The major types of Designed Experiments are:
- Full Factorials
- Fractional Factorials
- Screening Experiments
- Response Surface Analysis
- Mixture Experiments
- As their name implies, full factorial experiments look completely at all factors included in the experimentation.
- In full factorials, we study all of the possible treatment combinations that are associated with the factors and their levels. They look at the effects that the main factors and all the interactions between factors have on the measured responses.
- If we use more than two levels for each factor, we can also study whether the effect on the response is linear or if there is curvature in the experimental region for each factor and for the interactions.
- Full factorial experiments can require many experimental runs if many factors at many levels are investigated.
- Fractional factorials look at more factors with fewer runs.
- Using a fractional factorial involves making a major assumption – that higher order interactions (those between three or more factors) are not significant.
- Fractional factorial designs are derived from full factorial matrices by substituting higher order interactions with new factors.
- To increase the efficiency of experimentation, fractional factorials give up some power in analyzing the effects on the response. Fractional factorials will still look at the main factor effects, but they lead to compromises when looking into interaction effects.
- This compromise is called confounding.
- Just because we have confounded main factor and interaction effects doesn’t mean fractional factorials are a poor choice. The risks we are taking are well worth it.
- Three-way and higher interactions are rare and even two-way interactions are not that commonplace. The efficiency in experimentation more than makes up for the confounding of results that we get.
- Screening experiments are the ultimate fractional factorial experiments. These experiments assume that all interactions, even two-way interactions, are not significant.
- They literally screen the factors, or variables, in the process and determine which are the critical variables that affect the process output.
- There are two major families of screening experiments:
- Drs. Plackett and Burman developed the original family of screening experiments matrices in the 1940s.
- Dr. Taguchi adapted the Plackett-Burman screening designs. He modified the Plackett-Burman design approach so that the experimenter could assume that interactions are not significant, yet could test for some two-way interactions at the same time.
Response Surface Analysis
- Response surface analysis is an off-line optimization technique. Usually, 2 factors are studied; but 3 or more can be studied.
- With response surface analysis, we run a series of full factorial experiments and map the response to generate mathematical equations that describe how factors affect the response.
- EVOP (evolutionary operations) is an online optimization technique.
- Usually, two factors are studied using small, step changes in factor levels to incrementally explore the operating bounds of the process.
- The designs we have looked at so far work fine for variables like temperature, pressure, or time and even for material substitutions. But they will not work in situations where we need to study how changes in the formulation affect the final properties of a material.
- When dealing with formulations, there are added constraints on the experimenter. When dealing with composition, the sum of all of the weight fractions of all the components must add up to 1.0 and each of the individual components must have a weight fraction between 0 and 1.0. Mixture experiments provide techniques to operate within these constraints.
- When setting up an experimental strategy, it is usually best to start with screening experiments to separate out the important (significant) factors from the many factors in a process.
- From there we can experiment further on the significant factors and study their interactions with fractional factorial or full factorial experiments.
- In some cases, once we have identified the power factors, we may want to optimize the response using the power factors in one of the two major DOE techniques for optimizing processes, Response Surface Analysis or EVOP.