Written by: Todd Ellingson
When monitoring a process, it’s critical to know if that process is capable of meeting the required specifications. If process variability is high compared to the range of your customers’ specifications, then you will end up with lots of scrap. That’s bad.
But what can we do?
I’m glad you asked. It turns out there’s a statistic for this exact situation. It’s called the Process Capability statistic, abbreviated Cp. (Don’t ask me why it’s Cp and not PC, I guess dyslexia has been around a long time).
Cp is the width of the specification limits divided by the width of the process, i.e., divided by the process variability. The larger Cp is, the more capable the process is of meeting the specification requirements. The XBar & R chart above shows a Cp statistic of 1.022 in the box at the upper-left.
For example, it’s desirable to have a Cp value greater than one. This indicates the width of the specification limits (the numerator) is wider than the width of the process variability (the denominator). In other words, the process is operating within the specification limits.
It’s interesting to know the history of how Cp is calculated. Calculating Cp requires calculating a standard deviation as an intermediate step. But back in the day, before computers were widespread, it was fairly time consuming to calculate something like a standard deviation.
So 50 years ago this was all a hassle. Then some smart people figured out you could estimate the standard deviation using a function of the range, i.e., the maximum minus the minimum. And the range is easy to calculate. As a result, the Cp statistic was almost always calculated using a function of the range to estimate the standard deviation.
Today computers are everywhere, and it’s easy to calculate the standard deviation directly. But old habits die hard, and the traditional range method is still the most common way to calculate Cp.
With STATISTICA, you can calculate Cp either way (using the range method, or calculating the standard deviation directly). But in keeping with convention, the range method is used by default, as is done in most (probably all) other statistical software.