In this video, Dr. Richard Chua covers design of experiments (DOE) to determine what the best combination of settings for proven X's to optimize the output Y.
- Have you ever wondered how little sleep you can get away with the night before a test in order to study more? Or, have you ever worried if the temperature of the testing room will impact your performance? And just what is the best combination of sleep hours, study time, and room temperature? In a Six Sigma project, after the root causes or key X's have been proven earlier, now the main question in the Improve Phase is what is the best combination of settings for the proven X's to optimize output, Y? Let's go back to our example.
If the X's that impact test scores are hours of sleep, study time, and room temperature, then what is the best combination of these factors to improve test scores? The tool that is best suited for doing this is called Design of Experiments or DOE. To start, here is some basic DOE terminology: In this example, sleep duration, study time, and room temperature, are called the factors, or independent variables.
The output Y or test score is called the dependent variable. The settings for the factors are called levels. For example, sleep duration can be set at two levels; four and eight hours. A common experimental design is to set each factor at two levels. This design is called the two k factorial design, or two to the power of k, where k is the number of factors. In this example, there are three factors, so, it is a two to the power of three factorial design.
There is significance to this number because two to the power of three equals eight. And we have eight treatment combinations. In DOE, there are usually at least two sets of runs, or replecants so that any experimental error can be estimated. Also, to overcome any systematic bias, the runs for each treatment combination are carried out in random order. In other words, the order of the runs are randomized. You may ask, why not do a simple experiment where only one factor is varied? While it's easy to understand the effect of each individual factor with the one-factor-at-a-time approach, it's impossible to determine how the factors interact to impact the end results.
For example, are the test scores the same with eight hours of sleep when time spend studying is only two hours instead of six? Probably not. That is the beauty of DOE. It makes it possible to test the interaction of multiple factors along with the main effect of each factor. As a result, the best combination can be determined. Again, let's look at how test scores are affected by hours of sleep, study time, and room temperature. You can see the low high levels here.
The experiment was run and here are the results. Plotting these results, we can display the various effects, such as the main effect of each factor. Here is the main effects plot, showing the effect that each factor has on test scores, as each factor is increased, from the low level to the high level. The graph will be horizontally flat when there is zero effect. So, which variables have a significant effect on test scores? It looks like more sleep and more study time improve test scores, but higher temperatures have little effect.
Here is the plot showing the interactions among the three factors. If there is no interaction, the lines will be parallel. It looks like the interactions are not significant. The next graph is a Cube Plot, showing the results for all treatment combinations in this two k factorial design. The Cube Plot shows the three factors, represented by the three axes, X, Y, and Z. Sleep in on the X-axis, showing the low of four hours, and the high of eight.
Study time is on the vertical Y-axis, from low of two hours to high of six. And temperature is on the Z-axis, at low of 65 degrees, and high of 75. The corner points of this Cube Plot show the test scores for each possible treatment combination. The best score from the experiment is 95, and the best combination of settings is eight hours sleep, six hours study time, regardless of room temperature.
This example shows how DOE can be used to find the best combination of X settings to optimize the outcome, Y. Now, you know the best levels of sleep and study time to maximize your test scores.
Dr. Richard Chua builds upon his Six Sigma Foundations and Learning Minitab courses, and covers an array of topics, including measurement system analysis, descriptive statistics, hypothesis testing, design of experiments, statistical process control, and more.
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- Six Sigma and the organization
- Collecting the voice of the customer
- Project management basics
- Process maps
- Sampling in data collection
- Measurement system analysis
- Measuring performance using descriptive statistics
- Process performance measures
- Hypothesis testing
- Testing for means, variances, proportions, and independence
- Correlation and regression
- Using selection matrices
- Using failure modes and effects analysis
- Developing control plans
- Statistical process control