For continuous symmetrical distributions and specified tolerance interval characteristics, distribution-free tolerance intervals are presented that require substantially smaller sample sizes than those required for arbitrary continuous populations. In the case of one-sided tolerance intervals, about twice as many sample values are required for the general situation as for the symmetrical situation. For two-sided intervals, the additional sample values required for the general situation vary from about 35 percent to about 85 percent in the cases considered, depending on the specified tolerance interval characteristics. These intervals furnish at least rough protection against all possible violations of the symmetry assumption. In addition, some specialized one-sided and two-sided tolerance intervals are developed for life-test situations involving continuous symmetrical populations. Results for continuous symmetrical populations with known central median values are also presented; the life-testing versions of these intervals are especially useful.
"Distribution-Free Tolerance Intervals for Continuous Symmetrical Populations." Ann. Math. Statist. 33 (3) 1167 - 1174, September, 1962. https://doi.org/10.1214/aoms/1177704479