Example of Power and Sample Size for Plackett-Burman Design

A quality engineer plans a designed experiment to study the transparency of a plastic part. Before conducting the experiment, the engineer wants to ensure that the experiment will have adequate power. The engineer plans to examine 10 numeric factors. For a base design, the engineer selects a design with 12 experimental runs and 3 center points. The engineer wants to be able to detect an effect of 5 transparency units with no more than 4 replicates. Previous experimentation indicates that 4.5 is an adequate estimate of the standard deviation. The engineer decides to calculate the power for a model with main effects and a term for center points.

  1. Choose Stat > Power and Sample Size > Plackett-Burman Design.
  2. In Number of factors, enter 10.
  3. In Number of corner points, select 12.
  4. In Replicates, enter 1 2 3 4.
  5. In Effects, enter 5.
  6. In Number of center points, enter 3.
  7. In Standard deviation, enter 4.5.
  8. Click OK.

Interpret the results

The unreplicated design has a power of approximately 30%. With 3 replicates and 39 total runs, the design has nearly a 90% chance to detect an important effect. With 4 replicates and 51 total runs, the design has more than a 95% chance to detect an important effect. The power curve shows the relationship between power and effect size. The symbols on the curves represent the effect size of 5 that the engineer specified. The engineer decides that the 3 replicate design provides enough power.

Power and Sample Size

Plackett-Burman Design α = 0.05 Assumed standard deviation = 4.5 Method Factors: 10 Design: 12 Center pts (total): 3 Including a term for center points in model.
Results Center Total Points Effect Reps Runs Power 3 5 1 15 0.272032 3 5 2 27 0.720550 3 5 3 39 0.894838 3 5 4 51 0.963485
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