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.
Citations
More filters
TL;DR: In this paper, exact integer programming (IP) bounds on the number of words of length four for resolution IV regular designs and generalized word-length patterns (GWPs) for fractional factorial designs are improved.
8 citations
TL;DR: A modeling framework that exploits certain structures of the data, a method for constructing optimal designs under this proposed framework, and an evaluation of the performance and robustness of the constructed designs are presented.
Abstract: In many physical and computer experiments, the order in which the steps of a process are performed may have a substantial impact on the measured response. Often, the goal in these situations is to uncover the order that optimizes the response according to some metric. However, the brute force approach of performing all permutations quickly becomes impractical as the number of components in the process increases. Instead, we seek to develop order-of-addition experiments that choose an economically viable subset of permutations to test. The statistical literature on this topic is sparse, and many researchers rely on ad-hoc methods to study the effect of process order. In this work, we present a series of novel developments, including a modeling framework that exploits certain structures of the data, a method for constructing optimal designs under this proposed framework, and an evaluation of the performance and robustness of the constructed designs. We use data from a drug combination therapy problem to highlight the benefits of our approach.
8 citations
Cites background from "Minimum Aberration 2 k–p Designs"
...The generalized minimum aberration criterion includes the minimum aberration criterion (Fries and Hunter, 1980), the minimum G2-aberration criterion (Tang and Deng, 1999), and many optimality criteria as special cases (Xu, 2003; Xu et al., 2009)....
[...]
01 Jan 2005
TL;DR: In this article, the coset pattern matrix (CPM) is formally dened as an elaborate char- acterization of the aliasing patterns of a fractional factorial design, and the possibility of using CPM to check design isomorphism is investigated.
Abstract: The coset pattern matrix (CPM) is formally dened as an elaborate char- acterization of the aliasing patterns of a fractional factorial design. The possibility of using CPM to check design isomorphism is investigated. Despite containing much information about eect aliasing, the CPM fails to determine a design uniquely. We report and discuss small nonisomorphic designs that have equivalent coset pattern matrices. These examples imply that the aliasing property and the combinatorial structure of a design depend on each other in a complex manner. Based on CPM, a new optimality criterion called the minimum M-aberration criterion is proposed to rank-order designs. Its connections with other existing optimality criteria are discussed.
8 citations
Additional excerpts
...Traditionally, the wordlength pattern W0 = (A01, . . . , A0n) is used to characterize the aliasing patterns of d, where A0i is the number of effects of order i in G. Minimum aberration (MA) designs, which sequentially minimize A0i for 1 ≤ i ≤ n, are regarded as optimal (Fries and Hunter (1980))....
[...]
TL;DR: In this article, generalized aberration (GA) is used to quantify the suitability of an orthogonal array (OA) to be used as an experimental design for three-level OAs of strength 3.
7 citations
Cites background from "Minimum Aberration 2 k–p Designs"
...The GA criterion reduces to the G2 aberration criterion proposed by Tang and Deng (1999) for two-level OAs, which, in turn, reduces to the aberration criterion for regular two-level designs developed by Fries and Hunter (1980)....
[...]
TL;DR: In this paper, the vector space structure of regular q n−m -designs is exploited and a method for generating all such designs, without repetition, along with their confounded interactions, resolution numbers, alias sets and a decodable design number is presented.
Abstract: By exploiting the vector space structure of regular q n−m -designs we construct and demonstrate a method for generating all such designs, without repetition, along with their confounded interactions, resolution numbers, alias sets and a decodable design number
7 citations
References
More filters
471 citations
Book•
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