Margin of error and margin of error probability for tolerance intervals

A more precise tolerance interval is more useful and more informative. If a tolerance interval is not sufficiently precise, it can be too wide and include a much larger percentage of the population than you specify. Minitab's Sample Size for Tolerance Intervals can help you determine the precision of your tolerance intervals.

Suppose that p% is the targeted minimum percentage of the population for a tolerance interval. The following statistics define the precision of the tolerance interval:

·    Margin of error: The margin of error, m%, measures the additional percentage of the population, beyond the desired 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 for the margin of error probability can result in a tolerance interval that covers a much larger percentage of the population than the target, p%.

For example, suppose that want to calculate a tolerance interval that covers 90% of the population. Using the default margin of error probability of 0.05 (5%), you determine that the margin of error for the interval is 2%. Together, these statistics indicate that there is only a 5% chance that your interval will include 92% or more of the population. (92% = 90% [the targeted minimum percentage of the population, p%] + 2% [the margin of error, m%])