Sample Size Considerations

05/28/2008

How do you choose a sample size? is there a definite number or does it always depend on the population (# of parts being manufactured)?
In the real world, my boss always told me to get at least 30 pieces, and his reasoning was because it makes statistical sense. I think the reasoning does not have much weight. However, it seems that everywhere I worked the magic number is 30
Freddy B., Quality Assurance Engineer III

When you work with populations, such as in drawing samples from a homogenous lot to make decisions about lot acceptability, the sample size is determined with consideration to the power of the sample. Generally, you will have greater power to distinguish the deviation of the lot from the acceptability standards when:

·      there is a large difference between the lot mean and the acceptability standard;

·      the standard deviation of the population is small;

·      the sample is large;

·      the significance of the test is large. In other words, all else being equal, the power to detect a difference is better when you do not care if you make a false assertion.

You can calculate the sample size to detect a given difference at given significance (alpha) and power using statistical algorithms such as found at http://www.stat.ubc.ca/~rollin/stats/ssize/n2.aspl.
This topic is covered in more detail in our Black Belt course, as well as the Six Sigma Demystified and Six Sigma Handbook texts.
For process data, where control charts are the optimal tool, the subgroup size is determined with consideration to Rational Subgroup concerns. (See Rational Subgroups). The number of subgroups necessary to properly define the control limits is based on the process dynamics, as well as statistical concerns. Statistically, thirty subgroups provide a reasonable estimate of process variation when a subgroup size of 5 is used, but more subgroups are needed for smaller subgroup sizes. As a rule of thumb, I generally suggest 150 -200 observations, grouped in rational subgroups of size one to five. See also: Defining Control Limits.

Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).