Vangel, Mark G. New methods for one-sided tolerance limits for a one-way balanced random- effects ANOVA model. (English) Zbl 0761.62096 Technometrics 34, No. 2, 176-185 (1992). The problem of determining one-sided tolerance limits or, equivalently, one-sided confidence limits on a quantile of a normal population with variance \(\sigma^ 2=\sigma^ 2_ b+\sigma^ 2_ e\) is considered. The tolerance limits are obtained using data from a one-way balanced random- effects sample from this population. Two procedures are introduced – a simple approximate method based on an asymptotic expansion and a computer-intensive procedure that provides very nearly the nominal confidence in the presence of the nuisance variance-component ratio. For the computer-intensive procedure, tables are provided that eliminate the need for most of the computation for some important situations. Cited in 13 Documents MSC: 62J10 Analysis of variance and covariance (ANOVA) 62N05 Reliability and life testing Keywords:Behrens-Fisher problem; design allowable; nuisance parameters; composite material properties; one-sided tolerance limits; one-sided confidence limits; quantile; normal population; one-way balanced random- effects sample; asymptotic expansion; tables PDFBibTeX XMLCite \textit{M. G. Vangel}, Technometrics 34, No. 2, 176--185 (1992; Zbl 0761.62096) Full Text: DOI