# How does Minitab calculate % tolerance when I enter a one-sided tolerance for a gage R&R study?

## What is %tolerance?

One statistic that is directly affected by specification limits is the %tolerance statistic, which compares the tolerance with the study variation. Ideally, the tolerance should amply encompass the study variation, ensuring the variability due to Gage R&R and part-to-part variation do not push the process output beyond the specification limits.

When a process has two specification limits, the tolerance equals the difference between them, and %Tolerance equals the study variation of a given variation source divided by this tolerance. However, this method is invalid when you provide a single specification limit.

## Example of processes with one specification limit

Many processes operate with only one specification limit. For example, a lumber mill cuts beams to be perfectly straight, but the beams frequently warp during manufacture. Measurements of this warping have an upper specification limit to distinguish acceptable and not acceptable degrees of warping. However, these measurements have no lower specification limit because they cannot take values less than zero. In fact, zero represents a perfectly straight beam with no warping. In addition, some processes have a lower specification limit, but no upper specification limit. A cutlery manufacturer must verify the hardness of its knife blades is higher than 55 on the Rockwell C-scale. The lower specification limit is 55, but no upper specification limit exists.

## How does Minitab calculate %tolerance when I enter a one-sided tolerance

For these cases, Minitab uses the following method:
1. Minitab calculates a one-sided process variation by dividing the study variation statistic by 2.
2. Minitab defines the one-sided tolerance as the absolute value of the difference between the single specification limit and the mean value of all measurements.
3. Minitab calculates the %tolerance statistic by dividing the one-sided process variation by the one-sided tolerance.
TermDescription
Lthe single specification limit
the mean of all observations
###### Note

If the mean of all observations is less than the lower specification limit, or greater than the upper specification limit, the measurements deviate strongly from their acceptable range, and % tolerance is not calculated.