Article

# Simultaneous Tolerance Intervals for Normal Populations With, Common Variance

Technometrics (Impact Factor: 1.79). 02/1990; 32(1):83-92. DOI: 10.1080/00401706.1990.10484595

**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.

- [Show abstract] [Hide abstract]

**ABSTRACT:**This article provides methods for computing tolerance limits from a stratified random sample. It is assumed that the characteristic of interest is normally distributed within each stratum and that the within-stratum variances are equal. Approximate β-expectation and β-content tolerance limits are proposed for the population. The adequacy of the proposed limits is evaluated via simulation.Technometrics 02/1989; 31(1):99-105. DOI:10.1080/00401706.1989.10488480 · 1.79 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper considers the problem of constructing simultaneous prediction and tolerance intervals for sets of contrasts of normal variables in situations where simultaneous intervals are available. Tables are given with critical values used in simultaneous tolerance bounds for two classes of contrasts: pairwise many-one and profile type.Communication in Statistics- Theory and Methods 01/1991; 20(5-6):1861-1870. DOI:10.1080/03610929108830603 · 0.28 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Assuming the statistical model of the random effects one-way layout under the usual conditions (normality and independence) and considering a realization of this model, the present paper treats the problem of the computation of one-sided tolerance limits for the corresponding defining random variable on the basis of the Monte Carlo method. Since subpopulations occurring in this scope can be considered as batches and since the model under consideration is sometimes called ‘cluster sampling model’, it is obvious that the present problem has important applications in the field of statistical quality control.—The Monte Carlo approach together with its realization by a computer program for the determination of such tolerance limit factors proved elementary and effective. In particular, in the important cases of limited sampling information (costs), this approach led to more realistic values in comparison, with other approaches. An additional problem occurring in connection with simultaneous statistical inference was solved by means of the Bonferroni inequality. Finally, the paper contains a computer program (FORTRAN 77) the applicability and use of which is shown by numerical examples.Forschung auf dem Gebiete des Ingenieurwesens 03/1992; 58(4):77-82. DOI:10.1007/BF02561487 · 0.14 Impact Factor

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.