共查询到20条相似文献,搜索用时 15 毫秒
1.
The paper gives explicit formulae for analysing an experiment carried out in an affine resolvable proper block design. They follow from a randomization model, decomposed into stratum submodels. Analyses within the four relevant strata, and then the combined analysis, are considered in details. The paper is essentially an extension of some results presented in recent books, by Caliński and Kageyama [2000. Block Designs: A Randomization Approach, Volume I: Analysis. Lecture Notes in Statistics, vol. 150. Springer, New York; 2003. Block Designs: A Randomization Approach, Volume II: Design. Lecture Notes in Statistics, vol. 170. Springer, New York]. 相似文献
2.
《Journal of statistical planning and inference》2004,119(2):401-410
In this paper, we present a general construction of group divisible designs and rectangular designs by utilising resolvable and “almost resolvable” balanced incomplete block designs. As special cases, we obtain the following E-optimal designs: (a) Group divisible (GD) designs with λ2=λ1+1 and (b) Rectangular designs with 2 rows and having λ3=λ2−1=λ1+1. Many of the GD designs are optimal among binary designs with regard to all type 1 criteria. 相似文献
3.
《Journal of statistical planning and inference》1988,19(1):117-120
A class of resolvable incomplete block designs with three and four replications is obtained here starting from an additive Abelian group. 相似文献
4.
《Journal of statistical planning and inference》1999,81(1):195-199
(M,S)-optimality is used in computer search algorithms as a quick way of filtering out inefficient designs. We show that it does not work well for resolvable designs with unequal block sizes. Instead we suggest the use of a criterion based on the dual design. 相似文献
5.
《Journal of statistical planning and inference》2006,136(12):4450-4458
Whole-plot (WP) factors and sub-plot (SP) factors play different roles in fractional factorial split-plot (FFSP) designs. In this paper, we consider FFSP designs with resolution III or IV from the viewpoint of clear factorial effects, classify two-factor interactions (2FIs) into three types, and give sufficient and necessary conditions for the existence of FFSP designs containing various clear factorial effects, including two types of main effects and three types of 2FIs. The structures of these designs are also shown and illustrated with examples. 相似文献
6.
For two-level factorials, we consider designs in N=2 (mod 4) runs as obtained by adding two runs, with a certain coincidence pattern, to an orthogonal array of strength two. These designs are known to be optimal main effect plans in a very broad sense in the absence of interactions. Among them, we explore the ones having minimum aberration, with a view to ensuring maximum model robustness even when interactions are possibly present. This is done by sequentially minimizing a measure of the bias caused by interactions of successively higher orders. 相似文献
7.
Row-column designs may be considered to have two blocking schemes, namely the treatments by rows and treatments by columns component block designs. The (M,S)-optimality criterion is applied to row-column designs, and che connection between the (M,S)-optimal design and its component block designs is demonstrated. 相似文献
8.
Let EG(m, 2) denote the m-dimensional finite Euclidean space (or geometry) based on GF(2), the finite field with elements 0 and 1. Let T be a set of points in this space, then T is said to form a q-covering (where q is an integer satisfying 1?q?m) of EG(m, 2) if and only if T has a nonempty intersection with every (m-q)-flat of EG(m, 2). This problem first arose in the statistical context of factorial search designs where it is known to have very important and wide ranging applications. Evidently, it is also useful to study this from the purely combinatorial point of view. In this paper, certain fundamental studies have been made for the case when q=2. Let N denote the size of the set T. Given N, we study the maximal value of m. 相似文献
9.
A design is said to be super-simple if the intersection of any two blocks has at most two elements. In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple GDDs are useful in constructing super-simple BIBDs. The existence of super-simple (4,λ)‐GDDs has been determined for λ=2-6. In this paper, we investigate the existence of a super-simple (4,9)-GDD of group type gu and show that such a design exists if and only if u≥4, g(u−2)≥18 and u(u−1)g2≡0 (mod 4). 相似文献
10.
《Journal of statistical planning and inference》1997,58(1):5-27
A G-design of order n is a pair (P,B) where P is the vertex set of the complete graph Kn and B is an edge-disjoint decomposition of Kn into copies of the simple graph G. Following design terminology, we call these copies “blocks”. Here K4 - e denotes the complete graph K4 with one edge removed. It is well-known that a K4 - e design of order n exists if and only if n ≡ 0 or 1 (mod 5), n ⩾ 6. The intersection problem here asks for which k is it possible to find two K4 - e designs (P,B1) and (P,B2) of order n, with |B1 ∩ B2| = k, that is, with precisely k common blocks. Here we completely solve this intersection problem for K4 - e designs. 相似文献
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12.
Use of the (M,S) criterion to select and classify factorial designs is proposed and studied. The criterion is easy to deal with computationally and it is independent of the choice of treatment contrasts. It can be applied to two-level designs as well as multi-level symmetrical and asymmetrical designs. An important connection between the (M,S) and minimum aberration criteria is derived for regular fractional factorial designs. Relations between the (M,S) criterion and generalized minimum aberration criteria on nonregular designs are also discussed. The (M,S) criterion is then applied to study the projective properties of some nonregular designs. 相似文献
13.
