditions, point z. The date and time that the
experiment is begun is entered in cells C24 and C25 respectively. The production yield resulting from these factor settings is
entered in the “new observation” line of the table. Rows one and two are left blank for the first cycle of any phase. Rows 4,
5 and 6 are calculated fields based upon rows 1, 2 and 3. Factor settings are next changed to those of point a in the design
box and another batch of biodiesel is produced at these settings. The measured production yield is entered in the new
observation field for treatment combination a. This process is continued for points b, c and d within the design box
concluding phase one cycle one. The average yield for these first five batches of biodiesel is 88.8% which is above Kuwat’s
breakeven point. The maximum yield was obtained at point b and the minimum at point a.

Figure 9.25 Case Study XVI Phase 1, Cycle 1 - 22 EVOP Worksheet
EVOP 2
2
Worksheet
Process: Biodiesel
+1 0.95 d b
Cycle n: 1
Factor B 0 0.92 z
Catalyst Conc (wt % NaOH) Phase: 1
-1 0.89 a c
Response: Yield
0.30 0.32 0.34 f(5,n): - -
-1 0 +1
Factor A
MeOH : Oil Mass Ratio
3. New observation 89.0 86.8 90.8 88.4 88.9 New Std Dev = Range·f(5,n)
5. New sum (1 + 3) 89.0 86.8 90.8 88.4 88.9 New Sum of Std Dev
6. New average: (5 / n) 89.0 86.8 90.8 88.4 88.9 New Avg Std Dev
Date Nov 25 Nov 25 Nov 25 Nov 25 Nov 25
Time 07:00 10:00 13:00 16:00 19:00
A = (b + c - a - d)/2 = For Averages and New Effects: 2 s-bar / SQRT(n) = 0
For Change in Center Effect: 1.78 s-bar / SQRT(n) = 0
B = (b + d - a - c)/2 =
AB = (a + b - c - d)/2 =
(a + b + c + d - 4z)/5 =
Cycle # f(5,n)
Max Point = b 1 - -
2 0.30
4 0.37
Min Point = a 5 0.38
6 0.39
9 0.41
11 0.42
Table of f(5,n)
Enter Factor Names
Enter Factor Starting,
High and Low Values
Leave Blank
on Cycle 1
Enter Date and Time
Experiment Begun
Block Pt of
Max New Avg
Block Pt of
Min New Avg

Cycle two is a replicate of cycle one. The objective is to generate enough data points to detect a statistically significant signal
that a preferred operating condition exists within the design box. Previous sums and average yields are linked to the new
sums and average yields of the previous cycle. The previous sum of the standard deviation and the previous average
standard deviation are left blank for cycle two. New observations at the five treatment combinations are entered in line
three. This permits the calculation of a new average standard deviation. Since this standard deviation is only based upon ten
data points it is not recommended to make any changes in operating conditions based upon cycle two.

EVOP 2
2
Worksheet
Process: Biodiesel
+1 0.95 d b
Cycle n: 2
Factor B 0 0.92 z
-1 0.89 a c
Response: Yield
0.30 0.32 0.34 f(5,n): 0.30
-1 0 +1
Factor A
1. Previous Sum 89.0 86.8 90.8 88.4 88.9 Previous Sum of Std Dev
2. Previous Average 89.0 86.8 90.8 88.4 88.9 Previous Avg Std Dev
3. New observation 88.0 90.4 88.8 90.6 88.7 New Std Dev = Range·f(5,n) 1.67
4. Difference (2 - 3) 1.0 -3.6 2.0 -2.2 0.2 Difference Range 5.57
5. New sum (1 + 3) 177.0 177.2 179.6 179.0 177.6 New Sum of Std Dev 1.67
6. New average: (5 / n) 88.5 88.6 89.8 89.5 88.8 New Avg Std Dev 1.67
Time 22:00 01:00 04:00 07:00 10:00
A = (b + c - a - d)/2 = 0.96 For Averages and New Effects: 2 s-bar / SQRT(n) = 2.36
For Change in Center Effect: 1.78 s-bar / SQRT(n) = 2.10
B = (b + d - a - c)/2 = 0.26
AB = (a + b - c - d)/2 = 0.03
(a + b + c + d - 4z)/5 = 0.52
 (zero and Max(Effect)) = -1.27
Cycle # f(5,n)
Max Point = b 1 - -
2 0.30
 (zero and Min(Effect)) = -0.06 3 0.35
4 0.37
Min Point = z 5 0.38
6 0.39
9 0.41
11 0.42
Table of f(5,n)
Copied from New sum and
New average from Cycle 1
Leave Blank
on Cycle 2
Cycle 2 Std Dev is not
reliable - don't make
any decisions based
upon Cycle 2

Cycle three is the third replicate in phase one. Previous sums and averages of the yields are linked to the new sums and new
average yields of the prior cycle. The previous sum of the standard deviation and the previous average standard deviation
are linked to the new sum of the standard deviation and the new average standard deviation of cycle two. The maximum
new average yield is observed at point b while the minimum is observed at point z. The difference between the new average
yield at point b versus point z is 4.03. This value is above the standard error limit of 2.35 for changes in center effect
indicating that we have received a signal that point b represents a better operating condition than point z. But let’s be sure
about this conclusion. We are producing good product without affecting throughput rate or increasing impurities. There is
no harm to seek confirmation.

