Simultaneous Tolerance Intervals for Normal Populations With, Common Variance

Abstract

This article proposes simultaneous tolerance limits for L normally distributed populations with a common variance, assuming that independent random samples are available from the populations. Tables of factors are provided for both one-sided limits and two-sided intervals for the case of equal sample sizes. Approximations and formulas for exact computations are discussed for applications in which the sample sizes differ. The related problem of simultaneous prediction intervals for the L populations is also discussed as a special case of the simultaneous prediction intervals proposed by Hahn (1972). Citations are provided for tables of factors for both one- and two-sided simultaneous prediction intervals.

KEY WORDS:

• Multivariate t distribution
• Prediction interval
• Simultaneous inference