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Scholarly Works (2 results)

  • Article
  • Peer Reviewed
UC Riverside Previously Published Works (2013)
Fractional factorial designs with n treatments for 2m factorial experiments are considered to identify a class of (m2) models with the common parameters representing the general mean and the main effects while the uncommon parameter in each model represents a two factor interaction. A new property Pg(v1,. .,vg) of designs is introduced in this context to least squares estimate the uncommon parameters in g groups of models so that the estimates of vi such parameters in the ith group have a common variance (CV), where g is an integer satisfying 1≤g≤(m2), i=1, ..., g, v1+⋯+vg=(m2). The property P1(v1) is desirable to have for the fractional factorial designs to identify the (m2) models. The concept of CV designs having the property P1(v1) is introduced for the model identification. Several series of CV designs for general m and n are presented. For fixed values of n and m, Dn,m represents the class of all fractional factorial CV designs having the property P1(v1). CV designs in Dn,m have possible unequal values for the common variance. The smaller the common variance, the better the CV designs for the model identification. The concept of optimum common variance (OPTCV) design having the smallest common variance in Dn,m is also introduced. This paper presents some OPTCV designs. © 2013 Elsevier B.V.
    Cover page: Common variance fractional factorial designs and their optimality to identify a class of models
    • Thesis
    • Peer Reviewed
    UC Riverside Electronic Theses and Dissertations (2011)

    Models containing the general mean, main effects, and all possible k two-factor interaction effects are considered for factorial experiments with m factors observed at two levels each. Specifically, fractional factorial designs consisting of n runs which permit the identification and discrimination of the models of interest are evaluated and classified. The classifications are dependent on a new property introduced in this dissertation, denoted PV, g≥1, which relies on the structure of the variance-covariance matrix for the estimates of the model parameters. Designs with the property, PV, g≥1, permit to divide the models in the class considered into g groups so that all models in a group have equal variances for the least squares estimates of the k two-factor interaction effects. Ghosh-Tian optimum designs [Ghosh and Tian (2006)] for m=4, n=6,...,11, k=1, and m=5, n=7,...,16, k=1 are classified with respect to g values, g≥1, in the property PV and presented through illustrative examples.

    Several characterizations of designs with PV, g≥1, are provided for the case when k=1. Designs such as balanced designs, isomorphic designs and complementary designs with the property PV are proven to have P<1V for k=1. Tables identifying all such balanced designs are provided. It is noted that although D9.2 and D14 are not balanced, these designs in fact take a special form resulting in P<1V for k=1. These special forms are investigated in depth.

    In addition, the construction of all designs giving P<1V for m=3, n=5, 6, 7, 8, k=1 and m=4, n=6,...,16, k=1 are described. Further, occurrences of P<1V are presented for fractional factorial designs when m=5, n=7, 8, 9, k=1.

    Finally, additional characterizations of PV, g≥1, when P>1 are given and illustrated through various examples. Special designs are presented with the property P<1V for maxk which is the largest value of k in the models of interest that the design has the ability to identify and discriminate. It is shown that balanced designs will have P<1V for k=mC2 . Tables identifying all such balanced designs are provided.

      Cover page: Characterization of Special Variance Structures for Designs in Model Identification and Discrimination
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