# DOE Design of Experiments

## Experimental Design

**Factorial Experiments**

Design of Experiments (DOE) is an important tool within the Six Sigma & Lean Six Sigma toolbox. There are many reasons why any practitioner involved in process improvement, in any industry, should consider implementing Design of Experiments (DOE) / Statistical Experiment Planning. First, it helps us determine which process X’s or inputs are most critical or most influential. DOE also discovers any potential interactions between critical X’s. Designed Experiments determine what levels these critical inputs should operate at, so that our most important outputs stay within desirable levels of performance. It also determines if particular controllable input levels can help us minimize the impact of some uncontrollable ones. And lastly, the most important reason for executing Design of Experiments is to determine the defining relation of our process – Y as a function of X.

Let’s consider an example from an industry that touches all of our lives every day – healthcare insurance. The Secure Living Insurance Company (S.L.I.C.) conducts millions of transactions each year. In addition to the ultimate customer – “the Subscriber” or “Member” – me or you, who purchases SLIC coverage, SLIC also interacts with the healthcare provider. Things can get confusing pretty quickly when three or more parties are providing services, keeping track of these services, and communicating back and forth multiple times can be an overwhelming endeavour. One can imagine the opportunity for defects these interactions create.

Claims will be denied or paid incorrectly – literally resulting in hundreds or even thousands of defects such as overpayments, underpayments and incorrect payments. Each of these becomes rework, not to mention a whole bunch of angry members healthcare providers, and SLIC employees having to deal with these defects. The financial penalty for this is staggering. We have been assigned a project to reduce the occurrence of group renewals processed late. Business Metric that management uses to assess the problems is the percentage of renewals that are late for a given time period. This will be known as a defective rate and is based on discrete or binomial data. We calculate defective rates by counting up the number of events that did not meet the customer requirement and dividing by the total count of all the events.

Now, the process of loading a large group, one individual group member at a time, can start at any time. Again, the important thing is that all individuals of the group are loaded and ready by the renewal date. Renewal dates are different for different groups. Since the renewal date is a focal point for each group, we have to define our metric based on a date specific to a group. Let’s use a primary metric of number of days the group is ready to go before or after the Renewal date. It is a continuous variable that we will call simply the “number of days.”

As long as we get the group ready before the renewal date, the number of days is a positive number, i.e., we are ready early. Now, if the group was ready exactly on the target renewal date, then the number of days is zero, which is OK, too. And finally, if the group was late or not ready, the number of days would be negative; we don’t like that. This continuous metric also allows us to use the standard model for DOE, which has a continuous response variable.

Next, we just need to identify the X’s or factors. Some fine work through the Measure phase should yield a list of potential critical factors that are suspected to be driving the number of days early or late. Then, during the Analyze phase, targeted data collection leads to graphical analysis methods, where we visually explore central tendency, variation, distribution shape, consistency over time, and most importantly, relationships between certain factors, our X’s, and the Y of interest, number of days.

A good graphical analysis typically points to a few factors as being potentially strong drivers of variation in the process output, or Y. We decide to investigate these candidate factors further, using statistical analysis such as Regression or Contingency Tables and various Hypothesis Tests. All the while searching for relationships between the X’s, our Factors, and the Y of interest, our response variable.

The objective of DOE is to prove the connection, often called a causal relationship, between these factors and the output. The best way to accomplish this is through a planned effort, where we intentionally vary the factors while monitoring the effect on the response variable. Full Factorial DOE, is the most effective way to arrive at an answer that we can really count on. This approach will answer the question of which factors are really the strong drivers and which are not. Full Factorial DOE can allow us to make good decisions about certain hypotheses, in order to prove beyond a reasonable doubt, what will, and sometimes more importantly, what won’t improve the process. In addition, this type of experimentation and analysis is the only way to investigate and quantify the interactions between X’s. Full Factorials allow us to quantify the contribution or strength that a particular factor or interaction has on our response variable. This leads us ultimately to establishing the optimal settings of those critical factors or interactions.

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