Projection properties of three-level screening designs

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY Australian & New Zealand Journal of Statistics Pub Date : 2021-02-22 DOI:10.1111/anzs.12306

Mohammed A. Alomair, Stelios D. Georgiou, Manohar Aggarwal

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引用次数: 3

Abstract

Screening designs are important for finding the factors that have a major effect on industrial experiments. In regard to quantitative factors, certain experimenters prefer three-level rather than two-level factors because having three levels can provide some assessments for capturing curvature in the response. In a recent paper, Jones and Nachtsheim, Journal of Quality Technology43, 1–15, proposed a new class of designs called definitive screening designs. Definitive screening designs have more favourable properties than classical screening designs. In this paper, we study the projection properties of three-level screening designs. The comparison is based on several criteria such as D-efficiency, G-efficiency, A-efficiency and average of variance over a range of models that include main effects, interaction and quadratic terms. New designs are generated as projections of the full designs into a smaller factor dimensional space. The best projections and their properties are presented in a tabular form.

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三级筛分设计的投影特性

筛选设计对于发现对工业实验有主要影响的因素是很重要的。在定量因素方面，某些实验者更喜欢三层因子而不是两层因子，因为有三层因子可以对捕捉反应中的曲率提供一些评估。在最近的一篇论文中，Jones和Nachtsheim在《质量技术杂志》(Journal of Quality technology) 43期第1-15期提出了一种新的设计类型，称为最终筛选设计。决定性筛分设计比经典筛分设计具有更有利的性能。本文研究了三层筛分设计的投影特性。这种比较是基于若干标准，如d效率、g效率、a效率和包括主效应、相互作用和二次项在内的一系列模型的方差平均值。新设计作为完整设计的投影产生到一个较小的因子维度空间。最佳投影及其性质以表格形式呈现。

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来源期刊

Australian & New Zealand Journal of Statistics 数学-统计学与概率论

CiteScore

1.30

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association. The main body of the journal is divided into three sections. The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data. The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context. The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems.