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Robustness Experiments with Two Variance Components



A Aviles


In many experimental settings, different types of factors affect the measured response. The factors that can be set independently of each other are called crossed factors. Nested factors cannot be set independently because the level of one factor takes on a different meaning when other factors are changed. Random nested factors arise from quantity designations and from sampling and measurement procedures. The variances of the random effects associated with nested factors are called variance components. Factor effects on the average are called location effects. Dispersion effects are the effects of the crossed factors on the variance of a response. For situations where crossed factors have effects on the different variance components, then sets of dispersion effects must be identified and estimated to achieve robustness. The main objective of this research is to provide nearly D-optimal experimental design procedures for estimating the location effects of crossed factors, the variance components associated with two nested factors, and the dispersion effects that crossed factors may have on the two variance components. A general class of experimental designs for mixed-effects models with random nested factors, called assembled designs, is introduced in Avil¿s (2001). The use of assembled designs for robustness experiments is presented. In this paper, a practitioner¿s guide is presented for the use of assembled designs to estimate the location effects, the dispersion effects, and two variance components. A heuristic algorithm for finding a nearly D-optimal assembled design with two variance components for a given budget is provided. Ready to use computer programs for the presented experimental design procedures and analysis technique are also available. This paper is a ¿HOW TO¿ manual for robust design for the case of two variance components.
Proceedings Title
American Statistical Association 2001 Proceedings of the Section on Physical and Engineering Sciences
Conference Location
, 1, NV


assembled designs, crossed factors, D-Optimality, dispersion effects, hierarchical nested design, location effects, maximum likelihood, nested factors, variance components


Aviles, A. (2008), Robustness Experiments with Two Variance Components, American Statistical Association 2001 Proceedings of the Section on Physical and Engineering Sciences, , 1, NV (Accessed May 28, 2024)


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Created October 16, 2008