Sample Size for Tolerance Intervals

Calculating Sample Size - Nonparametric Method

  

Minitab also calculates sample size using the nonparametric method. The results for the nonparametric method include the following:

·    Achieved confidence: The exact confidence level that is associated with the specified sample size. The achieved confidence is usually greater than or equal to your desired confidence level. However, if your sample size is too small, the achieved confidence can be lower than the desired level.

·    Achieved error probability: The exact margin of error probability that is associated with the specified sample size. The achieved error probability is usually close to your desired level.

Example Output

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.

Interpretation

The results of the sample size calculations show that, 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.