Tolerance Intervals for the Distribution of True Values in the Presence of Measurement Errors

Abstract

A tolerance-interval procedure for the distribution N(θ, σ2 1 – σ2 2) is derived based on the mutually independent statistics , S 2 1, and S 2 2, which are distributed as follows: has a normal distribution with mean θ and variance σ2 1/n, n 1 S 2 1/σ2 1 is chi-squared with n 1, df, and n 2 S 2 1/σ2 2 is chi-squared with n 2, df. Application to the construction of tolerance intervals for the distribution of true values when observations are contaminated with measurement errors is explained. This includes the problem of constructing tolerance intervals in some growth-curve models. Numerical examples are given to illustrate the procedures.