Tables for Tolerance Limits for a Normal Population Based on Sample Mean and Range or Mean Range

Let x and r be respectively the observed mean and range in a random sample of size n from a normal population. Values of k 1 are tabulated which ensure a probability β that the pair of limits x ± k 1 r will include at least a proportion p of the population. For tolerance limits of the form x ± k 2 r, where x is the grand mean and r the mean range in N samples of size m each, necessary tables of the factor k 2 are provided for situations where m is either 4 or 5, these being common group sizes in control chart analysis.