Tolerance intervals are used to find where a given percentage of the population can be expected to be found. For example, we could use a small sample taken from a population of results to inform us about where we can expect to find 95 percent of the population. Further, we can specify that we are 95 percent confident that 95 percent of the population would be found within the stated interval.
Here, we will use the tolerance interval tool to find the interval in which we expect a percentage of the population to be found. We have investigated capability with the fill weights of syringe volumes in the previous recipes of this chapter.
Summarized results for means, sample size, and standard deviation are supplied. From these, we want to know where we could expect to find 99 percent of the population of syringe fill volumes with a 95 percent confidence interval. From a recent trial, 30 samples were taken, and these had a mean of 15.15 and a standard deviation of 0.231.
The following steps will use the values of mean, standard deviation, and sample size to generate a tolerance interval that will show 99% of the population with a 95 percent confidence interval:
- Navigate to Stat | Quality Tools and select Tolerance Intervals.
- In the drop-down list for Data, select Summarized data.
- Enter the Sample size as
30. - Enter the Sample mean as
15.15. - Enter the Sample standard deviation as
0.231. - Click on the Options button.
- In the Minimum percentage of population in the interval field, enter
99. - Click on OK.
The results generate a 95 percent tolerance for both a normal distribution and a nonparametric method. With summarized results from a mean, standard deviation, and sample size, we only obtain the normal method.
As we specified, 99 percent of the population between the interval of 14.374 to 15.926 show that we are 95 percent confident that 99 percent of the population may be found within this interval.
Here, we specified the summarized results. It is more advisable to use the raw data than the summarized results. Only referring to the mean and standard deviation does not reveal outliers in the data or other issues, such as time dependant errors.
Raw data is entered as a column, and this would then generate a graphical page showing a histogram of the data with confidence intervals and the normal probability plot.