What goes up must come down [multivariate failure analysis]

A particular reliability problem involving approximately 1000 variables that describes the aging, manufacturing process, and environmental history of a particular component is considered. The objective is to select the small subset of these variables which has the greatest apparent causal influence on failure. One approach uses regression analysis. However, with the extremely large number of candidate variates, the selected model might provide a high multiple correlation coefficient even though the true correlation coefficient, R, is close to zero. The authors point out quantitative constraints on the size of the selected model in order to reduce the probability of a randomly attained high R value. Graphs are provided showing a specified probability that R will be less than or equal to a certain value when the true multiple correlation coefficient is zero