Non-Parametric Tolerance Limits

Abstract

In this note are presented graphs of minimum probable population coverage by sample blocks determined by the order statistics of a sample from a population with a continuous but unknown cumulative distribution function (c.d.f.). The graphs are constructed for the three tolerance levels .90, .95, and .99. The number, m, of blocks excluded from the tolerance region runs as follows: m = 1(1)6(2)10(5)30(10)60(20)100, and the sample size, n, runs from m to 500. Thus the curves show the solution, β, of the equation 1−α=Iβ(n−m+1,m) for α=.90,.95,.99 over the range of n and m given above, where Ix(p,q) is Pearson's notation for the incomplete beta function. Examples are cited below for the one- and two-variate cases. Finally, the exact and approximate formulae used in computations for these graphs are given.