How to Calculate a Tolerance Interval in Excel

A tolerance interval is a range that is likely to contain a specific proportion of a population with a certain level of confidence.

We can use the following formula to calculate the lower and upper limits of a two-sided tolerance interval:

Tolerance Interval Limits: x̄ ± z_(1-p)/2√(n-1)(1+1/n)/X²_{1-α, n-1}

where:

• x̄: sample mean
• z: z critical value
• p: proportion of population to be contained in interval
• n: sample size
• X²: Chi-Square critical value with 1-α significance level and n-1 degrees of freedom

The following example shows how to calculate a tolerance interval in Excel for a given sample.

Example: Calculating a Tolerance Interval in Excel

Suppose we collect the following sample data:

Suppose we would like to create a tolerance interval that contains 99% of the population values with a 95% level of confidence.

We can use the following formulas in Excel to calculate this tolerance interval:

The tolerance interval turns out to be [15.102, 73.565].

We would interpret this to mean that this interval contains 99% of the population values with a 95% level of confidence.

Note that if we change the values for the confidence level or the proportion of the population in the interval, the lower and upper limits of the tolerance interval will automatically change.

Note: You can automatically calculate a tolerance interval for a given sample by using this online Tolerance Interval Calculator.

Additional Resources

The following tutorials explain how to calculate other intervals in Excel:

How to Construct a Prediction Interval in Excel
How to Calculate Confidence Intervals in Excel
How to Plot Confidence Intervals in Excel