Example of calculating sample size for a tolerance interval
main topic     interpreting results     session command     see also 

You manufacture round metal washers. You want to assess the variability in the thickness of your washers. You plan to measure a sample of washers and to calculate a tolerance interval that includes 95% of the population.

If your sample size is small, then the margin of error may be too large and the tolerance interval may greatly overestimate the variability in the thickness of your washers. You want to know how many washers you need to measure to achieve margins of error of 1% and 2% for the tolerance interval. You also want to know what margins of error you can achieve with samples of 50 or 100 washers.

1    Choose Stat > Power and Sample Size > Sample Size for Tolerance Intervals.

2    Select Calculate sample sizes.

3    In Margins of error, enter 1 2.

4    Click OK.

Session window output

Sample Size for Tolerance Intervals

 

 

Method

 

Confidence level                    95%

Percent of population in interval   95%

Margin of error probability        0.05

 

 

Sample size for 95% Tolerance Interval

 

  Margin  Normal  Nonparametric    Achieved  Achieved Error

of Error  Method         Method  Confidence     Probability

      1%    2480           4654       95.0%           0.049

      2%     525           1036       95.1%           0.048

 

Achieved confidence and achieved error probability apply only to nonparametric method.

Interpreting the results

The results of the sample size calculations show that, to achieve a margin of error of 1% using the normal method, you need to collect 2480 observations. In other words, with 2480 observations, the probability that a tolerance interval will contain 96% or more of the population is only 0.05.

If you are willing to accept a 2% margin of error, you need only 525 observations using the normal method.

To achieve a margin of error of 1% using the nonparametric method, you need to collect 4654 observations. With 4654 observations, the achieved error probability is 0.049. In other words, the probability that a tolerance interval will contain 96% or more of the population is only 0.049.

If you are willing to accept a 2% margin of error, then you need only 1036 observations for the nonparametric method. With 1036 observations, you achieve a confidence level of 95.1% and an error probability of 0.048.