'Sampling Inspection in Statistical Quality Control', Griffin's Statistical Monographs, Number 37, London. While Guenther provides a w correction factor: w*K 2, we will not employ it here in order to match the Minitab and SigmaXL results. The formula to be used is shown in this excerpt from the NIST Engineering Statistics Handbook. 'Two-sided Tolerance Limits for Normal Populations - Some Improvements', Journal of the American Statistical Association, 64, pages 610-620.

We will use the method developed by Howe in 1969. There are methods available for computing statistical tolerance intervals using a non-parametric approach for non-normal data. We are also assuming the data is normally distributed for this simpler example. Now, after the video, let’s give an example of a two-sided statistical tolerance interval use and calculate the interval using two platforms often used in Six Sigma training: Minitab and SigmaXL. The following short video by Keith Bower does a nice job of introducing the concept of statistical tolerance intervals and why you should use them. Blood pressure levels for a certain percentage of the population for a population segmentĪs you can imagine, the uses are endless.NOTE: One can also calculate one-sided intervals for a minimum or a maximum depending on the nature of the investigation. This would be a two-sided interval, the subject of our discussion. For example, suppose we wish to know with 95% confidence, the range of 90% of the individual values for a product based on a random sample. For that, we have the statistical tolerance interval.Īs defined, a statistical tolerance interval infers the location of a given proportion of the individual values at a given level of confidence. In decision-making, it is often more important to focus on individual values. However, confidence intervals for the mean are inferring the location of averages. That is used to calculate a confidence interval regarding the location of the population mean, the inference. The most familiar sample statistic is the sample mean. We take a representative sample from a population, compute sample statistics, and make an inference about a population parameter. In this blog, we will see how statistical tolerance intervals can be applied to infer the proportion of individual products within a population.

Confidence interval minitab 17