Abstract
The paper concerns a random property T of a manufactured product that must with high probability e.g. P* = 95% exceed a specified quantity ηa called the characteristic value (CV). However the product comes from any one of K different subpopulations that may represent such things as manufacturers, regions or countries; the distribution of T will generally differ from one subpopulation to another and so will the associated CV ηka, = 1,…,K. Moreover in applications such as the one we focus on in this paper where the subpopulations are species, the subpopulation of origin will, for both strategic or practical reasons, not be known. The problem confronted in this paper is the creation of a single CV for the population consisting of the union of all the subpopulations. A solution proposed long ago in the application concerning manufactured lumber that is addressed in this paper, selects a subset of the subpopulations using random samples of the T s, called the subset of controlling species CS, that includes the smallest of the {ηka} with high probability. The estimated CV for the entire population is then found by combining and treating as one, the samples for the subpopulations in CS. That method has been published in an ASTM standards document for the lumber industry to ensure the structural engineering strength of manufactured lumber. However this published method has been shown to have some unexpected and undesirable properties, leading to the search for an alternative and this paper. The paper presents and compares three subset selection methods. The simplest of the three methods is an extension of a classical nonparametric method for subset selection. The remaining two, which are more complex, are variations of nonparametric Bayesian methods. Each of the three is seen as a possible candidate for consideration by ASTM committees as a possible replacement for the ASTM method for lumber species depending on what criterion is ultimately used for its selection. But they may well apply in other contexts as well.
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Acknowledgements
We are indebted to Conroy Lum from FPInnovations for introducing the second author to the topic addressed in this report and for many helpful discussions during the course of the work. Thanks also to Kyle Hambrook and John Petkau for helpful discussions during the course of the work.
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Supported by a Collaborative Research and Development grant from the Natural Sciences and Engineering Research Council of Canada.
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Kondo, Y., Zidek, J.V., Taylor, C.G. et al. Bayesian Subset Selection Methods for Finding Engineering Design Values: an Application to Lumber Strength. Sankhya A 80 (Suppl 1), 146–172 (2018). https://doi.org/10.1007/s13171-018-00157-w
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DOI: https://doi.org/10.1007/s13171-018-00157-w