A BAYES CLASSIFIER WHEN THE CLASS DISTRIBUTIONS COME FROM A COMMON MULTIVARIATE NORMAL-DISTRIBUTION

Let (n-1) measurements be taken on a component of some manufactured product prior to the manufacture of the product. We want to decide to keep or reject this component before it is allowed to enter the manufacturing process, based on the relationship of these measurements to some post-manufacture measurement on the finished product. Let all measurements ("before" and "after"), taken together, form an n-dimensional random vector described by a multivariate normal distribution. This paper derives the mathematical relationships necessary for the design of a Bayes classifier for the component. The classifier has a relatively simple form, and can be easily implemented on a personal computer. The Bayes classifier is simple to implement, given that estimates of the mean vector and the covariance matrix of the measurement vector can be obtained. There are two situations where this new classifier is an attractive alternative to the traditional classifier: 1) The assumption of two distinct normal distributions for the good and bad classes is theoretically untenable, and 2) The estimation of two different covariance matricies would be difficult for economic or other practical reasons.