George E. P. Box

On the Experimental Attainment of Optimum Conditions

The work described is the result of a study extending over the past few years by a chemist and a statistician. Development has come about mainly in answer to problems of determining optimum conditions in chemical investigations, but we believe that the methods will be of value in other fields where experimentation is sequential and the error fairly small.

Some New Three Level Designs for the Study of Quantitative Variables

A class of incomplete three level factorial designs useful for estimating the coefficients in a second degree graduating polynomial are described. The designs either meet, or approximately meet, the criterion of rotatability and for the most part can be orthogonally blocked. A fully worked example is included.

Intervention Analysis with Applications to Economic and Environmental Problems

Abstract This article discusses the effect of interventions on a given response variable in the presence of dependent noise structure. Difference equation models are employed to represent the possible dynamic characteristics of both the interventions and the noise. Some properties of the maximum likelihood estimators of parameters measuring level changes are discussed. Two applications, one dealing with the photochemical smog data in Los Angeles and the other with changes in the consumer price index, are presented.

Science and Statistics

Abstract Aspects of scientific method are discussed: In particular, its representation as a motivated iteration in which, in succession, practice confronts theory, and theory, practice. Rapid progress requires sufficient flexibility to profit from such confrontations, and the ability to devise parsimonious but effective models, to worry selectively about model inadequacies and to employ mathematics skillfully but appropriately. The development of statistical methods at Rothamsted Experimental Station by Sir Ronald Fisher is used to illustrate these themes.

Robustness in the Strategy of Scientific Model Building

Publisher Summary Robustness may be defined as the property of a procedure which renders the answers it gives insensitive to departures, of a kind which occur in practice, from ideal assumptions. Since assumptions imply some kind of scientific model, I believe that it is necessary to look at the process of scientific modelling itself to understand the nature of and the need for robust procedures. Against such a view it might be urged that some useful robust procedures have been derived empirically without an explicitly stated model. However, an empirical procedure implies some unstated model and there is often great virtue in bringing into the open the kind of assumptions that lead to useful methods. The need for robust methods seems to be intimately mixed up with the need for simple models. This we now discuss.

Modeling Multiple Time Series with Applications

Abstract An approach to the modeling and analysis of multiple time series is proposed. Properties of a class of vector autoregressive moving average models are discussed. Modeling procedures consisting of tentative specification, estimation, and diagnostic checking are outlined and illustrated by three real examples.

Taguchi's parameter design: a panel discussion

It is more than a decade since Genichi Taguchis ideas on quality improvement were inrroduced in the United States. His parameter-design approach for reducing variation in products and processes has generated a great deal of interest among both quality practitioners and statisticians. The statistical techniques used by Taguchi to implement parameter design have been the subject of much debate, however, and there has been considerable research aimed at integrating the parameter-design principles with well-established statistical techniques. On the other hand, Taguchi and his colleagues feel that these research efforts by statisticians are misguided and reflect a lack of understanding of the engineering principles underlying Taguchis methodology. This panel discussion provides a forum for a technical discussion of these diverse views. A group of practitioners and researchers discuss the role of parameter design and Taguchis methodology for implementing it. The topics covered include the importance of vari...

Evolutionary Operation: A Method for Increasing Industrial Productivity

The rate at which industrial processes are improved is limited by the present shortage of technical personnel. Dr Box describes a method of process improvement which supplements the more orthodox studies and is run in the normal course of production by plant personnel themselves. The basic philosophy is introduced that industrial processes should be run so as to generate not only product, but also information on how the product can be improved.

Signal-to-noise ratios, performance criteria, and transformations

For the analysis of designed experiments, Taguchi uses performance criteria that he calls signal-to-noise (SN) ratios. Three such criteria are here denoted by SN T , SN L , and SN S . The criterion SN T was to be used in preference to the standard deviation for the problem of achieving, for some quality characteristic y, the smallest mean squared error about an operating target value. Leon, Shoemaker, and Kacker (1987) showed how SN T was appropriate to solve this problem only when σ y was proportional to μ y . On that assumption, the same result could be obtained more simply by conducting the analysis in terms of log y rather than y. A more general transformation approach is here introduced for other, commonly met kinds of dependence between σ y and μ y (including no dependence), and a lambda plot is presented that uses the data to suggest an appropriate transformation. The criteria SN L and SN S were for problems in which the objective was to make the response as large or as small as possible. It is arg...

Transformation of the Independent Variables

In representing a realationship between a response and a number of independent variables, it is preferable when possible to work with a simple functional form in transformed variables rather than with a more complicated form in the original variables. This paper describes and illustrates a procedure to estimate appropriate transformations in this context.