Screening Experiments Using Plackett-Burman Design

At the initial stages of industrial experimentation, it's common for an investigator to identify a large number of potential variables/factors, which usually results in a large number of runs for the experiment. To avoid this, the investigator might choose to first use a "screening design" to identify those factors that have large effects on the response. In such designs, only main effects are estimated; interactions between factors are usually considered insignificant and are neglected. The Plackett-Burman design type is a two level fractional factorial screening design for studying N-1 variables using N runs, where N is a multiple of 4. In this article, we will present an example using a Plackett-Burman design in DOE++.

Example

A company is producing a new chemical product. From previous experience, the design engineer thinks that the yield of this new product might be affected by eleven potential factors, including ambient temperature, humidity, load, fan speed, voltage, input material weight, vibration, current, motor speed, mixture temperature and the level of catalyst. To identify the important factors and determine the settings that will give the highest yield, the design engineer has to conduct experimental tests. If he runs a two level full factorial design, the total number of runs will be 2>11 = 2,048. This huge number of runs will be time-consuming and costly. Since he thinks that the interactions between these potential factors are unlikely to be extremely important, the design engineer decides to first run a Plackett-Burman design and determine the important factors.

The following settings were used for the Plackett-Burman experiment:

These are the steps to create a Plackett-Burman design in DOE++.

Step 1: Click Design Type on the folio's navigation panel, and then select Plackett-Burman Factorial.

Step 2: Rename the response by clicking Response 1 in the navigation panel and entering Yield for the name.

Step 3: Specify the number of factors by clicking the Factors heading in the navigation panel and choosing 11 from the Number of Factors drop-down list.

Step 4: Define each factor by clicking it in the navigation panel and editing its properties (from the table above) in the input panel. Note that the Load factor uses Qualitative levels and all other factors use Quantitative levels; this is specified in the Factor Type drop-down list. The first factor is defined as shown next.

Step 5: Click the Additional Settings heading in the navigation panel. Set the Base # of Runs to 12.

The following picture shows a summary of the design settings that were used for this example. Notice that the total number of runs is 12, which is equal to the total number of factors plus 1.

The 12 runs were conducted according to the engineer's design table. The factor combinations and the corresponding yield for each run are shown next.

The regression equation is obtained as:

Using the effect probability plot, the engineer was able to identify five important factors in the experiment. These are the input material weight, relative humidity, motor speed, catalyst and mixture temperature. These important factors are marked with red squares in the plot, as shown next.

Conclusion

Plackett-Burman designs are highly efficient designs. They use the minimum number of runs to quickly identify the factors with a significant effect on the response. The factors that are identified as important are then investigated more thoroughly in subsequent experiments.