Thursday, September 8, 2011

Process Capability (CpK)

From a manufacturing perspective, a capable process is one that can tolerate a lot of input variability. Said another way, a capable process produces the same end result despite large changes in material, controlled parameters or methods.

As the cornerstone of "planned, predictable performance," a robust/capable process lets manufacturing VPs sleep at night. Inversely, if your processes do not tolerate small changes in materials, parameters or methods, you will not make consistent product and ultimately end up making scrap.

To nerd out for a bit, the capability of a process parameter is computed by subtracting the lower specification limit (LSL) from the upper specification limit (USL) and dividing this by the standard deviation measured of your at-scale process:


The greater the Cp, the more capable your process. There are many other measures of capability, but all involve specifications in the numerator, standard deviation in the denominator and values of 1 or greater means "capable."

A closer look at this metric shows why robust processes are rarely found in industry:

  • Development sets the specifications (USL/LSL)
  • Manufacturing controls the at-scale variables that determine standard deviation.

And most of the time, development is rewarded for specifications that produce high yields rather than wide specifications that increase process robustness.

Let's visualize a capable process:


Here, we have a product quality attribute whose specifications are 60 to 90 with 1 stdev = 3. So Cp is (90-60)/6*3 = 30/18 = 1.6. The process has no problems meeting this specification and as you can see, the distribution is well within the limits.

Let's visualize an incapable process:


Again, USL = 90, LSL = 60. But this time, the standard deviation of the process measurements is 11 with a mean of 87.

Cp = (90 - 60)/ 6 * 11 = 30/66 = 0.45. We can expect the process to meet the specification approximately 45% of the time.

Closer examination shows that the process is also not centered and vastly overshoots the target; even if variability reduction initiatives succeeded, the process would still fail often because it is not centered.

If you are having problems with your process reliably meeting their specifications, apply capability studies to assess your situation. If you are not having problems with your process, apply capability studies to see if you are at risk of failing.

The take-away is that process robustness is a joint manufacturing/development effort, and manufacturing managers must credibly communicate process capability to development in order to improve process robustness.

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