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Tolerance Intervals for Normal Distribution

Revised: 09/08/2005

Introduction. Loosely speaking, a *tolerance
interval* for a measured quantity is the interval in which there is some
"likelihood" (or, of which you feel a some "level of confidence") that a
specified fraction of the population's values lie, based on a sample that
you measured from this population. Tolerance intervals have been widely used
in statistical process control. This page will calculate tolerance intervals
for any specified population fraction, and for any specified level of confidence,
from the mean and standard deviation of a finite sample, under the assumption
that the population is normally distributed. One-sided (upper and lower)
intervals, as well as the two-sided interval, are calculated.

Reference: NIST/Sematech *Engineering Statistics
Handbook*, Section 7.2.6.3

http://www.itl.nist.gov/div898/handbook/prc/section2/prc263.htm

The fields below are pre-loaded with sample data taken from one of the examples
in this Handbook.

Note: The very last line on the Handbook page:

"*The upper (one-sided) tolerance limit is therefore 97.07 + 1.8752*2.68
= 102.096.*"

is wrong. The standard deviation in their example is 0.0268, not 2.68, so
the answer should be 97.12, not 102.096 .

**These calculations are also available in a downloadable
Excel spreadsheet: tolintvl.xls .**

Instructions: Enter the five parameters (N, mean,
SD, confidence level, and coverage fraction) into the five cells below. Use
the Tab key after entering each value. The calculations will be updated whenever
you "leave" one of these five fields, either by tabbing out of it, or by
clicking in another field.

Before using this page for the first time, make sure you
read the JavaStat user interface guidelines.

Return to the Interactive Statistics page or to
the JCP Home Page

Send e-mail to John C. Pezzullo at