D-optimal designs for combined polynomial and trigonometric regression on a partial circle

Consider the D-optimal designs for a combined polynomial and trigonometric regression on a partial circle. It is shown that the optimal design is equally supported and the structure of the optimal design depends only on the length of the design interval and the support points are analytic functions of this parameter. Moreover, the Taylor expansion of the optimal support points can be determined efficiently by a recursive procedure. Examples are presented to illustrate the procedures for computing the optimal designs.     

A Survey of the Teaching of Statistics in M.B.A. Programs

A survey of business schools was conducted to obtain information about the current state of the teaching of business statistics to students enrolled in M.B.A. degree programs. The survey was undertaken for and presented at a June 1986 conference on “Making Statistics More Effective in Schools of Business,” held at the University of Chicago's Graduate School of Business. Information was elicited concerning both the required statistics sequence and elective statistics courses for M.B.A. students, as well as computer usage in these courses. This article summarizes the information obtained from the survey.     

Analyzing Supersaturated Designs by Means of an Information Based Criterion

The cost and time consumption of many industrial experimentations can be reduced using the class of supersaturated designs since this can be used for screening out the important factors from a large set of potentially active variables. A supersaturated design is a design for which there are fewer runs than effects to be estimated. Although there exists a wide study of construction methods for supersaturated designs, their analysis methods are yet in an early research stage. In this article, we propose a method for analyzing data using a correlation-based measure, named as symmetrical uncertainty. This method combines measures from the information theory field and is used as the main idea of variable selection algorithms developed in data mining. In this work, the symmetrical uncertainty is used from another viewpoint in order to determine more directly the important factors. The specific method enables us to use supersaturated designs for analyzing data of generalized linear models for a Bernoulli response. We evaluate our method by using some of the existing supersaturated designs, obtained according to methods proposed by Tang and Wu (1997 Tang , B. , Wu , C. F. J. (1997). A method for constructing supersaturated designs and its E(s ²)-optimality. Canadian Journal of Statistics 25:191–201.[Crossref], [Web of Science ®] , [Google Scholar]) as well as by Koukouvinos et al. (2008 Koukouvinos , C. , Mylona , K. , Simos , D. E. ( 2008 ). E(s ²)-optimal and minimax-optimal cyclic supersaturated designs via multi-objective simulated annealing . Journal of Statistical Planning and Inference 138 : 1639 – 1646 .[Crossref], [Web of Science ®] , [Google Scholar]). The comparison is performed by some simulating experiments and the Type I and Type II error rates are calculated. Additionally, Receiver Operating Characteristics (ROC) curves methodology is applied as an additional statistical tool for performance evaluation.     

A Frailty Model in Crossover Studies with Time-to-Event Response Variable

In this article, we develop a model to study treatment, period, carryover, and other applicable effects in a crossover design with a time-to-event response variable. Because time-to-event outcomes on different treatment regimens within the crossover design are correlated for an individual, we adopt a proportional hazards frailty model. If the frailty is assumed to have a gamma distribution, and the hazard rates are piecewise constant, then the likelihood function can be determined via closed-form expressions. We illustrate the methodology via an application to a data set from an asthma clinical trial and run simulations that investigate sensitivity of the model to data generated from different distributions.     

Evaluating the Effective Degrees of Freedom of the Delete-a-Group Jackknife

The delete-a-group jackknife is sometimes used when estimating the variances of statistics based on a large sample. We investigate heavily poststratified estimators for a population mean and a simple regression coefficient, where both full-sample and domain estimates are of interest. The delete-a-group (DAG) jackknife employing 30, 60, and 100 replicates is found to be highly unstable, even for large sample sizes. The empirical degrees of freedom of these DAG jackknives are usually much less than their nominal degrees of freedom. This analysis calls into question whether coverage intervals derived from replication-based variance estimators can be trusted for highly calibrated estimates.     

A study of several useful tests for ordered alternatives in the randomized block design

This study investigates the small sample powers of several tests designed against ordered location alternatives in randomized block experiments. The results are intended to aid the researcher in the selection process. Toward this end the small sample powers of three classes of rank tests — tests based on ‘within-blocks’ rankings (W-tests), ‘among-b locks’ rankings (A-tests), and ‘ranking after alignment’ within blocks (RAA-tests)— are compared and contrasted with the asymptotic properties given by Pirie (1974) as well as with the empirical powers of competing parametric procedures.     

Formulas for the Design of CUSUM Quality Control Charts

ABSTRACT

In the design of CUSUM control charts, it is common to use charts, tables, or software to find an appropriate critical threshold (h). This article provides an approximate formula to calculate the threshold directly from prespecified values of the reference value (k) and the in-control average run length (ARL₀). Formulas are also provided for choosing k and h from prespecified values of the in-control and out-of-control average run lengths.     

Optimal designs for experiments with mixtures: a survey

This is a survey article on known results about analytic solutions and numerical solutions of optimal designs for various regression models for experiments with mixtures. The regression models include polynomial models, models containing homogeneous functions, models containing inverse terms and ratios, log contrast models, models with quantitative variables, and mod els containing the amount of mixture, Optimality criteria considered include D-, A-, E-,φ_p- and I_λ-Optimalities. Uniform design and uniform optimal design for mixture components, and efficiencies of the {q,2} simplex-controid design are briefly discussed.     

Concurrent Design for Process Quality,Statistical Tolerance,and SPC

The rapid response to the requirements of customers and markets promotes the concurrent engineering (CE) technique in product and process design. The decision making for process quality target, SPC method, sampling plan, and control chart parameter design can be done at the stage of process quality plan based on historical data and process knowledge database. Therefore, it is a reasonable trend to introduce the concepts and achievements on process quality evaluation and process capability analysis, CE, and SPC techniques into process plan and tolerance design. A new systematic method for concurrent design of process quality, statistical tolerance (ST), and control chart is presented based on a NSFC research program. A set of standardized process quality indices (PQIs) for variables is introduced for meeting the measurement and evaluation to process yield, process centering, and quality loss. This index system that has relatively strong compatibility and adaptability is based on raisonne grading by using the series of preferred numbers and arithmetical progression. The expected process quality based on this system can be assured by a standardized interface between PQIs and SPC, that is, quality-oriented statistical tolerance zone. A quality-oriented ST and SPC approach that quantitatively specifies what a desired process is and how to assure it will realize the optimal control for a process toward a predetermined quality target.