EVOP 2
2
Worksheet
Process: Biodiesel
+1 0.95 d b
Cycle n: 3
Factor B 0 0.92 z
-1 0.89 a c
Response: Yield
0.30 0.32 0.34 f(5,n): 0.35
-1 0 +1
Factor A
1. Previous Sum 177.0 177.2 179.6 179.0 177.6 Previous Sum of Std Dev 1.67
2. Previous Average 88.5 88.6 89.8 89.5 88.8 Previous Avg Std Dev 1.67
4. Difference (2 - 3) 3.6 0.6 -4.7 -2.1 0.0 Difference Range 8.27
Time 13:00 16:00 19:00 22:00 01:00
B = (b + d - a - c)/2 = 0.79
AB = (a + b - c - d)/2 = 0.36
(a + b + c + d - 4z)/5 = 1.89
Cycle # f(5,n)
Max Point = b 1 - -
2 0.30
 (zero and Min(Effect)) = -1.06 3 0.35
4 0.37
Min Point = z 5 0.38
6 0.39
9 0.41
11 0.42
Table of f(5,n)
Copied from New Sum and
New Avg from Cycle 2
Absolute value of -4.03
exceeds Error Limit of 2.35.
A signal has been received
that point b is better than
point z.

Cycle four represents the fourth replicate. New observations are entered in line three. Point b is observed to represent the
maximum new average yield while point a represents the minimum. The difference between the new average yield at point
b versus point z is 4.01. This value is above the standard error limit of 2.00 calculated for the change in center effect
confirming the signal that point b represents a better operating condition than point z. Kuwat and his team decide to move
the standard operating conditions of the reactor to a MeOH : Oil Mass Ratio of 0.34 and a Catalyst Concentration of 0.95%
NaOH. These conditions will serve as the zero point of phase two. The twenty batches of phase one have been produced at
an average biodiesel yield of 88.9%.

EVOP 2
2
Worksheet
Process: Biodiesel
+1 0.95 d b
Cycle n: 4
Factor B 0 0.92 z
-1 0.89 a c
Response: Yield
0.30 0.32 0.34 f(5,n): 0.37
-1 0 +1
Factor A
4. Difference (2 - 3) -1.3 4.6 -1.3 1.1 3.8 Difference Range 5.92
Time 04:00 07:00 10:00 13:00 16:00
B = (b + d - a - c)/2 = 1.19
AB = (a + b - c - d)/2 = 0.56
(a + b + c + d - 4z)/5 = 1.21
Cycle # f(5,n)
Max Point = b 1 - -
2 0.30
 (zero and Min(Effect)) = 0.42 3 0.35
4 0.37
6 0.39
9 0.41
11 0.42
Table of f(5,n)
Signal has been confirmed -
point b is better than point z.
Move center point operating
conditions to point b for
Phase 2.

Phase two starts with a clean worksheet and a new starting point on the DOE mountain. Remember that we have no idea of
the topography of the yield with respect to factor A and factor B. We are defining a small experimental box
and illuminating the corner points with a penlight to see which corner we should jump to. Phase two, cycle one begins with
the factor settings as shown in Figure 9.25E. The first set of yield observations from the five experiments are entered in line
three. The new sums and averages for these yields are linked to the second cycle, line one and two respectively. The second
cycle yield observations allow the calculation of the standard error limits but as in phase one, we make no decisions based
upon cycle two on account of the uncertainty in the standard deviation. We proceed to cycle three and enter the yield
observations for the five treatment combinations. The maximum new average yield is observed at point b while the
minimum is observed at point a. The difference between the new average yield at point b versus point z is 3.00. This value is
above the standard error limit of 2.55 for changes in center effect indicating that we have received a signal that point b
represents a better operating condition than point z. We could proceed to confirmatory cycles but Kuwat and the operators
are excited about the improvements and would like to change the standard operating conditions of the reactor to point b
and proceed to phase three. The fifteen batches of phase two have been produced at an average biodiesel yield of 90.2%, a
slight improvement over the average yield of 88.9% obtained in phase one.

