Design of experiments (DOE) is one of the most valuable tools in the Six Sigma toolkit. It is the only tool that allows a proactive approach for process improvement. Unlike analysis of variance (ANOVA) or regression where past data is analyzed, DOE allows for the collection of realtime data and its analysis. It is ideally suited to address problems where more than one variable may affect an output and two or more variables may interact with one another.
Many companies experiment on their products and processes by focusing on one factor at a time, sometimes referred to as an OFAT experiment, while trying to hold everything else in the experiment constant. Using this approach has its drawbacks in that many experiments are usually necessary to study all the input variables and the optimum combination of all the inputs or variables may never be known. DOE on the other hand, when properly conducted, allows the experimenter to focus on a wide range of key input factors and will determine the optimum levels of each.
DOE is used wherever experimental data are collected and analyzed. It is used in all branches of scientific research and in every business sector today. The popularity of DOE is due to its tremendous power and efficiency and gives us the answers we seek with a minimum expenditure of time and resources.
Experimental design can be useful in a variety of areas:
- Basic research
- Discovering relationships
- Understanding technology
- Product design
- Establish robust tolerances
- Characterize components
- Include low grade components
- Include low grade materials
- Minimize variation
- Improve performance
- Process development
- Optimize variable settings
- Establish robust tolerances
- Find low cost solutions
- Reduce variation
- Improve process centering
- Reduce cycle-time
- Eliminate defects
- Improve product reliability
- Process improvement
- Solve problems
- Understand relationships
- Perform characterization studies
- Compare equipment and methods
- Measurement systems
- Conduct gage study
- Identify major sources of error
- Minimize measurement error
Like most statistical or Six Sigma tools, DOE has its own language which I’ll now address.
- Factors are the are the key process input variables (KPIV’s) that are the source of variation or have an influence on the mean of the output. We want to determine if a factor has an impact or effect on the response we’re trying to improve. Factors can be quantitative or qualitative. An example of a quantitative factor would be temperature or pressure. A qualitative factor such as material type may evaluate the effect of nylon versus polypropylene on part durability. Factors are the X’s in the equation, Y = F(X).
- Response is the process output we’re trying to improve. This is the Y in the equation, Y = F(X).
- Levels are the different factor values or settings used in an each experimental run of a DOE. For instance, if process temperature is one of the factors we’re interested in, it may have the levels 120 degrees F, 140 degrees F, and 160 degrees F.
- Main effect is the influence a single factor has on the response when it is changed from one level to another.
- Interactions occur when the effect of one factor on the output depends on the level of another factor. Depending on the type of experiment conducted, these interactions can be identified.
- Experimental error is the variation we see in the response or the output we want to improve when virtually identical test conditions exist.
- Repeats are the measurement of the response more than once under similar conditions.
- Replicates occur when the entire experiment is performed more than once for a given set of factors.
- Treatments in an experiment are the various factor levels that are set to carry out in an experimental run. For example, in a two factor, two level experiment where the factors are temperature and pressure, where the levels for temperature are 100 degrees C and 120 degrees C and the levels for pressure are 100 psi and 125 psi, one treatment or experimental run would be where temperature is set at 100 degrees C and pressure is set at 100 psi. Another treatment would be where temperature is set at 100 degrees C and pressure is set at 125 psi, and so on.
There are many different DOE designs. The following are just a few of the more common ones.
- Screening designs are those used to discover the most important factors in a process. Screening experiments are typically used initially when a large number of factors are being considered to determine which of the factors are significant for further study.
- Fractional factorial designs are a subset of a full factorial design and are typically used when the number of factors is between four and eight. In addition, the experimenter must assume some of the interactions will not occur.
- Full factorial designs are experiments that contain all combinations of all levels of all factors. No possible treatment combinations are omitted. The formula for the number of runs in a full factorial experiment is n = LF , where n = the number of experimental runs, L = the number of levels, and F = the number of factors.
As the name “design of experiments” implies, a majority of time should be spent on planning and design of an experiment so that good results can be achieved. At a basic level these steps include:
- Define the problem
- Establish the objective
- Select the response variable
- Select the variable factors
- Select the experimental design
- Conduct the experiment
- Collect the data
- Analyze the data
- Draw conclusions
- Achieve the objective
One of the fallacies of DOE is that it is a one-and-done process where you do one experiment and you’re finished. Typically, it is an iterative process where one experiment and it’s learnings lead to another experiment and then another, and so on.
In this brief article, I’ve tried to stress the importance of design of experiments in better understanding products, services, and processes. The experimenter must also understand that gaining this knowledge is a learning experience that requires patience and a disciplined approach. It cannot be rushed by taking shortcuts or not paying attention to details if learning is the ultimate goal.
Future articles will delve into other DOE topics.