Experimental Design

Design of Experiments or DOE are a standardized set of experiments to learn about, improve, and/or solve manufacturing problems.  They are not limited to manufacturing; indeed, they were actually created to aid agriculture, their use in manufacturing however is far greater.  Seminars in DOE are made to sound simple; the actual execution in manufacturing however, can be quite complicated and involved. Additionally, the tendency when choosing to run a DOE is to over reach, to answer all the questions in a short time rather than a more systematic approach that while longer and more time consuming is also far more likely to succeed.

Most seminars, which generally last 1 to 3 days, focus on just one type of DOE.  There are many different designs to choose from but just three main types of designs are generally all one needs.  Each of these has main types comes with its own advantage and disadvantages.

Screening Design

Advantages

•  Relatively small number of runs for a large number of factors.
•  Can be capable of a high degree of precision in estimate of effects.

Disadvantage

•  Most screening designs cannot be expanded into different experimental designs.

Factorial Designs

Advantages

• Estimation of interaction effects.
• High degree of precision in estimating effects.
• Easy to conceptualize.
• Center points can provide estimates of the lack of linearity of factor effects as well as when spaced out at the beginning, middle, and end of the DOE provide a check on process stability; center points should agree with each other.
• Can be broken down into fractional parts.  Breaking down a factorial into fractional parts has advantages beyond just time constraints.  A half fraction can also double as a screening design allowing verification that selected factor do have a significant effect while reducing resource constraints.  The two halves of the factorial can be used as a check of DOE results; how well the estimates agree with each other.

Disadvantages

• Large number of runs
• Potential for failed runs at the process extremes.  If there is a potential that when some combination of factors will not produce useable product consider a simple range finding study or simply run the machine or process for several minutes at that setting to verity if this setting would be a problem  If it is consider narrowing the process window or using an alternate design such as Box-Behken design which runs only one factor at a time at high levels.
• If interaction effects are small, or non-existent the additional resources spent attempting to estimate them might be wasted.
• Can be difficult to run correctly due to number of process changes to be made for each run.

Response Surface

Advantages

• Ability to define curved responses.
• Several designs available.  The Box-Behnken design can estimate higher order effects such as squared.  The Star Design can be used to find an optimum process setting.
• Easily expanded.
• Runs not at process extremes.

Disadvantages

• Large number of runs.
• Not easy to conceptualize.
• Difficult to analyze.

Considerations:

Factors:  There are two types of factors in a DOE; variable and categorical.  Each of these also have two types; fixed and random. Fixed factors are preselected, for example, machine speed to be set at 100 rpm or temperature at 200C.  Most DOEs use fixed factors. This document will not describe the few instances when random factors might be used.

Blocking:  Ideally a DOE should be completely randomized.  However, in some instances factor levels may be difficult to change.  Oven temperatures and injection molding temperatures are frequently difficult to change quickly and as such are set at one level for a portion of the DOE, then changed for another portion.   Categorical factor such as material isn’t always easy to change run to run, so a factor may be set at one level for a series of runs. Running at a specific factor level for several runs is calling blocking.  It is important to identify blocking in the DOE so that Blocking itself can be treated as a factor to determine if it had effect.

Factor levels:  The most basic for all designs are two levels, low and high.  A third midpoint can be used when an effect is not thought to be linear.  Center points can help but do not provide as good an estimate. When adding a third level to a factorial design consideration should be given to the expansion of the number of runs.  For example, a three factor, two level DOE requires 8 runs. Setting just one factor at three levels increases the number of runs to 12.

Replications:  A replication in a DOE is a duplication of all or some subset of the DOE treatments or runs.  Replications are different than repeat measurements. Repeat measurements might call for measuring three samples at each treatment condition.  Replication is the replication of the treatment condition at a second or multiple points in the DOE. Replications are very useful in uncontrolled processes where special causes of variation might occur at various points in the DOE.  Running multiple center points is a type of replication and is very useful for identifying if unknown process changes occurred.

Repeat measurements: The purpose of a DOE is to determine if different factor settings produce different output results.  To determine if two or more treatments in a DOE are different the mean of the treatments or runs must be estimated with sufficient precision that the signal to noise can determine the means different.   How different needs to be asked up front? Is the researcher looking for a two standard deviation difference; three standard deviations or just one?

The desire is to have a comfortable margin between the process output and the specification.  If a process currently operates say 4.5 standard deviations from the specification it already has a comfortable margin, and whether a DOE is necessary is questionable let alone the sample size.  However, for a process that operates just 3 or less standard deviations from the specification then steps to reduce variation and/or shift the process mean away from the specifications are necessary and sample sizes for that DOE can be crucial.

Center points:  When a process is not in a state of statistical control or monitored with a control chart that process may be subject to special causes of variation influencing the output.  Multiple center points are a way of knowing that the process can be returned to a repeatable “steady state.” Center points at the beginning, middle, and end of a DOE can document that the process started, ended, and operated throughout the DOE subject only to the independent variables being tested in the DOE.  The center points can also be compared with high and low setting to verify that that are in the middle.

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