共查询到20条相似文献,搜索用时 31 毫秒
1.
Supersaturated designs (SSDs) constitute an important class of fractional factorial designs that could be extremely useful in factor screening experiments. Most of the existing studies have focused on balanced designs. This paper provides a new lower bound for the \(E(f_{NOD})\)-optimality measure of SSDs with general run sizes. This bound is a generalization of existing bounds since it is applicable to both balanced and unbalanced designs. Optimal multi and mixed-level, balanced and nearly balanced SSDs are constructed by applying a k-circulant type methodology. Necessary and sufficient conditions are introduced for the generator vectors, in order to pre-ensure the optimality of the constructed k-circulant SSDs. The provided lower bounds were used to measure the efficiency of the generated designs. The presented methodology leads to a number of new families of improved SSDs, providing tools for directly constructing optimal or nearly-optimal k-circulant designs by just checking the corresponding generator vector. 相似文献
2.
Supersaturated design is a form of fractional factorial design in which the number of columns is greater than the number of experimental runs. Construction methods of supersaturated design have been mainly focused on two levels cases. Much practical experience, however, indicates that two-level may sometimes be inadequate. This paper proposed a construction method of mixed-level supersaturated designs consisting of two-level and three-level columns. The χ2 statistic is used for a measure of dependency of the design columns. The dependency properties for the newly constructed designs are derived and discussed. It is shown that these new designs have low dependencies and thus can be useful for practical uses. 相似文献
3.
In this paper we present a new method for constructing multi-level supersaturated designs with n rows, m columns and the equal occurrence property. We investigate the existence of multi-level supersaturated designs using a single generator vector and its k-cyclic permutations as rows. We find the conditions needed, in order this vector to generate a balanced supersaturated design. These conditions are simplified for the case of three level supersaturated designs. By using the proposed method three level supersaturated designs are constructed and explored. Moreover, many new, optimal and near optimal, multi-level supersaturated designs are provided as well. 相似文献
4.
Dey and Midha (Biometrika 83(2):484–489, 1996) constructed optimal block designs for complete diallel cross experiment using
triangular partially balanced incomplete block designs with two associate classes. They listed optimal block designs for the
lines in the range from 5 ≤ v ≤ 10. In this paper, we are also proposing additional optimal block designs for complete diallel cross experiment using two
associate class partially balanced block designs for some additional values of v. Our method yields designs for proper and non-proper settings for complete diallel cross experiments. The proper and non
proper designs are optimal in the sense of Kempthorne (Genetics 41:451–459, 1956) and non-proper designs are universally optimal
in the sense of Kiefer (A survey of statistical design and linear models, North Holland, Amsterdam, 1975). The list of practically
important designs is also given. 相似文献
5.
This paper generalizes Kunert and Martin’s (Ann Stat 28:1728–1742, 2000) method for finding optimal designs under a fixed
interference model, to find optimal designs under a mixed interference model. The results are based on the properties of information
matrices in fixed and mixed models given in Markiewicz (J Stat Plan Inference 59:127–137, 1997). The method is applied to
find a design which is optimal for any given variances of random neighbor effects.
Research partially supported by the KBN Grant Number 5 P03A 041 21. 相似文献
6.
A general method for construction of E(s
2)-optimal, two-level supersaturated designs (SSDs) with the equal occurrence property, from supplementary difference sets
is introduced. It is proved that SSDs constructed in this way are E(s
2)-optimal. Comparisons are made with previous works and it is shown that the proposed method gives promising results for the
construction of E(s
2)-optimal large SSDs. 相似文献
7.
Asymmetrical Factorial Designs Containing Clear Effects 总被引:1,自引:0,他引:1
The asymmetrical or mixed-level factorial design is a kind of important design in practice. There is a natural problem on how to choose an optimal (s
2)s
n
design for the practical need, where s is any prime or prime power. This paper considers the clear effects criterion for selecting good designs. It answers the questions of when an (s
2)s
n
design with fixed number of runs contains clear two-factor interaction (in brief 2fi) components and when it contains clear main effects or clear 2fis. It further gives the complete classification of (s
2)s
n
designs according to the clear 2fi components, main effects and 2fis they have. 相似文献
8.
