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.