Design of Experiments (DOE)
Design of Experiments is one of the most important tools used in the Improve phase of any comprehensive Six Sigma/ Lean Six Sigma project. This tool acts as the catalyst that propels a project from the Analyze phase to the Control phase. It is the element in DMAIC that allows for the “chemical reaction of discovering a solution.” (Note: Please visit Design of experiments Training if you would like to learn the subject in greater detail).
In DMAIC, we document any possible X’s affecting our output characteristics and narrow this list to the most likely ones. In the Analyze phase, we narrow this list even further, from the likeliest culprits to only the key X’s. When we start the Improve phase, we take this list of key X’s down to only the critical ones. We can now apply designed experiments to help us get the rest of the way. This tool will help us identify and prioritize the most critical X’s and their interactions that need to be controlled.
Douglas C. Montgomery was a famous designed experiments expert. He explains that a designed experiment is a test or series of tests in which purposeful or deliberate changes are made to relevant input variables in a process or system so that changes in the output responses can be observed and identified. In other words, we want to change our X’s deliberately and observe the results on the Y’s.
There are many reasons why any practitioner of Lean Six Sigma should employ the use of structured experiments in industry. First, it helps determine which X’s in a process are most critical and most influential. It also discovers any potential interactions between critical X’s. Designed experiments determine at what levels these critical inputs should operate so that our most important outputs stay within desirable levels and operate with minimum process variability. It also determines if particular controllable input levels can help us minimize the impact of some uncontrollable input variables. And lastly, the most important reason for executing designed experiments is to determine the defining relation of our process Y as a function of X. When we say about Y as a function of X, we have to show how this transfer function is actually derived.
The following is an outline for conducting factorial experiments:
- Step 1—State the practical problem.
- Step 2—State the experimental objective—why are you running a DOE?
- Step 3—Select the response variables, or the outputs.
- Step 4—Select the input variables, or factors.
- Step 5—Select the levels of interest for each input.
- Step 6—Select the experimental design.
- Step 7—Run the experiment and collect the data.
- Step 8—Analyze the results.
- Step 9—Draw statistical conclusions.
- Step 10-State the practical conclusions.
State the Practical Problem and Experimental Objective
To initiate we would like to determine which factors can help in the problem resolution. For this purpose, we will state how to define the experiment or combination of inputs that affect the output. We want to accomplish the objective by determining which controllable factors in the process, and which interactions, have the greatest impact on these two Y’s.
Select Response and Input factors
Next step is to select the response variables, or the outputs that we want to monitor for improvement. On the input side, there are many potential inputs we could consider. Usually, discussing which inputs to study during an experiment is a fairly involved process. We need experts from the process to assist us.
Select the Level of Interest
Then for each input that was selected, we must determine which levels of the input will be studied during the experiment. Just as before, process knowledge and discussion should be used to make these determinations.
Select the experimental design
Selecting the right experiment can be a very tricky process. We can build our experimental design by listing all of the possible treatment combinations for these variables. We can do it iteratively.
Running the experiment
The main activity is running the experiment and collecting the data. This step is never trivial and we should be selective and careful with our factors and levels.
One common starting point for analyzing a DOE is using an ANOVA table. ANOVA stands for analysis of variance. We can translate that into partitioning a variation. Through the use of DOE and the ANOVA table, for any given Y, we can find out what proportion of the variation in that Y can be directly attributed to a particular X or combination of Xs known as the interaction. Each Y of interest will have its own ANOVA table. There are six columns in any ANOVA table.
The columns are titled as:
- Degrees of freedom or DF
- Sum of Squares
- Mu Square
State Statistical and Practical Conclusions
The statistical conclusions should conclude that there is enough statistical evidence to suggest that the X’s are very likely to be significant if their P-values are less than 0.05. Those X’s with a higher P-value than 0.05 are not likely to be significant. The practical conclusions should be drawn that Y is a function of X and therefore the DOE should allow us the opportunity to write an equation.
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