1. Improve Phase Designing Experiments
Now we are going to continue with the Improve Phase “Designing Experiments”.

2. Designing Experiments
Graphical Analysis
DOE Methodology
Reasons for Experiments
Designing Experiments
Advanced Process Modeling: MLR
Process Modeling: Regression
Welcome to Improve
Wrap Up & Action Items
Within this module we will provide an introduction to Design of Experiments, explain what they are, how they work and when to use them.

3. Understand our problem and its impact on the business. (Define)
Project Status Review
Understand our problem and its impact on the business. (Define)
Established firm objectives/goals for improvement. (Define)
Quantified our output characteristic. (Define)
Validated the measurement system for our output characteristic. (Measure)
Identified the process input variables in our process. (Measure)
Narrowed our input variables to the potential “X’s” through Statistical Analysis. (Analyze)
Selected the vital few X’s to optimize the output response(s). (Improve)
Quantified the relationship of the Y’s to the X’s with Y = f(x). (Improve)
Please read the slide.

4. Define Measure Analyze Business Success Inputs Suppliers Outputs
Six Sigma Strategy
(X5)
(X6)
(X7)
(X9)
(X1)
(X8)
(X11)
(X4)
(X10)
(X3)
(X2)
Define
Measure
Analyze
Improve
Suppliers
Contractors
Employees
Customers
Inputs
Outputs
SIPOC
VOC
Project Scope
P-Map, X-Y Matrix,
FMEA,
Capability
Box Plot, Scatter
Plots, Regression
Fractional Factorial
Full Factorial
Center Points
Control Plan
Business Success
This is reoccurring awareness. By using tools we filter the variables of defects. When talking of the Improve Phase in the Lean Six Sigma methodology we are confronted by many Designed Experiments; transactional, manufacturing, research.

5. Reasons for Experiments
The Analyze Phase narrowed down the many inputs to a critical few now it is necessary to determine the proper settings for these few inputs because:
The vital few potentially have interactions.
The vital few will have preferred ranges to achieve optimal results.
Confirm cause and effect relationships among factors identified in Analyze Phase (e.g. Regression)
Understanding the reason for an experiment can help in selecting the design and focusing the efforts of an experiment.
Reasons for experimenting are:
Problem Solving (Improving a process response)
Optimizing (Highest yield or lowest customer complaints)
Robustness (Constant response time)
Screening (Further screening of the critical few to the vital few X’s)
Design where you’re going - be sure you get there!
Design of Experiments helps the Belt to understand the cause and effect between the process output or outputs of interest and the vital few inputs. Some of these causes and effects may include the impact of interactions often referred to synergistic or cancelling effects.

6. Desired Results of Experiments
Problem Solving
Eliminate defective products or services.
Reduce cycle time of handling transactional processes.
Optimizing
Mathematical model is desired to move the process response.
Opportunity to meet differing customer requirements (specifications or VOC).
Robust Design
Provide consistent process or product performance.
Desensitize the output response(s) to input variable changes including NOISE variables.
Design processes knowing which input variables are difficult to maintain.
Screening
Past process data is limited or statistical conclusions
prevented good narrowing of critical factors in Analyze
Phase.
When it rains it PORS!
Designed Experiments allow us to describe a mathematical relationship between the inputs and outputs. However, often the mathematical equation is not necessary or used depending on the focus of the experiment.
Problem Solving involves reducing or eliminating a specific problem in a process.
Optimizing is used to specifically hit some target value for the response variable.
Robust Design focuses on making the output response insensitive to fluctuations in the input variables whether they are process settings or noise variables.
Screening is used when there are many input variables to evaluate.

7. DOE Models vs. Physical Models
What are the differences between DOE modeling and physical models?
A physical model is known by theory using concepts of physics, chemistry, biology, etc...
Physical models explain outside area of immediate project needs and include more variables than typical DOE models.
DOE describes only a small region of the experimental space.
The objective is to minimize the response. The physical model is not important for our business objective. The DOE Model will focus in the region of interest.
Here we have models that are results of Designed Experiments. Many have difficulty determining DOE models from that of physical models. A physical model includes: biology, chemistry, physics and usually many variables, typically using complexities and calculus to describe. DOE models do not include any complex calculus: they include the most important variables and show variation of data collected. DOE will focus on the region of interest.

8. Definition for Design of Experiments
Design of Experiments (DOE) is a scientific method of planning and conducting an experiment that will yield the true cause and effect relationship between the X variables and the Y variables of interest.
DOE allows the experimenter to study the effect of many input variables that may influence the product or process simultaneously, as well as possible interaction effects (for example synergistic effects).
The end result of many experiments is to describe the results as a mathematical function Y = f (x)
The goal of DOE is to find a design that will produce the information required at a minimum cost.
Properly designed DOE’s are more efficient experiments.
Design of Experiment shows the cause and effect relationship of variables of interest X and Y. By way of input variables designed experiments have been noted within the Analyze Phase. DOE tightly controls the input variables and carefully monitors the uncontrollable variables.

