MATHEMATICAL ENGINEERING TECHNICAL REPORTS Some Characterizations of Affinely Full-dimensional Factorial Designs
نویسندگان
چکیده
A new class of two-level non-regular fractional factorial designs is defined. We call this class an affinely full-dimensional factorial design, meaning that design points in the design of this class are not contained in any affine hyperplane in the vector space over F2. The property of the indicator function for this class is also clarified. A fractional factorial design in this class has a desirable property that parameters of the main effect model are simultaneously identifiable. We investigate the property of this class from the viewpoint of D-optimality. In particular, for the saturated designs, the D-optimal design is chosen from this class for the run sizes r ≡ 5, 6, 7 (mod 8).
منابع مشابه
Some optimal criteria of model-robustness for two-level non-regular fractional factorial designs
We present some optimal criteria to evaluate model-robustness of non-regular two-level fractional factorial designs. Our method is based on minimizing the sum of squares of all the off-diagonal elements in the information matrix, and considering expectation under appropriate distribution functions for unknown contamination of the interaction effects. By considering uniform distributions on symm...
متن کاملMATHEMATICAL ENGINEERING TECHNICAL REPORTS Markov basis for design of experiments with three-level factors
We consider Markov basis arising from fractional factorial designs with threelevel factors. Once we have a Markov basis, p values for various conditional tests are estimated by the Markov chain Monte Carlo procedure. For designed experiments with a single count observation for each run, we formulate a generalized linear model and consider a sample space with the same sufficient statistics to th...
متن کاملFitting Second-order Models to Mixed Two-level and Four-level Factorial Designs: Is There an Easier Procedure?
Fitting response surface models is usually carried out using statistical packages to solve complicated equations in order to produce the estimates of the model coefficients. This paper proposes a new procedure for fitting response surface models to mixed two-level and four-level factorial designs. New and easier formulae are suggested to calculate the linear, quadratic and the interaction coeff...
متن کاملProposed Procedure for Estimating the Coefficient of Three-factor Interaction for 2^p 3^m 4^q Factorial Experiments (TECHNICAL NOTE)
Three-factor interaction for the two-level, three-level, and four-level factorial designs was studied. A new technique and formula based on the coefficients of orthogonal polynomial contrast were proposed to calculate the effect of the three-factor interaction The results show that the proposed technique was in agreement with the least squares method. The advantages of the new technique are 1) ...
متن کاملMATHEMATICAL ENGINEERING TECHNICAL REPORTS Markov chain Monte Carlo tests for designed experiments
We consider conditional exact tests of factor effects in designed experiments for discrete response variables. Similarly to the analysis of contingency tables, a Markov chain Monte Carlo method can be used for performing exact tests, when large-sample approximations are poor and the enumeration of the conditional sample space is infeasible. For designed experiments with a single observation for...
متن کامل