### Designed Experiments – A High Level Introduction

In an earlier article, I discussed the transformation function Y = f(X), where Y represents the output of a process.  The output is a function of the inputs (the X’s) that affect the output.

Designed Experiments are used to help us quantify the effect that the inputs have on the output of a process.  In order to help you understand how Designed Experiments work, let’s first define some terms.

The body of knowledge for Designed Experiments is often referred to as Design of Experiments, or DOE.  We experiment with different factors (the X inputs).  We use different levels of each factor when conducting the experiment, where the level indicates how much of the factor is used.  In an experiment we may also have factors that are held at fixed levels as well as random or noise factors with unpredictable levels.

Let me illustrate with a couple of examples.  The first is baking a cake.  The desired output for the cake is a golden brown, fully cooked cake.  We don’t want the cake to be burned, nor do we want the cake to be uncooked.  We know from experience that two of the factors that determine the output are time (how long the cake remains in the oven) and temperature (how hot the oven is during baking).   For time levels we might experiment with 20 minutes and 30 minutes; and for temperature levels, 350 degrees F and 375 degrees F.  A factor that we would want to hold at a fixed level would be the recipe for the cake, as using different ingredients might affect the output.   Random or noise variables might include the humidity level in the kitchen.

This is a simple experiment, with just two factors and two levels for each factor.  There are four resulting combinations of time and temperature – 350 degrees F and 20 minutes, 350 degrees F and 30 minutes, 375 degrees F and 20 minutes, and 375 degrees F and 30 minutes.  The experiment would be conducted by running several trials for each of the four combinations and collecting data on the resulting output.  In this case the output is a bit subjective, but we could use visual boundary samples to define the resulting color of the cake (for example unbaked, lightly baked, golden brown, well done, burned).  Our goal is to determine the best combination of time and temperature to consistently produce a golden brown cake.

Another example is bowling, where the output of the process is more objectively measured using the total score for a bowling game on a scale of zero to 300.  Factors that we could experiment with might be the use of a glove (yes or no), ball hardness (hard or soft), and the amount of oil on the lanes (freshly oiled lane or dry lane).  In this case (eight factors at two levels each) we have eight possible combinations.  Here are the combinations and the resulting scores:

 Glove Hardness Oil Score 1 Yes Hard Fresh oil 183 2 Yes Hard Dry 188 3 Yes Soft Fresh oil 191 4 Yes Soft Dry 174 5 No Hard Fresh oil 141 6 No Hard Dry 158 7 No Soft Fresh oil 159 8 No Soft Dry 154

Factors that we might want to keep fixed could include the bowler and the lane.  Different bowlers would obviously alter the scores, and using a lane that was worn differently could also impact the score.

If we look at the scores, we can see that in all cases better results were achieved when using a glove.   The average score was 184 when using a glove and 153 when not using a glove.  The combination of glove, dry lane and hard ball (188) or glove, oily lane and soft ball (191) gave the best results overall.  This indicates that there is an interaction between the ball hardness and the amount of oil on the lane.  The ability to determine the extent of such interactions is one of the advantages of DOE.  DOE is also more cost effective than experimenting with just one factor at a time.

This has been a very simplistic look at DOE.  In practice, we perform a statistical analysis of the results of the experiment to determine which factors and which interactions between factors have a significant impact on process output, and to what extent they impact the output.

Your comments or questions about this article are welcome, as are suggestions for future articles.  Feel free to contact me by email at roger@keyperformance.com.

About the author:  Mr. Roger C. Ellis is an industrial engineer by training and profession.  He is a Six Sigma Master Black Belt with over 45 years of business experience in a wide range of fields.  Mr. Ellis develops and instructs Six Sigma professional certification courses for Key Performance LLC.   For a more detailed biography, please refer to www.keyperformance.com.

On August 9th, 2015, posted in: Articles, Six Sigma by