A number of D-optimal weighing designs are constructed with the help of block matrices. The D-optimal designs (n,k,s)=(19,13,10), (19,14,7), (19,14,8), (19,15,7), (19,15,8), (19,17,6), (19,18,6), (23,16,8), (23,17,8), (23,18,8), (4n?1,2n+3,(3n+4)/2), (4n?1,2n+4,n+3), (4n?1,2n+4,n+2) where n≡0 mod 4 and a skew Hn exists, (31,24,8), (31,25,8) and many others are constructed. A computer routine leading to locally D-optimal designs is presented. 相似文献
14.
Designs for quadratic and cubic regression are considered when the possible choices of the controlable variable are points x=( x1,x2,…,xq) in the q-dimensional. Full of radius R, Bq(R) ={x:Σ4ix2i?R2}. The designs that are optimum among rotatable designs with respect to the D-, A-, and E-optimality criteria are compared in their performance relative to these and other criteria, including extrapolation. Additionally, the performance of a design optimum for one value of R, when it is implemented for a different value of R, is investigated. Some of the results are developed algebraically; others, numerically. For example, in quadratic regression the A-optimum design appears to be fairly robust in its efficiency, under variation of criterion. 相似文献
15.
In this paper, the notion of average total inspection (ATI) is introduced to ChSP-4(c1,c2) sampling plans. Procedures have been developed for the construction and selection of ChSP-4(c1, c2 plans, minimizing ATI at a given process average, while protection to the consumer is given in terms of the (i) average outgoing quality limit and (ii) limiting quality level.A wide range of c1 and c2 values are considered for developing tables which cover almost all practical situations. The procedure described is similar to that of Dodge and Romig. 相似文献
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17.
We consider a search design for the 2m type such that at most knonnegative effects can be searched among (l+1)-factor interactions and estimated along with the effects up to l- factor interactions, provided (l+1)-factor and higher order interactions are negligible except for the k effects. We investigate some properties of a search design which is yielded by a balanced 2m design of resolution 2l+1 derived from a balanced array of strength 2(l+1). A necessary and sufficient condition for the balanced design of resolution 2l+1 to be a search design for k=1 is given. Optimal search designs for k=1 in the class of the balanced 2m designs of resolution V (l=2), with respect to the AD-optimality criterion given by Srivastava (1977), with N assemblies are also presented, where the range of (m,N) is (m=6; 28≤N≤41), (m=7; 35≤N≤63) and (m=8; 44≤N≤74). 相似文献
18.
Basudeb Adhikary Rajendranath Panda 《Journal of statistical planning and inference》1983,7(4):387-405
In this paper some experimental situations are identified corresponding to which suitable response surface designs do not exist. A class of response surface designs is introduced to cope with these situations. Their analysis with and without blocking and methods of construction is discussed. 相似文献
19.
M. Hemavathi Eldho Varghese Shashi Shekhar Seema Jaggi 《Journal of applied statistics》2022,49(6):1364
Rotatable designs that are available for process/ product optimization trials are mostly symmetric in nature. In many practical situations, response surface designs (RSDs) with mixed factor (unequal) levels are more suitable as these designs explore more regions in the design space but it is hard to get rotatable designs with a given level of asymmetry. When experimenting with unequal factor levels via asymmetric second order rotatable design (ASORDs), the lack of fit of the model may become significant which ultimately leads to the estimation of parameters based on a higher (or third) order model. Experimenting with a new third order rotatable design (TORD) in such a situation would be expensive as the responses observed from the first stage runs would be kept underutilized. In this paper, we propose a method of constructing asymmetric TORD by sequentially augmenting some additional points to the ASORDs without discarding the runs in the first stage. The proposed designs will be more economical to obtain the optimum response as the design in the first stage can be used to fit the second order model and with some additional runs, third order model can be fitted without discarding the initial design.KEYWORDS: Response surface methodology, rotatability, orthogonal transformation, asymmetric, sequential experimentation, third order designs 相似文献
20.
This article outlines the structure of a generalized family of two-stage chain sampling plans, extending the concept of two-stage chain sampling plans of Dodge and Stephens (1966) which is an extension of the original work of Dodge (1955). Expressions are derived for the OC curves for two-stage chain sampling plans with (c1,c2) = (0,2) and (1,2). In the original work of Dodge (1955) only acceptance numbers of 0,1 were used and in the extension work of Dodge and Stephens (1966) acceptance numbers of (c1,c2) = (0,1), (0,2), (1,2), (0,3), (1,3), (0,4) and (1,4) were used with selected sets of values of k1 and k2 (the number of lots considered for cumulation in the first and second stage respectively). In this paper the OC curves are derived more generally for any k1 and k2combination for two-stage chain sampling plans with (c1,c2) = (0,2) and (1,2) and comparisons are made with respect to sample sizes and discriminating power, with the corresponding single and double sampling plans. 相似文献