9. One Factor at a Time is NOT a DOE
One Factor at a Time (OFAT) is an experimental style but not a planned experiment or DOE.
The graphic shows yield contours for a process that are unknown to the experimenter.
Pressure (psi) 75 80 85 90 95
Yield Contours Are
Unknown To Experimenter 30 31 32 33 34 35
120
125
130
135
Temperature (C) 7 2 1 4 3 6 5
Optimum identified
with OFAT
True Optimum available
with DOE
Let’s assume a Belt has found in the Analyze Phase that pressure and temperature impact his process and no one knows what yield is achieved for the various temperature and pressure combinations.
If a Belt inefficiently did a One Factor at a Time experiment, referred to as OFAT, one variable would be selected to change first while the other variable is held constant. Once the desired result was observed the first variable is set at that level and the second variable is changed. Basically, you pick the winner of the combinations tested.
The curves shown on the graph above represent a constant process yield if the Belt knew the theoretical relationships among all the variables and the process output of pressure. These contour lines are familiar if you have ever done hiking in the mountains and looked at an elevation map which shows contours of constant elevation.
In our example we decided to increase temperature trying to achieve a higher yield. After achieving a maximum yield with temperature we then decided to only change the other factor, pressure. We then came to the conclusion the maximum yield is near 92% because it was the highest yield noted in our seven trials.
With the Six Sigma methodology we use DOE which would have found a higher yield using equations.
Many sources state that OFAT experimentation is inefficient when compared with DOE methods. Some people call it hit or miss. Luck has a lot to do with results using OFAT methods.

10. Types of Experimental Designs
The most common types of DOE’s are:
Fractional Factorials
4-15 input variables
Full Factorials
2-5 input variables
Response Surface Methods (RSM)
2-4 input variables
KNOWLEDGE
Full Factorial
Response Surface
DOE is iterative in nature and may require more than one experiment at times.
As we learn more about the important variables our approach will change as well. If we have a very good understanding of our process maybe we will only need one experiment, if not we very well may need a series of experiments.
Fractional Factorials or screening designs are used when the process or product knowledge is low. We may have a long list of possible input variables (often referred to as factors) and need to screen them down to a more reasonable or workable level.
Full Factorials are used when it is necessary to fully understand the effects of interactions and when there are between 2 to 5 input variables.
Response surface methods (not typically applicable) are used to optimize a response typically when the response surface has significant curvature.

11. Nomenclature for Factorial Experiments
The general notation used to designate a full factorial design is given by:
Where k is the number of input variables or factors.
2 is the number of “levels” that will be used for each factor.
Quantitative or qualitative factors can be used. 2k
Full factorial designs are generally noted as 2 to the k where k is number of input variables or factors and 2 is the number of levels all factors used. In the table two levels and four factors are shown; using the formula how many runs would be involved in this design? 16 is the answer, of course.

12. Visualization of 2 Level Full Factorial
Temp
Press
350F
300F
(+1,-1)
(-1,-1)
500
600
(+1,+1)
(-1,+1)
Four experimental runs:
Temp = 300, Press = 500
Temp = 350, Press = 500
Temp = 300, Press = 600
Temp = 350, Press = 600 T P
T*P -1 +1
300
350 22
Coded levels for factors
Uncoded levels for factors
Let’s consider a 2 squared design which means we have 2 levels for 2 factors. The factors of interest are temperature and pressure. There are several ways to visualize this 2 Level Full Factorial design. In experimenting we often use what is called coded variables. Coding simplifies the notation. The low level for a factor is minus one while the high level is plus one. Coding is not very friendly when trying to run an experiment so we use non-coded or actual variable levels. In our example 300 degrees is the low level, 500 degrees is the high level for temperature.
Back when we had to calculate the effects of experiments by hand it was much simpler to use coded variables. Also when you look at the Prediction Equation generated you could easily tell which variable had the largest effect. Coding also helps us explain some of the math involved in DOE.
Fortunately for us MINITABTM calculates the equations for both coded and non-coded data.

13. Graphical DOE Analysis - The Cube Plot
Consider a 23 design on a catapult...
Stop Angle
Start Angle
0.9
2.1
2.4
5.15
3.35
8.2
4.55
1.5
Fulcrum
Run Start Stop Meters
Number Angle Angle Fulcrum Traveled A B C
Response
What are the inputs being manipulated in this design?
How many runs are there in this experiment?
This representation has two cubed designs and 2 levels of three factors and shows a treatment com table using coded inputs level settings. The table has 8 experimental runs. Run 5 shows start angle, stop angle very low and the fulcrum relatively high.

