Example of creating Tolerance Intervals
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A light bulb manufacturer wants to calculate the burn time (lower bound) that is exceeded by at least 95% of all light bulbs. The manufacturer collects a random sample of 100 observed burning times in order to calculate the lower tolerance bound.

1    Open the worksheet LIGHTBULB.MTW.

2    Choose Stat > Quality Tools > Tolerance Intervals.

3    Choose One or more samples, each in a column, and enter Hours.

4    Click Options. In Tolerance interval, choose Lower bound.

5    Click OK in each dialog box.

Session window output

Tolerance Interval: Hours

 

 

Method

 

Confidence level                   95%

Percent of population in interval  95%

 

 

Statistics

 

Variable    N      Mean   StDev

Hours     100  1248.004  84.118

 

 

95% Lower Tolerance Bound

 

            Normal  Nonparametric    Achieved

Variable    Method         Method  Confidence

Hours     1085.947       1070.700       96.3%

 

Achieved confidence level applies only to nonparametric method

Graph window output

Interpreting the results

The manufacturer is interested in the minimum burn time that most light bulbs will exceed. Minitab calculates tolerance intervals using both the normal and nonparametric methods. If you can reasonably assume that your data are normally distributed, use the normal method results. Otherwise, use the nonparametric results. See Normal and nonparametric methods for tolerance intervals for more details.

The normal probability plot shows an approximately linear pattern that is consistent with a normal distribution. Additionally, the Anderson-Darling test's p-value (0.340) is greater than any reasonable a level. Thus, there is not enough evidence to suggest that the data do not follow a normal distribution. Use the normal method results.

In the graph, the Normal lower bound (1085.947) appears in the box on the right. The statistics table also displays the sample size and point estimates of the mean burn time (1248.004 hours) and the standard deviation (84.118) for the entire light bulb population.

The manufacturer is 95% confident that at least 95% of all light bulbs produced will exceed 1085.947 hours of burn time.