Cp and Cpk calculator

What Cp and Cpk tell you

Process capability compares two things: how much a characteristic is allowed to vary, set by the specification limits, and how much it actually varies, measured by the standard deviation. Cp and Cpk put that comparison into a single number each.

Cp is the width of the specification divided by six standard deviations: (USL - LSL) / (6 x sigma). It asks whether the spread of the process could fit inside the tolerance, and it ignores where the process is centred.

Cpk takes the distance from the mean to the nearer specification limit and divides it by three standard deviations: the smaller of (USL - mean) and (mean - LSL), divided by (3 x sigma). It asks whether the process fits where it actually sits. Cpk is the number customers usually ask for, because a process can have plenty of room in theory and still be making parts out of tolerance at one edge.

Reading the numbers

• Below 1.00: the process is wider than the tolerance on at least one side. Some output is out of specification as a matter of routine.
• 1.00: three standard deviations just reach the nearer limit. There is no margin for the process to drift.
• 1.33: four standard deviations of room. This is the usual minimum requirement, and it is the line the calculator uses for a "capable" verdict.
• 1.67 and above: five standard deviations or more, commonly required for safety-related or otherwise critical characteristics.

Requirements vary by customer and by characteristic, so check the drawing, the control plan and any customer-specific requirements before you treat 1.33 as the target.

Cp against Cpk

Cpk can never be higher than Cp. The two are equal only when the process mean sits exactly in the middle of the specification. The gap between them is what being off-centre is costing you.

That makes the pair a quick diagnosis. A good Cp with a poor Cpk means the variation is fine and the process needs re-centring, which is usually the cheaper fix. A poor Cp means the variation itself is too large, and no amount of adjustment to the mean will rescue it. The calculator shows the capability on each side separately so you can see which limit is the tight one.

Which standard deviation to enter

This matters more than anything else on the page. Cp and Cpk are meant to use the short-term, within-subgroup standard deviation, estimated from a control chart as the average range divided by the constant d2, or the average moving range divided by 1.128 for individual readings. If you enter the ordinary standard deviation of all your readings taken together, the same formulas give you Pp and Ppk, the long-term performance indices, which are normally lower.

Either is a legitimate number. Just label the result for what it is.

Before you quote a capability figure

A capability index describes a stable process, so stability comes first. If the control chart shows points beyond the limits, runs or trends, the standard deviation is not describing one consistent process and the index means little. Control charts that speak up covers how to read those signals.

Three more conditions apply. The data should be roughly bell-shaped, because the formulas assume a normal distribution. There should be enough of it, with around 100 readings or 25 subgroups as the common rule of thumb. And the measurement system has to be good enough to see the variation, which is what a Gauge R&R study establishes.

Common questions

Can Cpk be negative?

Yes. A negative Cpk means the process mean is outside the specification limits, so more than half of the output is out of tolerance.

What if I only have one specification limit?

This calculator needs both limits. With a single limit only the one-sided index applies: the upper-side figure where there is only an upper limit, the lower-side figure where there is only a lower one, and there is no Cp.

Is anything I enter stored?

No. The calculation happens on this page, in your browser. The four values are held in the page address so that you can copy a link to a result.

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