Minimum Aberration 2 k–p Designs
TL;DR: In this article, the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution, and algorithms are presented for constructing these minimum aberration designs.
Abstract: For studying k variables in N runs, all 2 k–p designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution. Algorithms are presented for constructing these minimum aberration designs.
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01 Jan 2006
TL;DR: In this paper, the authors studied the analogous issue for blocked regular symmetric factorial designs and identified the connection between the estimation capacity of a blocked mixed factorial design and its complementary subset.
Abstract: Following the ideas of Cheng, Steinberg and Sun (1999) and Cheng and Muk- erjee (1998) for the unblocked case, Cheng and Mukerjee (2001) considered the issue of constructing blocked regular symmetrical factorial designs with maximum estimation ca- pacity. The present work aims at studying the analogous issue for blocked regular mixed factorial designs. By using the nite projective geometric approach, we identify the gen- eral connection between the estimation capacity of a blocked mixed factorial design and its complementary subset. Furthermore, the necessary and sucien t conditions for a blocked mixed factorial design to have maximum over estimation capacity are obtianed for some special parameters.
TL;DR: This paper proposes and studies a method for selecting the optimal robust parameter designs when some of the control-by-noise interactions are important, and discusses how to search for the best designs according to this method.
Abstract: In robust parameter design, both control factors and noise factors are studied, and the objective is to choose the settings of control factors that are insensitive to the noise factors. Information concerning control-by-noise interactions is particularly useful for achieving this objective. In this paper, we propose and study a method for selecting the optimal robust parameter designs when some of the control-by-noise interactions are important. We then discuss how to search for the best designs according to this method and present some results for designs of 8 and 16 runs.
01 Jan 2012
TL;DR: Fractional Factorial Design is a subset or fraction of full factorial designs that are seldom used in practice for large k (k ≥ 7) and are chosen according to the resolution or minimum aberration criteria.
Abstract: Motivation: for economic reasons, full factorial designs are seldom used in practice for large k (k ≥ 7). Fractional Factorial Design: a subset or fraction of full factorial designs. " Optimal " fractions: are chosen according to the resolution or minimum aberration criteria. Aliasing of effects: a price one must pay for choosing a smaller design.
Additional excerpts
...I Fries and Hunter (1980): For any two 2k−p designs d1 and d2, let r be the smallest integer such that Ar (d1) 6= Ar (d2)....
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TL;DR: In this article , the authors proposed two criteria for selecting fractional factorial split-plot (FFSP) designs, i.e., minimum aberration criterion and minimum deviation criterion, and some optimal FFSP designs under the two criteria are tabulated.
Abstract: In practical factorial experiments, we sometimes find that complete randomization of the order of the runs is infeasible because it is more difficult to change the levels of some factors than the others, especially in some engineering experiments. Then, fractional factorial split-plot (FFSP) designs represent a practical option in such situations. The difficult-to-change factors are called whole plots (WP) factors, and the other factors are called subplot (SP) factors. The WP and SP factors do not have the same importance in many experiments. Then, the popular minimum aberration criterion is not suitable any more for choosing FFSP designs. This paper proposes two criteria for selecting FFSP designs. Algorithms for constructing the optimal FFSP designs under the two criteria are proposed. Some optimal designs under the two criteria are tabulated.
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471 citations
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23 Jun 1976
TL;DR: In conclusion, the size of Industrial Experiments, Fractional Replication--Elementary, and Incomplete Factorials are found to be about the same as that of conventional comparison experiments.
Abstract: Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.
311 citations
09 Jun 1976
271 citations
TL;DR: Incomplete Factorials, Fractional Replication, Intermediate Factorial, and Nested Designs as discussed by the authors are some of the examples of incomplete Factorial Experiments and incomplete fractional replicates.
Abstract: Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.
252 citations