EVOP 2
2
Worksheet
Process: Biodiesel
+1 0.98 d b
Cycle n: 1
Factor B 0 0.95 z
-1 0.92 a c
Response: Yield
0.32 0.34 0.36 f(5,n): - -
-1 0 +1
Factor A
Time 07:00 10:00 13:00 16:00 19:00
B = (b + d - a - c)/2 =
AB = (a + b - c - d)/2 =
(a + b + c + d - 4z)/5 =
Cycle # f(5,n)
Max Point = b 1 - -
2 0.30
4 0.37
6 0.39
9 0.41
11 0.42
Table of f(5,n)
Enter zero point factor
values from point b,
phase 1, cycle 4.
Adjust high and low
values accordingly.
Leave Blank
on Cycle 1
Enter Date and Time
Experiment Begun
Block Pt of
Max New Avg
Block Pt of
Min New Avg

EVOP 2
2
Worksheet
Process: Biodiesel
+1 0.98 d b
Cycle n: 2
Factor B 0 0.95 z
-1 0.92 a c
Response: Yield
0.32 0.34 0.36 f(5,n): 0.30
-1 0 +1
Factor A
4. Difference (2 - 3) 4.2 2.4 0.1 -2.8 -0.9 Difference Range 7.02
Time 22:00 01:00 04:00 07:00 10:00
B = (b + d - a - c)/2 = 2.10
AB = (a + b - c - d)/2 = -1.36
(a + b + c + d - 4z)/5 = 1.64
Cycle # f(5,n)
Max Point = b 1 - -
2 0.30
4 0.37
6 0.39
9 0.41
11 0.42
Table of f(5,n)
Copied from New sum and New
average from Phase 2, Cycle 1
Leave Blank
on Cycle 2

EVOP 2
2
Worksheet
Process: Biodiesel
+1 0.98 d b
Cycle n: 3
Factor B 0 0.95 z
-1 0.92 a c
Response: Yield
0.32 0.34 0.36 f(5,n): 0.35
-1 0 +1
Factor A
4. Difference (2 - 3) -3.9 1.8 -2.0 2.2 4.2 Difference Range 8.17
Time 13:00 16:00 19:00 22:00 01:00
B = (b + d - a - c)/2 = 2.39
AB = (a + b - c - d)/2 = -0.27
(a + b + c + d - 4z)/5 = 0.17
Cycle # f(5,n)
Max Point = b 1 - -
2 0.30
4 0.37
6 0.39
9 0.41
11 0.42
Table of f(5,n)
point z. Move center point
operating conditions to point
b for Phase 3.

Phase three, cycle one begins at a MeOH : Oil Mass Ratio of 0.36 and a Catalyst Concentration of 0.98% NaOH. The high (+1)
and low (-1) values of the factors are as shown in Figure 9.32. Yield observations at the five treatment combinations are
entered into line three. Similarly, yield observations are entered in cycle two for line three. Cycle three yield observations
result in point b being identified as the new average maximum. The difference between the new average yield at point b
versus point z is 3.89. This value is above the standard error limit of 1.40 for changes in center effect indicating that we have
received a signal that point b represents a better operating condition than point z. But notice that the yield for point a is the
same as point z. This causes Kuwat and the team some concern so they decide to continue at the current operating
conditions to cycle four. Point b is validated in cycle four as the new average yield maximum at 95.8%. The difference
between the new average yield at point b versus point z is 4.53. Since this value is above the standard error limit of 1.34 for
changes in center effect, point b represents a better operating condition than point z. The reactor operating conditions
should be moved to a MeOH : Oil Mass Ratio of 0.38 and a Catalyst Concentration of 1.01% NaOH in phase four. The twenty
batches of phase three have been produced at an average biodiesel yield of 92.5%, a significant improvement over the
average yield of 88.9% obtained in phase one.

EVOP 2
2
Worksheet
Process: Biodiesel
+1 1.01 d b
Cycle n: 1
Factor B 0 0.98 z
-1 0.95 a c
Response: Yield
0.34 0.36 0.38 f(5,n): - -
-1 0 +1
Factor A
Date Dec 1 Dec 1 Dec 1 Dec 1 Dec 1
Time 07:00 10:00 13:00 16:00 19:00
B = (b + d - a - c)/2 =
AB = (a + b - c - d)/2 =
(a + b + c + d - 4z)/5 =
Cycle # f(5,n)
Max Point = b 1 - -
2 0.30
4 0.37
6 0.39
9 0.41
11 0.42
Table of f(5,n)
Enter zero point factor
values from point b,
phase 2, cycle 3.
Adjust high and low
values accordingly.
Leave Blank
on Cycle 1
Enter Date and Time
Experiment Begun
Block Pt of
Max New Avg
Block Pt of
Min New Avg