The aim of this paper is to derive methodology for designing ‘time to event’ type experiments. In comparison to estimation,
design aspects of ‘time to event’ experiments have received relatively little attention. We show that gains in efficiency
of estimators of parameters and use of experimental material can be made using optimal design theory. The types of models
considered include classical failure data and accelerated testing situations, and frailty models, each involving covariates
which influence the outcome. The objective is to construct an optimal design based of the values of the covariates and associated
model or indeed a candidate set of models. We consider D-optimality and create compound optimality criteria to derive optimal designs for multi-objective situations which, for example,
focus on the number of failures as well as the estimation of parameters. The approach is motivated and demonstrated using
common failure/survival models, for example, the Weibull distribution, product assessment and frailty models. 相似文献
9.
Min-Hsiao Tsai 《Metrika》2009,70(3):355-367
Consider the problem of discriminating between two rival response surface models and estimating parameters in the identified
model. To construct designs serving for both model discrimination and parameter estimation, the M
γ-optimality criterion, which puts weight γ (0≤γ≤1) for model discrimination and 1 − γ for parameter estimation, is adopted.
The corresponding M
γ-optimal product design is explicitly derived in terms of canonical moments. With the application of the maximin principle
on the M
γ-efficiency of any M
γ'-optimal product design, a criterion-robust optimal product design is proposed. 相似文献
10.
The Optimality of Single-group Designs for Certain Mixed Models 总被引:1,自引:0,他引:1
Thomas Schmelter 《Metrika》2007,65(2):183-193
In this paper optimal designs for the estimation of the fixed effects (population parameters) in a certain class of mixed
models are investigated. Two classes of designs are compared: the class of single-group designs, where all individuals are
observed under the same approximate design, and the class of more-group designs with the same mean number of observations
per individual as before, where each individual can be observed under a different approximate design. It is shown that any
design that is Φ-optimal in the class of single-group designs is also Φ-optimal in the larger class of more-group designs.
The considered optimality criteria only have to satisfy mild assumptions, which is eg the case for the D-criterion and all
linear criteria. 相似文献
11.
We consider the problem of comparison of one test treatment (τ0) with a set of v control treatments (τ1, τ2, …, τv) using distance optimality [DS-optimality] criterion introduced by Sinha (1970) in some treatment-connected design settings.
It turns out that the nature of DS-optimal designs is quite similar to that for the usual A−, D− and E− optimality criteria. However, the optimality problem is quite complicated in most situations. First we deal with the CRD
model and derive DS-optimal allocations for a given set of treatments. The results are almost identical to the A-optimal allocations
for such problems. Then we consider a block design set-up and examine the nature of DS-optimal designs. In the process, we
introduce the method of weighted coverage probability and maximize the resulting expression to obtain an optimal design.
Received: December 1999 相似文献
12.
In literature, Williams Square change-over designs balanced for first residual effects of treatments have been proved to
be universally optimal. Here, an attempt has been made to show that these designs are robust against missing of last α [≤v−1; v being the number of periods in the design for v treatments] observations from an experimental unit.
Received May 2000 相似文献
13.
The paper deals with a method for the analysis of highly fractionated factorial designs proposed by Raghavarao and Altan in
Metrika 58:185–191 (2003). We show that the method will find “active” factors with almost any set of random numbers. Once
that an alias set is found active, Raghavarao and Altan claim that their method can resolve the alias structure of the design
and identify which of several confounded effects is active. We show that their method cannot do that. The error in Raghavarao
and Altan’s arguments lies in the fact that they treat a set of highly dependent (sometimes even identical) F-statistics as
if they were independent. 相似文献
14.
In this paper we construct all possible orthogonal arrays OA(18,q, 3,2) with 18 runs and 3 ≤ q ≤ 7 columns and present those that are nonisomorphic. A discussion on the novelty and the superiority of many of the designs
found in terms of isomorphism and generalized minimum aberration has been made.
