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In the last section we talked about calculating the control limits of a process and we had some formulas and predefined factors to work with. Well, those were by far the simplest tools available to a six sigma-compliant process. We still have some more formulas ahead to help us see where our process is going to. Remember the “XR” Chart? Remember that we had Upper and Lower limits and a mean line splitting the area in between? Well, this line is important for something called “capability.”

A capable process will render the maximum percentage possible of good parts according to specifications. Let’s review our X, R chart again. All the individual measures whose averages have been graphed in the X section of the chart can be grouped up into more manageable quantities so they can be translated into a bar graph. For example, let’s say the control limits are set at 0.100” and 0.300” which sets the process’ mean line at 0.200”. All the samples or individual measures used on the graph can be put in the same group every 0.020” and thus we’ll have 10 groups. With those numbers we create a bars chart which receives the sophisticated name of Histogram. If we join the top of each column with a line we’ll get a bell-like curved line or a Gauss curve. The Gauss curve will show on processes that are affected by natural variation (the kind of variation that we cannot do much about) and that yield the best possible quality product. Notice that most of the measurement averages fall on and around the mean line, while smaller amounts spread towards the sides. Always there will be some measures going on beyond the control limits but such numbers are usually considered of low importance.

Now let’s move on to the good stuff. The Gauss curve is divided in six sections. The first two on each side of the mean line are worth 34.13% of the total number of samples. The next two on each side are worth 13.6% and the last two on each side are worth 2.135%. Each of these sections is called a Standard Deviation Unit or sigma for short.

These sigma units are used to calculate the capability of a process by means of capability indexes. The ones that we want to know about are the CP and the CPK. The CP index is interested in having the natural variation under control and assumes the process is contained within the specification limits. Its formula is


Where sigma

And where D2 can have the following equivalents.


N D2
2 1.128
3 1.693
4 2.059
5 2.326
Please refer to the last article for more on factor tables.
CP should be > 1.33 for the process to be capable.

The CPK index takes into account both the variation and the centrality of the process and is defined by the formula

When resolving it we choose the minimum value which has to be CPK > 1.33 for its process to be capable, although most of the times a value of 1.0 is arguably acceptable.

Just to recap, we want a process that not only keeps within specification limits but also within control limits. No tendencies towards one limit or the other, but always on the center, so that any piece that falls beyond control or even specification limits be so small (0.03%) that it’ll be ok to ignore it. In other words we will be working under 6σ.

As you can appreciate through these brief articles there is a lot more involved with the six sigma methodology. In fact, I just touched the basics to get a beginner started. Regarding the deeper stuff—well, let’s make way for the black belt guys to talk about it.