The Design of Optimum Multifactorial Experiments

Abstract A problem which often occurs in the design of an experiment in physical or industrial research is that of determining suitable tolerances for the components of a certain assembly; more generally of ascertaining, the effect of quantitative or qualitative alterations in the various components upon some measured characteristic of the complete assembly. It is sometimes possible to calculate what this effect should be; but.it is to the more general case when this is not so that the methods given below apply. In such a case it might appear to be best to vary the components independently and study separately the effect of each in turn. Such a procedure, however, is wasteful either of labour or accuracy, while to carry out a complete factorial experiment (i.e. to make up assemblies of all possible combinations of the n components) would require Ln assemblies, where L is the number of values (assumed constant) at which each component can appear. For L equal to 2 this number is large for moderate n and quite impracticable for n greater than, say, 10. For larger L the situation is even worse. What is required is a selection of N assemblies from the complete factorial design which will enable the component effects to be estimated with the same accuracy as if attention had been concentrated on varying a single component throughout the N assemblies.