Simultaneous Two-Sided Prediction Intervals to Contain at Least l Out of k Future Means from a Normal Distribution

Abstract

Given the sample mean

and the sample standard deviation s computed from a random sample of size n from a N (μ, σ²) distribution, factors r = r(l, k, m, n; γ) are given such that the two-sided prediction interval

± rs will contain at least l out of k future means, computed from samples of size m, with (100γ)% confidence. The original n observations, and the additional k samples of m observations each, are assumed to be independent samples from the same normal population. Values of r are given for γ =0.90, 0.95, 0.99; n =8(1)12, 15, 20, 25, 30, 40, 60, 120, 240, 480, m =1, 5(5)20; k =1(1)9 and l = k; k = 10, 15, 20(10)60, 80, 100 and l = k − j, for j = 0,1.

Keywords:

• prediction limits
• control charts
• multivariate t distribution
• tables