Two-Sided Tolerance Limits for Normal Populations—Some Improvements

Abstract

Ellison has shown that the Wald-Wolfowitz tolerance limits for a normal distribution, , are good only to 0(n/N ²), rather than to 0(1/N ²). Here is distributed normally with mean μ and variance σ²/N while s ²/σ² is distributed as χ² _n /n independently of Thus, for n>N ² the usual values of λ are incorrect; Ellison has proposed an alternative in this case. This paper derives new λ's which have two advantages over the Wald-Wolfowitz and the Ellison limits. First, they are shown to be better approximations. Secondly, they are easily calculated in the sense that only tables of the normal and χ² distributions are required and the solution of a non-linear equation is not required.