zbMATH — the first resource for mathematics

Singular factorial designs resulting from missing pairs of design points. (English) Zbl 0642.62048
In industry, experiments are often conducted sequentially due to equipment limitations dictating that only one or two simultaneous runs may be made. In this situation, early termination of the experiment results in missing points, leading to a loss in efficiency or, worse, to a singular subdesign with nonestimable model parameters. We investigate the specific problem of singularity when two points are lost from a factorial design based on n two-level factors. The method is based on the inner products of the coordinate vectors of the omitted design points and leads to some results on the nonexistence of fractional factorial designs.

62K15 Factorial statistical designs
62J10 Analysis of variance and covariance (ANOVA)
Full Text: DOI
[1] Andrews, D.F.; Herzberg, A.M., The robustness and optimality of response surface designs, J. statist. plann. inference, 3, 249-257, (1979) · Zbl 0409.62058
[2] Brownlee, K.A.; Kelly, B.K.; Loraine, P.K., Fractional replication arrangements for factorial experiments with factors at two levels, Biometrika, 35, 268-276, (1948) · Zbl 0033.19702
[3] Burton, R.C.; Connor, W.S., On the identity relationship for fractional replicates in the 2^{n} series, Ann. math. statist., 28, 762-767, (1957) · Zbl 0081.36405
[4] Daniel, C.; Wilcoxon, F., Factorial 2^{p-q} plans robust against linear and quadratic trends, Technometrics, 8, 269-278, (1966)
[5] Dickinson, A.W., Some run orders requiring a minimum number of factor level changes for the 2^{4} and 25 main effects plans, Technometrics, 16, 31-37, (1974) · Zbl 0275.62069
[6] Franklin, M.F.; Bailey, R.A., Selection of defining contrasts and confounded effects in two-level experiments, Applied statistics, 26, 321-326, (1977)
[7] Greenfield, A.A., Selection of defining contrasts in two-level experiments, Applied statistics, 25, 64-67, (1976)
[8] John, P.W.M., On identity relationships for 2^{n-r} designs having words of equal length, Ann. math. statist., 37, 1842-1843, (1966) · Zbl 0141.34806
[9] John, P.W.M., Statistical design and analysis of experiments, (1971), Macmillan New York
[10] John, P.W.M., Missing points in 2^{n} and 2n-k factorial designs, Technometrics, 21, 225-228, (1979) · Zbl 0421.62063
[11] John, P.W.M., The growth of experimental design in engineering, () · Zbl 0203.51801
[12] Margolin, B.H., Orthogonal main effects plans permitting estimation of all two-factor interactions for the 2^{n}3m factorial series of designs, Technometrics, 11, 747-762, (1969) · Zbl 0183.48503
[13] Moore, L.M., Ordering the points in factorial experiments to protect against early termination, ()
[14] Plackett, R.L.; Burman, J.P., The design of optimum multifactorial experiments, Biometrika, 33, 305-325, (1946) · Zbl 0063.06274
[15] Smith, D.E.; Schmoyer, D.D., First-order ‘interruptible’ designs, Technometrics, 24, 55-58, (1982)
[16] Steinberg, D.M.; Hunter, W.G., Experimental design: review and comment, Technometrics, 26, 71-97, (1984) · Zbl 0549.62048
[17] Webb, S.R., Non-orthogonal designs of even resolution, Technometrics, 10, 291-300, (1968) · Zbl 0174.22501
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.