相似文献
15.
Various optimal criteria have been proposed to rank asymmetrical fractional factorial designs. Among them, the generalized
minimum aberration and the minimum moment aberration criteria are the most popular ones and have received much attention.
Recently, Liu et al. (Stat Sin 16:1285–1297, 2006) proposed the minimum
χ
2 criterion in terms of level-combinations. In this paper, the equivalency of the generalized minimum aberration and the minimum
χ
2 criteria is reported, which not only provides another justification for each other but also develops some theoretical results
for designs with generalized minimum aberration and some lower bounds for the generalized wordlength pattern. Besides, an
analytic relationship between generalized minimum aberration and minimum moment aberration is obtained for asymmetrical fractional
factorial designs. 相似文献
16.
Combined-optimal designs (Li and Lin, 2003) are obviously the best choices for the initial designs if we partition the experiment
into two parts with equal size to obtain some information about the process, especially for the case not considering the blocking
factor. In this paper, the definition of combined-optimal design is extended to the case when blocking factor is significant,
and this new class of designs is called blocked combined-optimal designs. Some general results are obtained which relate 2k−pIII initial designs with their complementary designs when , where n=2k−p. By applying these results, we are able to characterize 2k−pIII combined-optimal designs or blocked combined-optimal designs in terms of their complementary designs. It is also proved that
both 2k−pIII combined-optimal and blocked combined-optimal designs are not minimum aberration designs when and n−1−k > 2. And some combined-optimal and blocked combined-optimal designs with 16 and 32 runs are constructed for illustration.
2000 Mathematics Subject Classifications: 62K15, 62K05 相似文献
17.
In this paper, a simple and obvious procedure is presented that allows to estimate π, the population proportion of a sensitive
group, in addition to T, the probability that the respondents belonging to the sensitive group tell the truth whenever questioning directly. Properties
of the estimators of π and T as well as sample size allocation are studied. And, efficiency comparisons are carried out to investigate the performance
of the proposed method. It is found that the proposed strategy is more efficient than Warner's (1965) strategy, and has an
additional advantage of deciding the optimal survey technique for practical situations.
Received: October 2000 相似文献
18.
Motivated by the effect hierarchy principle, Zhang et al. (Stat Sinica 18:1689–1705, 2008) introduced an aliased effect number pattern (AENP) for regular fractional factorial designs and based on the new pattern proposed a general minimum lower-order confounding (GMC) criterion for choosing optimal $2^{n-m}$ designs. Zhang et al. (Stat Sinica 18:1689–1705, 2008) proved that most existing criteria can be obtained by functions of the AENP. In this paper we propose a simple method for the calculation of AENP. The method is much easier than before since the calculation only makes use of the design matrix. All 128-run GMC designs with the number of factors ranging from 8 to 32 are provided for practical use. 相似文献
19.
This paper gives an analytical expression for the best linear unbiased estimator (BLUE) of the unknown parameters in the linear
Haar-wavelet model. From the analytical expression, we solve for the eigenvalues of the covariance matrix of the BLUE in analytical
form. Further, we use these eigenvalues to construct some conventional discrete optimal designs for the model. The equivalences
among these optimal designs are demonstrated and some examples are also given.
相似文献
20.
Optimal designs under general dependence structures are usually difficult to specify theoretically or find algorithmically.
However, they can sometimes be found for a specific dependence structure and a particular parameter value.
In this paper, a class of generalized binary block designs with t treatments and b blocks of size k>t is considered. Each block consists of h consecutive complete blocks and, at the end, an incomplete block of size k−ht (if k > ht). For a suitable number of blocks, a universally optimal design is found for a first-order stationary autoregressive process
with positive correlations. Optimal generalized binary designs and balanced block designs are also considered. Some constructions
for a universally optimal design are described. A negative dependence parameter, and some other dependence structures, are
also considered. 相似文献