Cp compares the tolerance to the process spread. Cpk also looks at where the center sits. When Cp holds and Cpk falls, the process has a centering problem: something moved the average. Here Cp stays at 2.03 to 2.04 while Cpk falls from 1.63 to 0.98, so the search is for what moved the average, not what added variation.
The chart says the process moved. Capability says how much room is left. Two numbers answer it: Cp, which compares the tolerance to the spread, and Cpk, which also looks at where the center sits.
The inputs
The tolerance runs from 23.980 to 24.020, a width of 0.040. Estimate the process spread from the average range: sigma is the average range divided by 2.326, the constant for subgroups of five.
- Cp is the tolerance width divided by six sigma.
- Cpk is the smaller of two numbers: the upper limit minus the average, over three sigma, or the average minus the lower limit, over three sigma.
Before and after
Stable stretch, subgroups 1 to 11, 55 pieces. Average 24.0040, average range 0.00764, sigma 0.00328. Cp is 2.03 and Cpk is 1.63.
Recent stretch, subgroups 15 to 19, 10:40 to noon, 25 pieces. Average 24.0104, average range 0.00760, sigma 0.00327. Cp is 2.04 and Cpk is 0.98.
What the gap says
Cp barely moved, from 2.03 to 2.04. The spread is the same. Cpk fell from 1.63 to 0.98, so the whole distribution slid toward the upper limit. A Cpk under 1.00 means the nearest limit is less than three sigma away. If this continues, parts will go over.
The gap between the two is the diagnosis. A small gap means the process is centered. A large gap means a centering problem: look for what moved the average. Both low means a spread problem: look for what is adding variation. Here the gap grew from 0.40 to 1.06. This is centering.
Do not recenter yet. An offset change would pull the average back and hide the cause, and the lathe would drift again.
One caution. This is a quick look at 25 pieces, not a formal study. It tells you where to look. Use a larger run when you need a number to show a customer, and ask your customer what minimum they want.
Read more: Cpk vs Ppk.
The mistake to avoid
Reading Cpk without Cp. One number cannot tell you whether to look at centering or at spread, and that is the difference between a ten minute fix and a week of searching.
- Pick one characteristic and list its last 25 pieces in order.
- Work out Cp and Cpk, and write down the gap between them.
- Decide whether the next question is about centering or about spread.
Open the printable Monday Board
Related on ShopFloorOps
The part, the machine, the shift and every number in this book (shaft SH-3306 on Lathe 3) are a made-up example. The tool sidebars show ShopFloorOps tools, which I make and sell. Every chapter teaches the step itself, so you can use your own forms. New to a term? See the quality glossary.