Assessing the bias in blocked two level fractional factorial designs with respect to confounding pattern

Authors

  • Jamilu Garba Ahmadu Bello University, Zaria, Nigeria.
  • Abubakar Yahaya Ahmadu Bello University, Zaria, Nigeria.
  • Hussaini Dikko Ahmadu Bello University, Zaria, Nigeria.

DOI:

https://doi.org/10.14419/ijamr.v3i2.1119

Published:

2014-03-22

Abstract

Blocked two-level fractional factorial designs are very useful in screening experiment and other areas of scientific research. In some experiments, apart from the main effects, some two-factor interactions may be important and should be estimated. Thus, the postulated model should include all main effects, some important two-factor interactions and blocking effects. The remaining two factor interaction and some other higher order interactions not included in the postulated model may confound and bias the estimate of the effects in the model which in turn lower the precision of the parameter estimate. It is therefore necessary to select an optimal design from the design space that will minimize this bias (contamination). In this article, two designs were selected with respect to confounding pattern and the bias accounted in the estimation of the regression coefficient of the postulated models were evaluated and compared. The confounding pattern of design I and II is (0, 6, 1) and (4, 2, 2) respectively; it was observed that bias accounted in the estimation of regression coefficient is higher in design II.

 

Keywords: Confounding Pattern, Defining Contrast Subgroup, Defining Words, Minimum Aberration, and Word-Length Pattern.

Author Biographies

Jamilu Garba, Ahmadu Bello University, Zaria, Nigeria.

Department of Mathematics,Ahmadu Bello University, Zaria, Nigeria.

Graduate Assistant

Abubakar Yahaya, Ahmadu Bello University, Zaria, Nigeria.

Department of Mathematics,Ahmadu Bello University, Zaria, Nigeria.

Lecturer II

Hussaini Dikko, Ahmadu Bello University, Zaria, Nigeria.

Department of Mathematics,Ahmadu Bello University, Zaria, Nigeria.

Lecturer I

References

Box, G.E.P. and Hunter, J.S. The 2k-p fractional factorial designs, Technometrics, 3, (1961), 311-351.

Chen, H. and Cheng, C.S. Theory of optimal blocking of 2n-m design, The Annals of statistics, 27, (1999), 1948-1973.

Cheng, C.S. and Tang, B. A general theory of minimum aberration and its applications, Annals of Statistics, 33, (2005), 944-958.

Cheng, S.W. and Wu, C.F.J. Choice of optimal blocking schemes in two-level and three-level designs, Technometrics, 44, (2002), 269-277.

Franklin, M.F. Constructing tables of minimum aberration Pn-m designs, Technometrics, 26, (1984), 225-232.

Fries, A. and Hunter, W.G. Minimum aberration 2k-p designs, Technometrics, 22, (1980) , 601-608.

Ke, W. and Tang B. Selecting 2m-p designs using a minimum aberration criterion when some two-factor interactions are important, Technometrics, 45, (2003), 352-360.

Ke, W., Tang, B., and Wu, H. Compromise plans with clear two-factor interactions, Statistica Sinica, 15, (2005), 709-715.

Sitter, R.R., Cheng, J., and Feder, M. fractional resolution and minimum aberration in blocked 2n-k designs, Technometrics 39, (1997), 382-390

Tang, B. Theory of J-characteristics for fractional factorial design and projection justification of minimum G2 aberration, Biometrika, 88, (2001), 401-407.

Tang, B. Orthogonal arrays robust to non-negligible two-factor interactions, Biometrika, 93, (2006), 137-146

Tang, B., and Deng, L.Y. Minimum G2-aberration for non-regular fractional factorial designs. Annals of Statistics, 27, (1999), 1914-1926.

Tang, B., and Deng, L.Y. Construction of generalized minimum aberration design of 3, 4, and 5 factors, J. of Stat. Planning and inference, 113, (2003), 335-340.

Ke, W., Optimal selection of blocked two-level fractional factorial designs, Applied Mathematical Sciences, 1, (2007), 1069-1082.

Xu, H. Blocked regular fractional factorial designs with minimum aberration, The Annals of Statistics, 34, (2006), 2534-2553.

Xu, H., and Lau, S. Minimum aberration blocking schemes for two and three-level fractional factorial designs, Journal of statistical planning and inference, 136, (2006), 4088-4118.

Xu, H., and Mee, R. W. (2010) Minimum aberration blocking schemes for 128-Run Designs, Journal of statistical planning and inference, 140, 3213-3229.

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