One-sided tolerance limits for unbalanced one-way random effects models: a generalized Mee and Owen procedure

Abstract

This article proposes a new procedure for obtaining one-sided tolerance limits in unbalanced random effects models. The procedure is a generalization of that proposed by Mee and Owen for the balanced situation, and can be easily implemented, because it only needs a non-central-t table. Two simulation studies are carried out to assess the performance of the new procedure and to compare it with one of the other procedures laid out in previous statistical literature. The article findings show that the new procedure is much simpler to compute and performs better than the previous ones, having inferior values of the gamma bias in a wide range of situations, representative of many actual industrial applications, and behaving also reasonably well in more extreme sampling situations. The use of the new limits is illustrated by an application to an actual example from the steel industry.

Keywords:

• Characteristic values
• Non-central-t
• Statistical algorithms
• Steel industry
• Tolerance intervals
• Unbalanced cluster sampling

2000 Mathematics Subject Classification :

• 62F25
• 62-04
• 62P30

Acknowledgements

The authors would like to thank Calidad Siderúrgica and the Instituto para la Promoción de Armaduras Certificadas, two Spanish steel industry associations, for their support and motivation in this research. The authors are also grateful to the editor and the anonymous referee, whose comments and suggestions on an earlier version led to some improvements in this article.