William G. Hunter

Minimum Aberration 2 k–p Designs

For studying k variables in N runs, all 2 k–p designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution. Algorithms are presented for constructing these minimum aberration designs.

A Review of Response Surface Methodology: A Literature Survey

Response surface methodology, an experimental strategy initially developed and described by Box and Wilson, has been employed with considerable success in a wide variety of situations, especially in the fields of chemistry and chemical engineering. It is the purpose of this paper to review the literature of response surface methodology, emphasizing especially the practical applications of the method. A comprehensive bibliography is included.

Experimental Design: Review and Comment

We review major developments in the design of experiments, offer our thoughts on important directions for the future, and make specific recommendations for experimenters and statisticians who are students and teachers of experimental design, practitioners of experimental design, and researchers jointly exploring new frontiers. Specific topics covered are optimal design, computer-aided design, robust design, response surface design, mixture design, factorial design, block design, and designs for nonlinear models.

Determining the Most Profitable Target Value for a Production Process

In this paper the question of what is the best setting for the target value of an industrial process is explored. A simple graphical procedure is described which takes into account the regular and reduced selling prices, the give-away cost, and the proc..

Some Problems Associated with the Analysis of Multiresponse Data

Experience has shown that unless special care is exercised in analyzing multiresponse data serious mistakes can be made. In this paper some problems associated with fitting multiresponse models are identified and discussed. In particular, three kinds of dependencies are considered: dependence among the errors, linear dependencies among the expected values of the responses, and linear dependencies in the data. Since ignoring such dependencies can lead to difficulties, a method is described for detecting and handling them. The concepts involved are illustrated with a chemical example.

Designs for Discriminating Between Two Rival Models

In most statistical literature on the design of experiments it is assumed that the correct form of the mathematical model is known and the problem is to select the experimental conditions so that some criterion is satisfied, for example, the parameters are estimated with maximum precision. Such an approach, however, ignores one important question that often confronts experimenters who, instead of having only one model known to be correct, have a number of rival candidate models to consider. Such situations can arise, for example, at the outset of investigations on the kinetics of solid-catalyzed gas reactions in chemical engineering. Often the immediate question in these circumstances is: how should experiments be planned so that the inadequate models can be detected and hence eliminated most eliiciently? In this paper a sequential design procedure is proposed for discriminating between two rival models. The basic idea is to select for the next experimental point that at which the models differ the most. ...

The Experimental Study of Physical Mechanisms

This paper is concerned with the dual problem of generating and analyzing data in experimental investigations in which the goal is to develop a suitable mechanistic model. The problem is first distinguished from that of response surface methodology. With regard to the analysis of data, topics that are discussed include the behavior of estimated constants with an inadequate model, a diagnostic technique for modelbuilding, and the importance of visual scrutiny of data. With regard to the generation of data, the concept of placing a model in jeopardy is discussed. Designs for model discrimination and for parameter estimation are considered.

Monitoring Sewage Treatment Plants: Some Quality Control Aspects

Common features of environmental quality data are serial correlation, seasonality, missing values, nonconstant variance, and nonnormal distributions. These features are found in air and water quality data, in biological and chemical data, and in data fr..

The Design of Experiments for Parameter Estimation

This paper is concerned with the design of experiments to estimate the parameters in a model of known form, which may be nonlinear in the parameters. This problem was discussed in detail by Box and Lucas for the case where N, the number of experiments, is equal to p, the number of parameters. The present work is an extension to cases where N is greater than p. Conditions are established under which, when the number of experiments is a multiple of the number of parameters, replication of the best design for p experiments is an optimal design for N experiments. Several chemical examples are discussed; in each instance, the best design consists of simply repeating points of the original design for p experiments. An example is also mentioned where the best design does not consist of such replication.

A Joint Design Criterion for the Dual Problem of Model Discrimination and Parameter Estimation

Two objectives of much experimentation in science and engineering are (i) to establish the form of an adequate mathematical model for the system being investigated and (ii) to obtain precise estimates of the model parameters. In the past, statistical design procedures have been proposed for tackling either one of these problems separately. Investigators, however, frequently want to perform experiments which will shed light on both questions simultaneously. In this paper, therefore, we present a design criterion which takes both objectives into account. The basic design strategy is to emphasize model discrimination when there is considerable doubt as to which model is best and gradually shifting the emphasis to parameter estimation as experimentation progresses and discrimination is accomplished. It is assumed that experiments can be performed sequentially. The use of the design criterion is illustrated with an example.