14. Graphical DOE Analysis - The Cube Plot
This graph is used by the experimenter to visualize how the response data is distributed across the experimental space.
How do you read or interpret this plot?
What are these?
Stat>DOE>Factorial>Factorial Plots … Cube, select response and factors
Catapult.mtw
MINITABTM generates various plots, the cube plot is one. Open the MINITABTM worksheet “Catapult.mtw”.
This cube plot is a 2 cubed design for a catapult using three variables:
Start Angle
Stop Angle
Fulcrum
Here we used coded variable level settings so we do not know what the actual process setting were in non-coded units. The data Means for the response distance are the boxes on the corners of the cube. If we set the stop angle high, start angle low and fulcrum high we would expect to launch a ball about 8.2 meters with the catapult, make sense?

15. Graphical DOE Analysis - The Main Effects Plot
This graph is used to see the relative effect of each factor on the output response.
Stat>DOE>Factorial>Factorial Plots … Main Effects, select response and factors
Which factor has the largest impact on the output?
Hint: Check the slope!
The Main Effects Plot shown here displays the effect that the input values have on the output response.
The Y axis is the same for each of the plots so they can be compared side by side.
Which has the steepest Slope? What has the largest impact on the output?
Answer > Fulcrum

16. Main Effects Plot Creation
Run # Start Angle Stop Angle Fulcrum Distance
Avg Distance at Low Setting of Start Angle: = 18.8/4 = 4.70
Avg. distance at High Setting of Start Angle: = 9.40/4 = 2.34
Start Angle
Stop Angle
Fulcrum
Main Effects Plot (data means) for Distance
2.0
2.8
3.6
4.4
5.2
Dist -1 1
In order to create the Main Effects Plot we must be able to calculate the average response at the low and high levels for each Main Effect. The coded values are used to show which responses must be used to calculate the average.
Let’s review what is happening on this slide. How many experimental runs were operated with the start angle at the high level of 1? The answer is 4 experimental runs shows the process to run with the start angle at the high level. The 4 experimental runs running with the start angle at the high level are run number 2, 4, 6 and 8. If we take the 4 distances or process output and take the average, we see the average distance when the process had the start angle running at the high level was 2.34 meters. The second dot from the left in the Main Effects Plots shows the distance of 2.34 with the start angle at a high level.

17. Interaction Definition
When B changes from low to high the output drops very little. A - + Y
Lower
Higher B- B+
Output
When B changes from low to high the output drops dramatically.
Interactions occur when variables act together to impact the output of the process. Interactions plots are constructed by plotting both variables together on the same graph. They take the form of this graph. Note the relationship between variables A and Y changes as the level of variable B changes. When B is at its high (+) level variable A has almost no effect on Y. When B is at its low (-) level A has a strong effect on Y. The feature of interactions is non-parallelism between the two lines.

18. Degrees of Interaction Effect- + Y
Low
High B- B+
No Interaction
Strong Interaction
Full Reversal
Moderate Reversal
Some Interaction
Degrees of Interaction can be related to non-parallelism and the more non-parallel the lines are the stronger the interaction.
A common misunderstanding is that the lines must actually cross each other for an interaction to exist but that is NOT true. The lines may cross at some level OUTSIDE of the experimental region.
Parallel lines show absolutely no interaction and in all likelihood will never cross.

19. Interaction Plot Creation-1 1
1.5
2.5
3.5
4.5
5.5
6.5
Fulcrum
Start Angle
Mean
Interaction Plot (data means) for Distance
( )/2 = 1.20
Run # Start Angle Stop Angle Fulcrum Distance
( )/2 = 3.48
Calculating the points to plot the interaction is not as straight forward as it was in the Main Effects Plot. Here we have four points to plot and since there are only 8 data points each average will be created using data points from 2 experimental runs. This plot is the interaction of Fulcrum with Start Angle on the distance. Starting with the point indicated with the green arrow above we must find the response data when the fulcrum is set low and start angle is set high (notice the color coding MINITABTM uses in the upper right hand corner of the plot for the second factor). The point indicated with the purple arrow is where fulcrum is set high and start angle is high. Take a few moments to verify the remaining two points plotted.
Let’s review what is happening here. The dot indicated by the green arrow is the Mean distance when the fulcrum is at the low level as indicated by a -1 and when the start angle is at the high level as indicated by a 1. Earlier we said the point indicated by the green arrow had the fulcrum at the low level and the start angle at the high level. Experimental runs 2 and 4 had the process running at those conditions so the distance from those two experimental runs is averaged and plotted in reference to a value of 1.2 on the vertical axis. You can note the red dotted line shown is for when the start angle is at the high level as indicated by a 1.

