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TEST

, Volume 16, Issue 3, pp 598–612 | Cite as

Bayesian tolerance intervals for the balanced two-factor nested random effects model

  • Abrie J. Van der Merwe
  • Johan HugoEmail author
Original Paper

Abstract

Statistical intervals, properly calculated from sample data, are likely to be substantially more informative to decision makers than obtaining a point estimate alone and are often of paramount interest to practitioners and thus management (and are usually a great deal more meaningful than statistical significance or hypothesis tests). Wolfinger (1998, J Qual Technol 36:162–170) presented a simulation-based approach for determining Bayesian tolerance intervals in a balanced one-way random effects model. In this note the theory and results of Wolfinger are extended to the balanced two-factor nested random effects model. The example illustrates the flexibility and unique features of the Bayesian simulation method for the construction of tolerance intervals.

Keywords

Tolerance intervals Random effects Bayesian procedure Monte Carlo simulation Predictive density 

Mathematics Subject Classification (2000)

62F15 62F25 62P30 65C05 

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2007

Authors and Affiliations

  1. 1.Department of Mathematical StatisticsUniversity of the Free StateBloemfonteinRepublic of South Africa
  2. 2.Department of StatisticsNelson Mandela Metropolitan UniversityPort ElizabethRepublic of South Africa

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