The problem of determining one-sided tolerance limits or, equivalently, one-sided confidence limits on a quantile of a normal population with variance σ 2=σ b2+σ e2 is considered in this article. 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. Tolerance limits for strength are routinely used in structural design. Material strength, particularly for composite materials, often exhibits considerable between-batch variability. A tolerance limit that provides nearly the nominal confidence is usually preferable to a conservative limit, since a conservative tolerance limit underestimates the capability of the material. An aircraft-industry application to determining tolerance limits for composite material properties in the presence of between-batch variability is discussed.
The mission of Technometrics is to contribute to the development and use of statistical methods in the physical, chemical, and engineering sciences. Its content features papers that describe new statistical techniques, illustrate innovative application of known statistical methods, or review methods, issues, or philosophy in a particular area of statistics or science, when such papers are consistent with the journal's mission. Application of proposed methodology is justified, usually by means of an actual problem in the physical, chemical, or engineering sciences. Papers in the journal reflect modern practice. This includes an emphasis on new statistical approaches to screening, modeling, pattern characterization, and change detection that take advantage of massive computing capabilities. Papers also reflect shifts in attitudes about data analysis (e.g., less formal hypothesis testing, more fitted models via graphical analysis), and in how important application areas are managed (e.g., quality assurance through robust design rather than detailed inspection).
Building on two centuries' experience, Taylor & Francis has grown rapidlyover the last two decades to become a leading international academic publisher.The Group publishes over 800 journals and over 1,800 new books each year, coveringa wide variety of subject areas and incorporating the journal imprints of Routledge,Carfax, Spon Press, Psychology Press, Martin Dunitz, and Taylor & Francis.Taylor & Francis is fully committed to the publication and dissemination of scholarly information of the highest quality, and today this remains the primary goal.
This item is part of a JSTOR Collection.
For terms and use, please refer to our Terms and Conditions
Technometrics
© 1992 American Statistical Association
Request Permissions
