# The Six Sigma Knowledge Gap

Statistical probability should be used only when we lack knowledge of the situation and cannot obtain it at a reasonable cost.

I recently attended a presentation using a control chart. The control chart showed a process in statistical control at about an 8-percent reject rate. The presenter noted that the process was stable and went on with her presentation. I barely avoided shouting that, while stability is nice, an 8-percent reject rate is not acceptable. The 8-percent level represents a certain amount of ignorance about the process; a level I find unacceptable. The problem is that the presenter didn’t think of it that way at all. To her, 8 percent represented a considerable accomplishment.

This blog is for those of you who, like me, want to scream that, as long as improvement is economically justified, “It’s never good enough!”

I will present a way of measuring ignorance; a simple-to-compute statistic which highlights the fact that there is always something to learn about how to improve a given process.

First, let’s take a look at the philosophy that underlies statistics. Philosopher Leonard Peikoff said

“Statistics are applicable only when: 1. You are unavoidably ignorant about a given concrete; 2. Some action is necessary and cannot be deferred.”

Leonard Peikoff, The Art of Thinking, 1992

In other words, if you’re trying to determine a course of action, your best bet is to acquire knowledge, not to blindly use statistics to guide you. While it’s true that we don’t want to tamper with a stable process, it’s also true that we don’t want to settle for anything other than the best level of quality we can provide. Control charts guide us away from tampering, but they don’t tell us how we can improve the process. Only new knowledge can do that.

Statistical probability should be used only when we lack knowledge of the situation and cannot obtain it at a reasonable cost. If we have direct knowledge about a situation, or can get it through a bit of research or by consulting someone who has it, then we should not blindly follow the statistical probabilities. In other words, if you know something about the situation, you should act on what you know.

Statistics are an expression of ignorance. They should only be used when ignorance is unavoidable, i.e., when knowledge is absent and unobtainable. Statistics are not knowledge. They are a calculation that permits action in the face of ignorance. This is the critical point missed by the presenter. She assumed that if she simply stated the level of ignorance, further improvement was not necessary.

## Properly Used, Statistics Measure Ignorance or, Conversely, Knowledge

Assume that you want to buy a new piece of production machinery. Think of the important variables in the process as a list of 100 items, all of them unknown. You begin by creating a list of those items you believe to be important and prepare a plan to control as many of these items as possible. Let’s say you start with 75 items. Assuming that every item on your list is actually an important variable, these 75 items are special causes—things that affect your process and must be controlled. The remaining 25 items are common causes of variation, unknown to you but also important causes of process variability even though any one of these causes will have only a small effect.

From this starting point, you conduct a process capability study and, using statistics, quantify your knowledge as explaining all but ±0.003″ of variation in the process. There are some out-of-control data points. After investigating these, you identify five more important variables. The process stabilizes, that is, all of the remaining points on the control chart fall within the control limits.

Let’s assume that the control limits for the X-chart are now ±0.002″. In philosophical terms, this means that you acquired ±0.001″ of new knowledge, but ±0.002″ of ignorance still remains. As time goes by and you learn more, the control limits will measure the amount of your learning. If in a year the control limits are at ±0.001″, then you’ve learned enough to reduce the process variation by 50 percent.

As soon as you acquire this knowledge, the previous statistics become irrelevant. Gaining knowledge is the equivalent of converting special causes into common causes. This is like discovering more and more items on the list of things that cause your process to vary. You may never discover every item on the list, but with statistics to help you keep score, it’s fun to try. One way to make it even more fun is to plot a “knowledge chart.”

## How to Plot a Knowledge Chart

Record the process standard deviation from your most recent process control chart, for example:

S_{0}=10

For each subsequent complete control chart, compute the process standard deviation, such as:

S_{1}=9

Compute your relative knowledge, k, as:

k=100\%\ \times \frac{\left( S_{0}-S_{1} \right)}{S_{0}}

For our example,

k=100\%\ \times \frac{\left( 10-9 \right)}{10}=10\%

As you reduce your ignorance to zero, the knowledge measure will go to 100 percent. It’s a fun way to keep track of your quality progress!

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