Contents: Variety and Quality. Variability loss and tolerance. Determining tolerances. Tolerance design and experimental design. Offline and online quality control. Parameter design and tolerance design: case study. Experimental design for smaller is better characteristics. Experimental design for larger is better characteristics. Bypassing the S/N ratio: spring experiment. Experimental design for dynamic characteristics.

Introduction to quality engineering. designing quality into products a

A comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods. A uniform approach is applied to each chapter, which contains four parts: a definition followed by a list of results; a short list of references to related topics in the book; one or more references to proofs; and references to applications. The use of extensive cross-referencing to topics within the book and external referencing to proofs allows for definitions to be located easily as well as interrelationships among subject areas to be recognized. A Matrix Handbook for Statisticians addresses the need for matrix theory topics to be presented together in one book and features a collection of topics not found elsewhere under one cover. These topics include: * Complex matrices * A wide range of special matrices and their properties * Special products and operators, such as the Kronecker product * Partitioned and patterned matrices * Matrix analysis and approximation * Matrix optimization * Majorization * Random vectors and matrices * Inequalities, such as probabilistic inequalities Additional topics, such as rank, eigenvalues, determinants, norms, generalized inverses, linear and quadratic equations, differentiation, and Jacobians, are also included. The book assumes a fundamental knowledge of vectors and matrices, maintains a reasonable level of abstraction when appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics. A Matrix Handbook for Statisticians is an essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing. It also serves as an excellent self-study guide for statistical researchers.

A matrix handbook for statisticians

Order Restricted Statistical Inference.

Balanced Loss Functions (BLFs) which reflect both goodness of fit and precision of estimation are described. Optimal estimates relative to BLFs are derived for estimation of a scalar mean, a vector mean and a vector of regression coefficients. Properties of these estimates are compared with those of maximum likelihood (ML) estimates and Bayesian posterior means. Sampling properties, or average operating characteristics, of optimal BLF estimates, ML estimates and posterior means are compared. The robustness of these estimates’ and estimators’ performance with respect to departures from the loss functions for which they are optimal is analyzed. It is concluded that BLFs and their associated optimal estimates will probably be useful in many estimation problems.

Bayesian and Non-Bayesian Estimation Using Balanced Loss Functions

The class of complex star-dagger matrices for which A∗ and A† commute, is investigated. Some fundamental properties are given and a canonical form is derived. The interaction of this class of matrices with other common classes of special matrices, which as group matrices, EP matrices, and idempotents, will be looked into

Matrices for which A∗ and A† commute

The reverse order law (AB)− = B−A−

Selective assembly is an effective approach for improving the quality of a product that is composed of two mating components, when the quality characteristic of the product is the clearance between the mating components. In this approach, the components are sorted into several groups according to their dimensions, and the product is assembled by randomly selecting mating components from corresponding groups. A number of previous studies focused on equal width partitioning schemes, in which the dimensional distributions of the two components are partitioned so that all groups have equal widths. When there is a large difference between the variances of the two component dimensions, equal width partitioning will result in a large number of surplus components due to differences between the numbers of components in corresponding groups. Some authors have proposed a method of manufacturing the component with smaller variance at three shifted means to cope with this difficulty. In the present paper, an optimal m...

Optimal process design in selective assembly when components with smaller variance are manufactured at three shifted means

An unbiased estimator for the common mean of k normal distributions is suggested. A necessary and sufficient condition for the estimator Lo have a smaller variance than each sample mean is given. In the case of estimating the common mean vector of k p-variate (p ≤ 3) normal distributions a combined unbiased estimator may be used. We give a class of estimators which are better than the combined estimator when the loss is quadratic and the restriction of unbiasedness is removed.

A note on estimating the common mean of k normal distributions and the stein problem

Selective assembly is an effective approach for improving a quality of a product assembled from two types of components, when the quality characteristic is the clearance between the mating components. Mease et al. (2004) have extensively studied optimal binning strategies under squared error loss in selective assembly, especially for the case when two types of component dimensions are identically distributed. However, the presence of measurement error in component dimensions has not been addressed. Here we study optimal binning strategies under squared error loss when measurement error is present. We give the equations for the optimal partition limits minimizing expected squared error loss, and show that the solution to them is unique when the component dimensions and the measurement errors are normally distributed. We then compare the expected losses of the optimal binning strategies with and without measurement error for normal distribution, and also evaluate the influence of the measurement error.

Nobuo Shinozaki

Papers

The reverse order law (AB)− = B−A−

Optimal process design in selective assembly when components with smaller variance are manufactured at three shifted means

A note on estimating the common mean of k normal distributions and the stein problem

Optimal Binning Strategies under Squared Error Loss in Selective Assembly with Measurement Error

Two principal points for multivariate location mixtures of spherically symmetric distributions