Step-wise group screening designs with errors in observations

The performance of step-wise group screening In terms of the expected number of runs and the expected number of incorrect decisions, Is considered. A method for obtaining optimal step-wise designs Is presented, for the cases in which the direction of each defective factor is assumed to be known a-priori and the observations are subject to error.     

Construction of minimum aberration blocked two-level regular factorial designs

ABSTRACT

In this article, we consider the construction of minimum aberration 2^{n ? k}: 2^p designs with respect to some existing combined wordlength patterns, where a 2^{n ? k}: 2^p design is a blocked two-level design with n treatment factors, 2^p blocks, and N = 2^q runs with q = n ? k. Two methods are proposed for two situations: n ? 2^{q ? p} ? 1 and n > N/2. These methods enable us to obtain some new minimum aberration 2^{n ? k}: 2^p designs from existing minimum aberration unblocked and blocked designs. Examples are included to illustrate the theory.     

Balanced and partially balanced incomplete block designs with autocorrelation errors

The paper aims to find variance balanced and variance partially balanced incomplete block designs when observations within blocks are autocorrelated and we call them BIBAC and PBIBAC designs. Orthogonal arrays of type I and type II when used as BIBAC designs have smaller average variance of elementary contrasts of treatment effects compared to the corresponding Balanced Incomplete Block (BIB) designs with homoscedastic, uncorrelated errors. The relative efficiency of BIB designs compared to BIBAC designs depends on the block size k and the autocorrelation ρ and is independent of the number of treatments. Further this relative efficiency increases with increasing k. Partially balanced incomplete block designs with autocorrelated errors are introduced using partially balanced incomplete block designs and orthogonal arrays of type I and type II.     

A formula for a missing plot in a general incomplete block design,when recovery of interblock information is used

In this paper, Yate's missing plot technique is used to derive the formula for substitution in a missing plot in a general incomplete block design, where blocks are assumed to be independent normal. The use of penalized normal equations, using BLUPS, makes this task simpler.     

Modified minimax estimation of regression coefficients

Working with the linear regression model (1.1) and having the extraneous information (1.2) about regression coefficients the problem exists how to build estimators (1.3) with the risk (1.4) which enable to utilize the known information in order to reduce their risk as compared with the risk (1.6) of the LSE (1.5). Solution of this problem is known for the positive definite matrix T, namely in form for estimators (1.8) and (1.10).First, it is shown that the proposed estimators (2.6),(2.9) and (2.16) based on psedoinversions of the matrix L represent the solution of the problem of the positive semidefinite matrix T=L'L.Further, the problem of interpretability of estimators in the sense of the inequality (3.1) exists; it is shown that all mentioned estimators are at least partially interpretable in the sense of requirements (3.2) or (3.10).     

Experimental designs and their efficiencies for spatially correlated observations in two dimensions

Optimality of experimental designs for spatially correlated observations is investigated.come two dimensional correlation structures are discussed and an attempt has been made to find optimal or nearly optimal design for each sitution.The solution lend to designs similar to that used for repeated measurements.The relative efficiency of the proposed designs in comparison to randomized latin square designs is tabulated for some cases.     

Construction of New Three-Level Response Surface Designs

Response surface methodology is widely used for developing, improving, and optimizing processes in various fields. In this article, we present a method for constructing three-level designs in order to explore and optimize response surfaces combining orthogonal arrays and covering arrays in a particular manner. The produced designs achieve the properties of rotatability, predictive performance and efficiency for the estimation of a second-order model.     

Taguchi methods: linear graphs of high resolution

An important reason behind the success of the Taguchi methodology in qual- ity assurance has been the use of statistical methods, presented in a way that is accessible to the nonexpert user. Among the tools used to simplify the sta- tistical design of experiments has been the linear graph, apparently introduced by Taguchi. However, he did not consider the resolution of the corresponding designs (the higher the resolution, the more accurate the conclusions). For example, it will be shown that half of the linear graphs given by Taguchi for the L₁₆(2¹⁵) orthogonal array correspond to designs of resolution III, when designs of resolution IV are available (with the same lines in the linear graphs but with different assignments to the columns of the orthogonal array). A nontraditional but very straightforward method is presented for obtaining the alias chains and the linear graphs corresponding to an orthogonal array. The procedure can be easily understood and employed by nonstatisticians to find an experimental design of the highest possible resolution. The design can be used to obtain products or processes that are robust to variation.     

An infinite class of PBIB designs

In this paper, an infinite class of partially balanced incomplete block (PBIB) designs of m+1 associate classes is constructed through the use of a series of row-orthogonal matrices known as partially balanced orthogonal designs (PBOD) of m-associate classes. For the purpose, a series of PBOD is obtained through a method described herein. An infinite class of regular GD designs is also reported.     

Decompositions of λ K v

In a series of 2 papers, Kang, Du and Tian solved the existence problem for G-decomposition of λ K _n when G is any simple graph with 6 vertices and 7 edges, except when G is the graph T=K ₄∪K ₂. Notice that a T-decomposition can be considered to be a Pairwise Balanced Design in which each block of size 4 has been matched to a block of size 2. In this paper we remove this exception for all λ≥2. The case when λ=1 is also addressed. This paper is written in honor of Frank Hwang on the occasion of his 65th birthday.