SIX SIGMA: The Variables (Part 3 of 3)

The Leverage Principle

 

According to the Pareto principle, 20% of the variables contribute 80% to the output or variation in Y. We even have a name for these variables. The variables that exert undue influence over the outcome of a process are called “vital few” whereas the ones that have a lesser impact are called “trivial many”. Hence, this is known as the “leverage principle”. 

“Let us illustrate the concept of leverage variables. We all know that the total variance of an output is the addition of the individual variances of the independent components. Now, let’s imagine that we have a process with six independent variables (Xs) and one Critical to Quality characteristic or dependent variable (Y). Expressed in equation form we would write: Y = f (X1, X2, … X6).” 

“Moreover, let’s say that we take some measurements and determine the baseline condition of total variance presented on the first line.” 

Since the objective is to reduce variability, we would ask ourselves the following question: What combination of individual variation minimizes total output variability?  

To illustrate how each variable influences the result we could try three strategies: a) reduce the variation of all Xs by one unit; b) Reduce the variation of all Xs to zero except for X2; and c) reduce the variation of X2 by three units.  

As we can see, the third strategy is superior to the other two because with a change of only three units in total reduction we obtain a 20.9% improvement over the baseline condition. X2 exerts an undue influence in the total cause system; therefore, it is leverage in nature.