In a class last month I was asked to explain a number that occurs in some measurement system evaluations and which is known as the precision to tolerance ratio (P/T ratio). As I will show in this column, it turns out to be related to the capability ratio.

We will need some notation in what follows.  So, let the product measurements be denoted by X.  These product measurements may be thought of as consisting of two components. The value of the item being measured may be denoted by Y, while the error of the measurement may be denoted by E. Thus, X = Y + E. If we think about these quantities as variables, then the variation in the product measurements, Var(X), can be thought of as: 

where Var(Y) is the variation in the stream of product values, and Var(E) is the variation in the stream of measurement errors.

 …