• Journal of the Korean Statistical Society
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• v.11 no.1
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• pp.1-11
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• 1982

Srivastava and Anderson(1970) illustrate a method of obtaining Balanced (but not orthogonal) Resolution $IV^*$ designs starting with a BIB design. The incidence matrix of a BIB design with parameters (v, b, r, k, and $\lambda$) is utilized to obtain Balanced Resolution $IV^*$ designs with m factors and n=2b runs, where $m \leq v$. In this paper, the same idea is extended to the case of PBIB designs to obtain Partially Balanced Resolution $IV^*$ designs. In the designs obtained here the variances are balanced and the covariances are partially balanced with respect to the main effects. A proof of this property of Partially Balanced Resoultion $IV^*$ designs is given. The efficiency of Partially Balanced Resolution $IV^*$ designs is also considered and examples of Partially Balanced Resoultion $IV^*$ designs are included.

• Journal of Korean Society for Quality Management
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• v.38 no.1
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• pp.42-51
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• 2010

For the fractional factorial designs, the resolution-IV designs can be used when we want to estimate the main effects and to investigate the structure of the non-negligible two-factor interaction effects, when the three-factor and higher order interaction effects are all negligible. However we need to add the additional treatment combinations in order to identify the influential interactions for the resolution-IV fractional factorial designs. In this paper we investigate the statistical structure for 3-level resolution-IV designs constructed by fold-over scheme and introduce a method for analyzing the influential two-factor interactions.

• Proceedings of the Korean Society for Quality Management Conference
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• 2010.04a
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• pp.129-138
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• 2010

For the fractional factorial designs, the resolution-IV designs can be used when we want to estimate the main effects and to investigate the structure of the non-negligible two-factor interaction effects, when the three-factor and higher order interaction effects are all negligible. However we need to add the additional treatment combination in order to identify the influential interactions for the resolution-IV fracrtional factorial designs. In this paper we investigate the statistical structure for 3-level resolution-IV designs constructed by fold-over scheme and introduce a method for analyzing the influential two-factor interactions.

• Journal of Korean Society for Quality Management
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• v.28 no.3
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• pp.59-67
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• 2000

In analysis of resolution IV fractional factorial experiments, the main effects only are analyzed, even though we can get some useful information on the confounded 2-factor interactions. In this paper, we introduce an exploiting method of the confounded structure of interactions, especially for the near minimal resolution IV 3$^{t}$ fractional factorial designs developed by Anderson and Thomas (1979). Moreover, in this paper the application way of the proposed method is also discussed by analyzing some simulated data.

• Journal of the Korean Statistical Society
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• v.32 no.3
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• pp.235-244
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• 2003

In unreplicated factorial or fractional factorial experiments, the presence of one or more outliers can seriously affect the analysis of variance. Using the normal plot of t residuals to identify outliers in factorial or fractional factorial is an easy method to find these dubious points. In some cases, the t residuals form the identical pairs. One can not tell from the plot which is doubtful. This phenomenon occurs for all minimal designs of resolution IV, which fits the model containing all main effects and some two-factor interactions, whether it is orthogonal or not. In these kinds of models, when we drop one point or two points (not foldover pair) from the fraction, the phenomenon of identical pairs of t residuals may still occur. In this paper, the theoretical background of the phenomenon and its sequences will be investigated in detail.