Robert A. McLean

A unified approach to mixed linear models

Abstract The mixed model equations as presented by C. R. Henderson offers the base for a methodology that provides flexibility of fitting models with various fixed and random elements with the possible assumption of correlation among random effects. The advantage of teaching analysis of variance applications from this methodology is presented. Particular emphasis is placed upon the relationship between choice of estimable function and inference space.

Extreme Vertices Design of Mixture Experiments

The extreme vertices design is developed as a procedure for conducting experiments with mixtures when several factors have constraints placed on them. The constraints so imposed reduce the size of the factor space which would result had the factor levels been restricted to only 0 to 100 per cent. The selection of the vertices and the various centroids of the resulting hyper-polyhedron as the design is a method of determining a unique set of treatment combinations. This selection is motivated by the desire to explore the extremes as well as the center of the factor space. A non-linear programming procedure is used in determining the optimum treatment combination.

Applications of Replacement Theory

Abstract This paper describes a practical procedure for applying existing theory to obtain “approximate optimum” replacement policies for homogeneous pieces of equipment. In addition, the problem of detecting changes in time-to-failure distributions, the relation of these distributions to the life cycles of equipment, and common mistakes that can result in improper policies are discussed. Application of the procedure is illustrated by two examples encountered by Union Carbide Corporation—Nuclear Division personnel.

Randomized Complete Block Designs in Industrial Studies

The use of randomized complete block designs is considered as a proactive method for collecting data to develop further understanding of the sources of variation affecting process outputs. The purpose of the randomized block design has traditionall..

On the Evaluation of Percentage Change: Control Versus Treatment Groups

Experimenters faced with the task of evaluating the effect of a treatment frequently must determine the significance of the percentage change observed for a treatment mean relative to the mean of a control. A common error is to treat the mean of control data as a constant rather than a random variable. This error is explored, and a procedure for properly handling such a comparison is presented.

A Scientific Approach to Experimentation for Consulting Statisticians

An orderly approach for designing and carrying out scientific experiments is presented. The role of the consulting statistician is emphasized...

Design of Experiments: A Realistic Approach.

Review of Some Basic Statistical Concepts Some Intermediate Data Analysis Concepts A Scientific Approach to Experimentation Completely Randomized Design (CRD) Randomized Complete Block Design (RCBD) Nested (Hierarchical) and Nested Factorial Designs Split Plot Type Design Latin Square Type Designs 2n Factorial Experiments (Complete and Incomplete Blocks) Fractional Factorial Experiments for Two-Leveled Factors Three-Level Factorial Experiments Mixed Factorial Experiments and Other Incomplete Block Designs Response Surface Exploration Appendices