Estimating the accuracy of the coverages of outer β‐content tolerance intervals, which control both tails of the normal distribution

Tolerance limits which control both tails of the normal distribution so that there is no more than a proportion β1 in one tail and no more than β2 in the other tail with probability γ may be computed for any size sample. They are computed from X̄ ‐ k1S and X̄ ‐ k2S, where X̄ and S are the usual sample mean and standard deviation and k1 and k2 are constants previously tabulated in Odeh and Owen [3]. The question addressed is, “Just how accurate are the coverages of these intervals (– Infin;, X̄ – k1S) and (X̄ + k2S, ∞) for various size samples?” The question is answered in terms of how widely the coverage of each tail interval differs from the corresponding required content with a given confidence γ′.