Unreplicated factorial design

Pan, G. (1999). The impact of unidentified location effects on dispersion effects identification from unreplicated factorial designs. Technometrics, 41, 313-326. 

Pan, G. and Taam, W. (2002). On generalized linear model method for detecting dispersion effects in unreplicated factorial designs. Journal of Statistical Computation and Simulation, 72, 431-450. 

Ye, K. Q. and Hamada, M. (2000). Critical values of the Lenth method for unreplicated factorial designs. Journal of Quality Technology, 32, 57-66. 

We now consider factorial experiments in which there is no replication of design factor combinations and no use of noise factors. The idea of identifying dispersion effects in unreplicated factorials again has roots in the work of Taguchi. It was first studied in detail by Box and Meyer (1986) and has since attracted considerable interest and research. 

Liao, C. T. (2000). Identification of dispersion effects from unreplicated 2n k fractional factorial designs. Computational Statistics and Data Analysis, 33, 291-298. 

McGrath, R. N. and Lin, D. K. J. (2001). Testing multiple dispersion effects in unreplicated fractional factorial designs. Technometrics, 43, 406-414. 

Wang, P. C. (2001). Testing dispersion effects from general unreplicated fractional factorial designs. Quality and Reliability Engineering International, 17, 243-248. 

Daniel Voss is Professor of Statistics and Chair of the Department of Mathematics and Statistics of Wright State University. His interests are in design and analysis of experiments and multiple comparisons, with special interest in the analysis of unreplicated factorial experiments. 

Equation 9.8 suggests the use of a 2 factorial design to study the effect of the temperature. Equation 9.9 would require a first-order Scheffe design at each temperature (simplex vertices). In fact two independent measurements of solubility were carried out at each point. Also unreplicated test points were set up at the midpoints of the binary mixtures (points 7-12) that would allow use of a more complex model, if necessary. The resulting design is given in table 9.14. 

Furthermore, if the factorial points in the design are unreplicated, one may use the center points to construct an estimate of error with tIq — degrees of freedom. 

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