Multivariate Diagnostic Tests: A Review of Different Methods

There are many instances where the quality of a product is determined by the joint level of several characteristics. Under these types of situations, one wishes to detect quickly any departure from a satisfactory level, while at the same time it is of interest to know which characteristic(s) is(are) responsible for the deviation. The most common and popular solution to the first query is to use a T 2 control chart which is an aggregate monitoring function, when the mean vector of the correlated characteristics is the major concern and the normal approximation may be used. However, the answer to the second query is not so easy. The lack of a simple method of selecting the ‘out of control’ variable has made the routine use of T 2 control chart impractical so far. This paper provides a review of different techniques available to identify the culprit variable(s), when a T 2 control chart gives an out-of-control signal.