### Measuring Process Performance – Average and Variation

Process performance is universally described in practice by collecting data and calculating the mean (i.e. the mathematical average) performance.  Unfortunately, the variation around the mean is almost never included when describing process performance.  This is a critical oversight that is addressed by the Six Sigma methodology.

Let me illustrate with an example that I often use in the classroom.    One of the critical performance metrics in the airline industry is on time departure.  Performance is measured by comparing the scheduled time of departure to the actual time of departure.  The actual time of departure is defined as the time that the plane is pushed away from the boarding gate.  In this example, a number of data points were collected for Airline A and for Airline B.   In the case of Airline A, flights depart an average of 10 minutes late.  In the case of Airline B, flights depart an average of 20 minutes late.

When presented with this information, and only this information, students always indicate that they prefer the performance of Airline A.   However, the average performance only tells part of the story.  What we know about the average value is that half of the time the performance is better than average, and half of the time the performance is worse than average.

For the purposes of this discussion, we will assume that the data in both cases is normally distributed and that flights can and do depart early.  Further analysis of the data shows that airline A has a huge amount of variation around the mean, while Airline B has very little variation.   Variation is typically described by calculating the standard deviation of the data.  In our example, Airline A has a standard deviation of ten minutes and Airline B has a standard deviation of one minute.  The impact is that Airline A’s flights can be expected to depart anywhere between 20 minutes before the scheduled time of departure and 40 minutes after the schedule departure.  Airline B’s flights can be expected to depart 20 minutes after the scheduled departure, plus or minus three minutes.

In light of this additional information, which airline do you now prefer?  Students now choose Airline B.  They are not willing to arrive at the gate only to find out that a flight operated by Airline A departed prior to the scheduled time, nor are they willing to wait for an excessive amount of time.  Airline B is preferred because the variation in performance is small.

The lesson here is that when describing process performance and when working on process improvement, the amount of variation in performance is at least as important (if not more important) than the average performance.