Cp is the simplest capability index. It answers one question: how many times does the natural process spread fit into the tolerance window. The natural spread is taken as six sigma, three on each side of the average, because almost every part from a stable process falls inside that band. The formula is Cp = (USL − LSL) / (6σ).
A Cp of 1.00 means the spread exactly fills the tolerance, so even a perfectly centred process will produce a small fraction of parts just outside the limits. A Cp above 1.00 means there is room to spare. Many plants use 1.33 as a general rule of thumb for an acceptable minimum, because it leaves a margin of one sigma on each side, though the figure your customer expects may differ.
Cp has a blind spot. It uses only the width of the tolerance and the width of the spread. It never looks at where the process average actually sits. A process could have a Cp of 2.00 and still make 100 percent scrap if the average were parked outside the limits. That is why Cp is often called the potential capability.
Standard Procedure
- 1Calculate the tolerance width: USL minus LSL.
- 2Multiply the short-term sigma by 6 to get the natural spread.
- 3Divide the tolerance width by the spread to get Cp.
- 4Compare Cp with your plant's or customer's minimum, commonly 1.33 as a rule of thumb.
Lesson Summary
- ✓Cp measures potential: the ratio of tolerance width to six-sigma spread.
- ✓Cp ignores the process average, so a high Cp does not guarantee good parts.