Designed Experiments – Introduction

Classical experiments focus on 1FAT (one factor at a time) at two or three levels and attempt to hold everything else constant (which is impossible to do in a complicated process). When DOE is properly constructed, it can focus on a wide range of key input factors or variables and will determine the optimum levels of each of the factors.

It should be recognized that the Pareto principle applies to the world of experimentation. That is, 20% of the potential input factors generally make 80% of the impact on the result. The classical approach to experimentation, changing just one factor at a time, has shortcomings. Too many experiments are necessary to study the effects of all the input factors. The optimum combination of all the variables may never be revealed. The interaction (the behavior of one factor may be dependent on the level of another factor) between factors cannot be determined. Unless carefully planned and the results studied statistically, conclusions may be wrong or misleading. Even if the answers are not actually wrong, non-statistical experiments are often inconclusive. Many of the observed effects tend to be mysterious or unexplainable. Time and effort may be atrophied through studying the wrong variables or obtaining too much or too little data. The Design of experiments overcomes these problems by careful planning.

In short, DOE is a methodology of varying a number of input factors simultaneously, in a carefully planned manner, such that their individual and combined effects on the output can be identi?ed.

• Many factors can be evaluated simultaneously, making the DOE process economical and less interruptive to normal operations.

• Sometimes factors having an important influence on the output cannot be controlled (noise factors), but other input factors can be controlled to make the output insensitive to noise factors.

• In -depth, statistical knowledge is not always necessary to get a big bene?t from standard planned experimentation.

• One can look at a process with relatively few experiments.

• The important factors can be distinguished from the less important ones.

Concentrated effort can then be directed at the important ones. Since the designs are balanced, there is confidence in the conclusions drawn. The factors can usually be set at the optimum levels for verification. If important factors are overlooked in an experiment, the results will indicate that they were overlooked. Precise statistical analysis can run using standard computer/programs. Frequently, results can be improved without additional costs (other than the costs associated with the trials).

Design Principles Experimental Objectives:

Some experimental design objectives are discussed below.

Comparative objective:

lf several factors are under investigation, but the primary goal of the experiment is to make a conclusion about whether a factor, in spite of the existence of the other factors, is “significant,” then the experimenter has a comparative problem and needs a comparative design solution.

Screening objective:

The primary purpose of this experiment is to select or screen out the few important main effects from the many lesser important ones. The screening designs also terms main effects or fractional factorial designs.

Response surface (method) objective:

This experiment is designed to let an experimenter estimate interaction (and quadratic) effects and, therefore, give an idea of the (local) shape of the response surface under investigation. For this reason, they are termed response

RSM designs are used to:

• Imprint over or optimal process settings

• Troubleshoot process problems and weak points

• Make a product or process more robust against external influences

• Design Principles

• Optimizing responses when factors are proportions of a mixture objective.

If an experimenter has factors that are proportions of a mixture and wants to know the “best” proportions of the factors to maximize (or minimize) a response, then a mixture design is required.

Optimal fitting of a regression model objective:

If an experimenter wants to model a response as a mathematical function (either known or empirical) of a few continuous factors, to obtain “good” model parameter estimates, then a regression design is necessary. Response surface, mixture and regression designs are not featured as separate entities in this Primer. It should be noted that most good computer programs will provide these models. The best design sources are often full factorial (in some cases with replication) and screening designs.