Faulkenberry-Weeks sample size calculation for tolerance intervals

[Bashburz]

The Power and Sample Size Explorer is lacking an option for tolerance intervals. It is often desirable to get a minimum sample size for a tolerance interval based on the desired margin of error and its probability.

Faulkenberry-Weeks is such an approach. Find inspiration in what Minitab does: Methods and formulas for Sample Size for Tolerance Intervals - Minitab

[mia_stephens]

Hi @Bashburz , thanks for submitting this request. In JMP 17, a sample size explorer for tolerance intervals is available under Confidence Intervals > Margin of Error for One Sample Mean.

From the JMP Documentation: "For the tolerance interval on a proportion q of the population, the margin of error or bound is computed based on approximate procedures described in Krishnamoorthy and Mathew (2009)."

Does this satisfy your request?

[Bashburz]

Hi @mia_stephens,

thank you very much for pointing this functionality out to me. I think that it is already very useful for planning of data collection.

However, it does not answer all the questions regarding tolerance intervals. There is some ambiguity in the terms used: "margin of error" in JMP refers to the half-width of the tolerance interval. This is of course a useful parameter that the interval explorer allows to predict. But there is a further consideration that is also called margin of error in the literature:

Margin of error: The margin of error, m%, measures the additional percentage of the population, beyond the target of p%, that might be included in the interval.

Margin of error probability: The margin of error probability is the probability that the interval will be wider than p% by m% or more. Common values for the margin of error probability include 0.01, 0.05, and 0.1. Larger values can result in a tolerance interval that covers a much larger percentage of the population than the target, p%.

So it's a further quantitation of the risk that the predicted tolerance interval will be wider than calculated. Therefore, I think that implementation of the Faulkenberry-Weeks approach into the existing caluclation will bring additional benefit.

[mia_stephens]

Thank you @Bashburz for this additional information. We have passed this along to the development team for consideration in a future release.