EVOP 2
2
Worksheet
Process: Biodiesel
+1 1.01 d b
Cycle n: 2
Factor B 0 0.98 z
-1 0.95 a c
Response: Yield
0.34 0.36 0.38 f(5,n): 0.30
-1 0 +1
Factor A
4. Difference (2 - 3) 0.5 2.3 -2.8 1.5 -0.3 Difference Range 5.16
Time 22:00 01:00 04:00 07:00 10:00
B = (b + d - a - c)/2 = 3.44
AB = (a + b - c - d)/2 = 0.51
(a + b + c + d - 4z)/5 = -0.10
Cycle # f(5,n)
Max Point = b 1 - -
2 0.30
4 0.37
6 0.39
9 0.41
11 0.42
Table of f(5,n)
Leave Blank
on Cycle 2

EVOP 2
2
Worksheet
Process: Biodiesel
+1 1.01 d b
Cycle n: 3
Factor B 0 0.98 z
-1 0.95 a c
Response: Yield
0.34 0.36 0.38 f(5,n): 0.35
-1 0 +1
Factor A
4. Difference (2 - 3) 1.8 -0.7 -1.5 -1.1 -0.3 Difference Range 3.34
Time 13:00 16:00 19:00 22:00 01:00
B = (b + d - a - c)/2 = 3.45
AB = (a + b - c - d)/2 = 0.63
(a + b + c + d - 4z)/5 = 0.63
Cycle # f(5,n)
Max Point = b 1 - -
2 0.30
4 0.37
6 0.39
9 0.41
11 0.42
Table of f(5,n)
point z.

EVOP 2
2
Worksheet
Process: Biodiesel
+1 1.01 d b
Cycle n: 4
Factor B 0 0.98 z
-1 0.95 a c
Response: Yield
0.34 0.36 0.38 f(5,n): 0.37
-1 0 +1
Factor A
4. Difference (2 - 3) 0.9 0.6 -1.7 -4.0 -1.7 Difference Range 4.85
Time 04:00 07:00 10:00 13:00 16:00
B = (b + d - a - c)/2 = 3.45
AB = (a + b - c - d)/2 = 0.06
(a + b + c + d - 4z)/5 = 1.14
Cycle # f(5,n)
Max Point = b 1 - -
2 0.30
4 0.37
6 0.39
9 0.41
11 0.42
Table of f(5,n)
Signal has been confirmed -
point b is better than point z.
Move center point operating
conditions to point b for
Phase 4.

• It has taken nine days and fifty-five batches to cause a yield increase of 3.6%.
• The key point of this improvement process was that no defective batches were
produced and no reduction in throughput was incurred.
• Consequently, the improvement came without cost.
• If there were other response variables which Kuwat was interested in, such as the
concentration of a specific impurity, separate EVOP worksheets would be carried
through for these response variables.
• Decisions about changes in operating conditions would have to be justified against
all response variables.
• Evolutionary Operation is well suited to processes with constraints on their output
response due to market demands or constraints on their input factors due to design
limitations.
• In the latter case it is better to avoid input limitations which constrain output
responses through the judicious use of Design for Lean Six Sigma.
Summary

References
1. Anderson, Mark J. and Whitcomb, Patrick J., DOE Simplified – Practical Tools for Effective Experimentation, Productivity Press,
New York, NY, 2000
2. Barker, Thomas B., Quality by Experimental Design, Marcel Dekker, New York, NY, 1994
3. Barnett, E. Harvey, Introduction to Evolutionary Operation, Industrial and Engineering Chemistry, Vol 52, No 6, 1960, 500-503
4. Box, George E.P., Evolutionary Operation: A Method for Increasing Industrial Productivity, Applied Statistics, 1957, 81-101
5. Box, George E.P. and Draper, Norman R., Evolutionary Operation: A Statistical Method for Process Improvement, John Wiley &
Sons, New York, NY, 1969
6. Francis, Febe et al, Use of Response Surface Methodology for Optimizing Process Parameters for the Production of -amylase by
Aspergillus Oryzae, Biochemical Engineering Journal, Vol. 15, 2003, 107-115
7. John, Peter W.M., Statistical Design and Analysis of Experiments, Macmillan Publishing Co., New York, NY, 1971
8. Montgomery, Douglas C., Introduction to Statistical Quality Control, 5th Edition, John Wiley & Sons, New York, NY, 2005
9. Myers, Raymond H., Montgomery, Douglas C., and Anderson-Cook, Christine M., Response Surface Methodology, 3rd edition,
John Wiley & Sons, Inc., Hoboken, NJ, 2009
10. Plackett, R.L. and Burman, J.P., The Design of Optimum Multifactorial Experiments, Biometrika, Vol. 33, 1946, 305-325
11. Schmidt, Stephen R., Launsby, Robert G., Understanding Industrial Designed Experiments – Blending the Best of the Best
Designed Experiment Techniques, 4th edition, Air Academy Press, Colorado Springs, CO, 1998

Evolutionary Operation

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