In part-1 we discussed the key differences between Process Capability analysis and Process Performance analysis. In this post, we’ll cover the basics of the Cp and Pp Indices.
Let’s say you have collected some final inspection data: you measured some parts, recorded the data, and compared each reading against a spec to check whether the part passed or failed. We are going to begin by visualizing this data as a simple histogram as shown in the picture below.
Next, we are going to add the Upper Spec Limit (USL) and Lower Spec Limit (LSL) to the histogram., and calculate the Spec Width as shown below.
Spec Width = USL – LSL
Similarly, we will also calculate the Process Width. The simplest way to think about the process width is “the difference between the largest value you measured, and the smallest value you measured" (Note: This is an approximation).
Process Width = Max Measured Value – Min Measured Value
And finally, we calculate the capability index as the ratio of the spec width to the process width.
Cp or Pp = Spec Width / Process Width
Here are a few visuals of good and bad processes as indicated by a Pp Index:
Obviously, the larger the Cp of Pp value the better. From the picture it’s clear that the larger the spec width relative to the process width, the less likely you are to have an out of specification condition with a shift in the process.
You want more white space - a buffer zone - between your process limits and your spec limits. That way, you will simply have a lot more room for error. But, the spec width is defined by the designer - typically your customer. So as a manufacturing engineer, you have to design your manufacturing process to consistently deliver a very narrow process width relative to the spec width.
One additional requirement, is that the process should be centered on the nominal (target). In other words, the average of the values you measured should match the nominal (target) of the spec. We'll discuss process centering in the next post.