20. Graphical DOE Analysis - The Interaction Plots
Stat>DOE>Factorial>Factorial Plots … Interactions, select response and factors
When you select more than two variables MINITABTM generates an Interaction Plot Matrix which allows you to look at interactions simultaneously. The plot at the upper right shows the effects of Start Angle on Y at the two different levels of Fulcrum. The red line shows the
effects of Fulcrum on Y when Start Angle is at its high level. The black line represents the effects of Fulcrum on Y when Start Angle is at its low level.
Note: In setting up this graph we selected options and deselected “draw full interaction matrix”
Based on how many factors you select MINITABTM will create a number of interaction plots.
Here there are 3 factors selected so it generates the 3 interaction plots. These are referred to as 2-way interactions.

21. Graphical DOE Analysis - The Interaction Plots
Stat>DOE>Factorial>Factorial Plots … Interactions, select response and factors
The plots at the lower left in the graph below (outlined in blue) are the “mirror image” plots of those in the upper right. It is often useful to look at each interaction in both representations.
Choose this option
for the additional
plots.
MINITABTM will also plot the mirror images, just in case it is easier to interpret with the variables flipped. If you care to create the mirror image of the interaction plots, while creating interaction plots, click on “Options…” and choose “Draw full interaction plot matrix” with a checkmark in the box. These mirror images present the same data but visually may be easier to understand.

22. Define the Practical Problem Establish the Experimental Objective
DOE Methodology
Define the Practical Problem
Establish the Experimental Objective
Select the Output (response) Variables
Select the Input (independent) Variables
Choose the Levels for the Input Variables
Select the Experimental Design
Execute the experiment and Collect Data
Analyze the data from the designed experiment and draw Statistical Conclusions
Draw Practical Solutions
Replicate or validate the experimental results
Implement Solutions
Please read the slide.

23. Generate Full Factorial Designs in MINITABTM
“DOE”>”Factorial”>”Create Factorial Design…”
It is easy to generate Full Factorial Designs in MINITABTM. Follow the command path shown here. This is the output that MINITABTM will create. They are color coded using the Red, Yellow and Green. Green are the “go” designs, yellow are the “use caution” designs and red are the “stop, wait and think” designs. It has a similar meaning as do street lights.

24. Create Three Factor Full Factorial Design
Stat>DOE>Factorial>Create Factorial Design
Let’s create a three factor Full Factorial Design using the MINITABTM command shown at the top of the slide. This design we selected will give us all possible experimental combinations of 3 factors using 2 levels for each factor.
Be sure to have changed the “Number of factors:” to 3. Also be sure not to forget to click on the “Full factorial” line within the “Designs” box.

25. Create Three Factor Full Factorial Design
In the “Options…” box of the upper left MINITABTM display, one can change the order of the experimental runs. To view the design in standard order (not randomized for now) be sure to uncheck the default of “Randomize runs”. “Un-checking” means no checkmark is in the white box next to “Randomize runs”.

26. Create Three Factor Full Factorial Design
Now we need to enter the names of the three factors as well as the numbers for the levels we want in Factors. To reach this display click on “Factors…” in the “Create Factorial Design” window. Remember when we discussed non-coded levels? The process settings of 140 and 180 for the start angle are examples of non-coded levels.

27. Three Factor Full Factorial Design
Hold on! Here we go….
Here is the worksheet MINITABTM creates. If you had left the randomize runs selection checked in the “Options…” box, your design would be in a different order than shown. Notice the structure of the last 3 columns where the factors are shown. The first factor, Start Angle, goes from low to high as you read down the column. The second factor, Stop Angle, has 2 low then 2 high all the way down the column and the third factor, Fulcrum, has 4 low then 4 high. Notice the structure just keeps doubling the pattern. If we had created a 4 factor Full Factorial Design the fourth factor column would have had 8 rows at the low setting then 8 rows at the high setting. You can see it is very easy to create a Full Factorial Design. This standard order as we call it is not the recommended order in which an experiment should be run. We will discuss this in detail as we continue through the modules.
One warning to you as a new Belt using MINITABTM… never copy, paste, delete or move columns within the first 7 columns or MINITABTM may not recognize the design you are attempting to use.
Is our experiment done? Not at all. The process must now be run at the 8 experimental set of conditions shown above and the output or outputs of interest must be recorded in columns to the right of our first 7 columns. After we have collected the data we will then analyze the experiment. Remember the 11 step DOE methodology from earlier?

28. At this point you should be able to:
Summary
At this point you should be able to:
Determine the reason for experimenting
Describe the difference between a physical model and a DOE model
Explain an OFAT experiment and its primary weakness
When shown a Main Effects Plots and interactions, determine which effects and interactions may be significant.
Create a Full Factorial Design
Please read the slide.

29. 29