Alternate Responses

Standard Deviation as Response

Whenever an experimental run results in the production of several samples for each run, the experimenter may consider entering the standard deviation of the per run sample as a secondary response.

For example, each run of a design produces 4 parts to be tested/measured. It would be incorrect in this case to tell the software that there were 4 replicates. Enter this raw data into a spreadsheet, calculate the run average and standard deviation. Copy and paste the average and standard deviation values back into two responses in Design-Expert for analysis. By using the averages, the process variation is reduced, allowing the power of the design to increase. Analyzing the standard deviation may provide some insight into factor settings that reduce the variability of the process.

Fraction Defective Response

Often experimenters wonder if it is okay to use “fractuib of defects” as a response measurement, especially when the defect rate is quite low, perhaps measured in parts per million. The question becomes, how big of a sample size is needed?

There is a rule of thumb that relates sample size (n) and fraction defective (p): np ≥ 5 or even np ≥ 10.

Here is a table based on this minimum rule.

Fraction Defective (p) Sample Size (n) np=
.10 (10%) 50 5
.05 (5%) 100 5
.02 (2%) 250 5
.01 (1%) 500 5
.005 (0.5%) 1000 5

Even using the np ≥ 5 criteria, the sample size gets very large as the defect rate decreases. This sample size is the number of units needed for each run to achieve a reasonable power for detecting a meaingful change in the response.

To properly size a design where the responses are proportions see Upfront Power for Proportions for more details.