## Statistics as a System by Ron Sedlock

*“Quality is the result of the system.”* --W. Edwards Deming

__Statistics as a System__

The true test of a quality professional is the person’s ability to make good and timely decisions. Decision making on the processes that make up a system can be enhanced using statistics.

Our processes talk to us. The problem is the talk is in the language of numbers. To many, numbers are like a foreign language. What is a process trying to say?

The answer to this question is the use of statistics as a system. A system of statistics has three elements – Central Tendency, Dispersion and Shape (Figure 1). Just looking at 1 (or even 2) of these elements can lead to a bad decision. They are not independent. Each element “depends” on the other two.

As a review, let us talk about each element. Then we will talk about the interactions.

Central tendency is the “typical” number from a set of numbers. Usually, the set of numbers is a sample from a population. The average is the most common measure used. Some other measures of central tendency are median and mode.

Dispersion is the variation of a set of numbers. The range (high minus low) is a “quick and dirty” measure. A more accurate measure of the variation is the standard deviation or sigma. Another measure is the variance which is sigma squared.

The Shape of a set of numbers is the third element. It is probably the most ignored element. The normal distribution (bell-shaped) is the most common one used. Its shape is a special case of the Weibull distribution. Other shapes, such as bimodal and skewed, are very important to include in our decision making.

**Central Tendency and Dispersion**

When we have an average (the X-bar) of a sample, we have an estimate of the central tendency of the entire population (the mean). What does the average **infer** about the mean of the population. Hence, the term **infer**ential statistics. Confidence limits around the average is calculated using the measure of dispersion (sigma). This is the basis of the Central Limit Theory.

**Shape and Dispersion**

Calculating the dispersion on multi-modal and skewed data will inflate sigma. Is multi-modal caused by different inputs or by overadjustment? Overadjustment is what Deming called “tampering with the process”. Here is where a tool like the Box and Whisker Plot (Figure 2) can help. Skewness can indicate a pattern of wear. Here monitoring the skewness coefficient is useful.

**Central Tendency and Shape **

When the average is calculated on bimodal data, the average will be “in the valley” between the two modes*, i.e. fewer numbers at the average*. In skewed data, the average will not be the typical number. Now you know why house prices always use the median price not the average price.

**Central Tendency, Dispersion and Shape**

At this point you should see that statistics is a system. All three interact with one another. Here are some problems I have seen:

Problem 1: Currently many people want to reduce sigma (Lean Six Sigma). Done properly it is useful, but if you are off target (central tendency) and reduce sigma, you will be more consistently off target.

Problem 2: Using 2 sigma control limits on processes. The tighter-the-better mentality. The rationalization is that we create a “warning zone” between 2-sigma and 3-sigma. The issue is how do we react to a reading in the warning zone. Do we look for an assignable cause that does not exist (alpha error)? Do we adjust a stable process (tampering with the process)? Do we not report readings in the warning zone?

Problem 3: Not paying attention to patterns in the data (the shape). Rules for patterns are well identified on control charts. Assignable causes of patterns are important. Reacting to patterns reduces beta error and anticipates problem ahead of time.

**Conclusion **

Using the three elements of statistics and their interactions leads the way better decision-making. Better decision-making leads to organizational excellence.

*“Like quality, statistics is the result of the system.”* --Ron Sedlock

*Ron Sedlock has over 48 years of quality experience. He began his career studying under the personal tutorage of Dr. W. Edwards Deming and Dr. Joseph M. Juran. He has been a member of ASQ or ASQC since 1976 and has held most ASQ Certifications. He is a military veteran serving with the 1 ^{st} Air Cavalry in Vietnam.*

*He can be reached at **rsedlock@msn.com*

__ __

Acknowledgement:

I had many personal conversations Dr. Deming. I will be eternally grateful for his guidance and words of wisdom. His books have a wealth of information.

DONE