The Problem with Swiss Army Knife Control Charting

I’m an advocate of using the I-chart as the default control chart. If I am teaching statistical process control (SPC) and can only teach one chart, the I-chart is always the one that I teach. It’s the only control chart I cover in my Lean Six Sigma Green Belt training. It’s the only chart that I teach in Process Excellence Leadership training. It’s the only chart I use if the data I’m looking at are reasonably close to symmetric (note that I didn’t say “normal”,) unless I have some compelling need for greater sensitivity. I teach that the I-chart is the “Swiss army knife” of control charts.

But I still sometimes use other control charts.

The Problem

Organizations don’t do SPC for the fun of it. They do it because it helps them achieve their goals. Organizations exist to produce things of value for the benefit of customers, investors, and employees. They do this by transforming inputs into outputs of higher value via processes. They can do this better if they minimize variability of outcomes, which can best be accomplished by controlling the sources of variation in the inputs and processes. This is where SPC comes in. SPC is a methodology that uses statistical guidelines to help separate “special cause” and “common cause” variation. If a special cause of variation exists, it signals the need to act. Special cause variation is defined as a change of such a large magnitude that its cause can probably be identified if looked for at once. SPC operationally defines such a change as a measurement result more than 3 standard deviations from the process mean for whatever process metric is being monitored.

A problem might exist if the process generates measurements that are highly skewed, even when it is not being influenced by special causes of variations. Such processes are quite common in the real world. For example, nearly all measurements produced by geometric dimensioning and tolerancing are skewed, as are measurements of time-based phenomena such as those encountered in services industries including the healthcare and hospitality industries. Highly skewed distributions produce a relatively high percentage of results more than 3 standard deviations from the mean even if no special causes exist. In other words, they produce many “false alarms” that will trigger a search for a problem when there is no problem. The false alarms may even lead to tampering, thereby causing a stable process to become unstable.

I-Charts Don’t Solve the Problem

The skewed distribution problem is exacerbated by using I-charts. I-charts are relatively insensitive to moderate departures from normality, and very insensitive if the non-normality still produces a symmetric distribution. But for the data described above, this is not the case. If you use the I-chart for these data you will experience many false alarms. It’s just that simple.

The problem is to determine if a process is or is not being influenced by special causes of variation. A process distribution might appear as skewed because of special cause outliers, or because it naturally produces skewed data. The I-chart treats all data beyond 3 sigma as outliers; it doesn’t help you separate the natural, common cause process outcomes from special cause outcomes. Is the point beyond 3 sigma an outlying chicken, or a common cause egg? I.e., is the process being influenced by special causes, or only common causes? If the process data are naturally skewed you can’t answer this question using an I-chart.

A Simple Solution

The solution that I recommend is to begin your investigation with averages charts, also known as x-bar charts. Averages tend to have distributions that are approximately normal, even if the individual values are skewed. This means that, for a process with a skewed distribution that is not influenced by special causes, averages are much more likely to produce results that stay within 3 standard deviations of the mean than I-charts. It’s the best of both worlds: few false alarms, but still sensitive to special causes. If you have a nice run of subgroup averages without a special cause, plot a histogram of the data and see if the distribution looks skewed or symmetric. If the latter, you can use I-charts with confidence. If the former, stick with averages charts, or find a statistician or Master Black Belt to help you find a more advanced solution.

Stable Does Not Mean Normal

Before ending this article, I’d like to address another pet peeve of mine. I believe that too many teachers of SPC obsess on the need for normality. They confuse normality with the absence of special causes, also known as statistical control. I usually attribute this misunderstanding to a lack of experience with the real world, where normal distributions are so rare as to be virtually non-existent. By insisting on normality we encourage tampering and all of the problems associated with this approach to “process management.”

On the other hand, I am also impatient with people who insist that all non-normality be ignored. These individuals advocate using I-charts in all situations, regardless of the risk of false alarms. This attitude may also be due to a lack of experience. However, I’ve seen SPC lose its credibility when concerned process owners look for special causes over-and-over again without finding them. Like the boy who cried “Wolf!”, out-of-control signals become something to ignore. Eventually so does SPC.

My approach, which favors the I-chart but doesn’t make its use dogma, provides a rational middle ground.