A Method for Analyzing Multiple Factor Experiments - Its Application to a Study of Gun Perforating Methods

Frequently in engineering research, problems involving a large number of variables (factors) are encountered. A traditional method of interpretation is for the project engineer to present his results in the form of families of curves obtained by varying factors one at a time. When several values (called levels) are required to characterize each variable properly the number of test points necessary may become prohibitive. It is possible under certain conditions to test only a portion of all of the combinations of the factors and still draw reliable conclusions. This paper describes and demonstrates the use of a powerful statistical method for handling problems of this type. The accurate and fairly inexpensive solution to the laborious calculations was made possible by the use of an electronic data processing machine. The first part of the paper deals with the method of analysis in sufficient detail so that its application in general engineering research problems can be seen. The second part describes the actual application to a study of gun perforating methods. Introduction One of the most perplexing problems faced by engineers is that of properly interpreting the results of experiments involving large numbers of supposedly independent variables. Reservoir engineers are constantly attempting to evaluate the effect that the various phases of well completion have upon oil production. Research engineers design laboratory experiments to evaluate various factors in as economic a manner as possible. The classical method of studying the effect of controllable factors is to vary a single factor at a time. This "single-factor-at-a-time" method is extremely inefficient when compared to the technique called factorial design. For a simple experiment involving two factors, each at two values (levels), the use of factorial design results in an increase in precision of 50 per cent over that in the equivalent single-factor-at-a-time experiment and, as the example becomes more complicated, the difference in efficiency between the two methods increases markedly. This advantage of factorial experiments, sometimes called "hidden replication," is based on the fact that all of the observations contribute to the determination of the effect of each factor. In the single-factor method, on the other hand, only a small proportion of the total number of observations is used. When factors do not operate independently the are said to interact. An example of interaction between factors can be seen in PVT studies where the effect of varying the temperature is dependent upon the pressure of the system.