Process Capability (Cpk) Calculator for Balancing
Process capability tells you whether a balancing process is reliably producing parts inside tolerance, or merely producing them inside tolerance on average. A process can have an excellent average and still fail constantly, because what escapes to the customer is governed by spread, not by the mean.
This calculator computes Cpk for a balancing operation, where the specification is one-sided: residual unbalance cannot be negative, and the only limit that matters is the upper one.
Balancing Process Capability (Cpk) Calculator
Units cancel, so any consistent unit works — g·mm, oz·in, g·cm — as long as all three fields use the same one.
On this page
The formula, and why balancing uses the one-sided form
The general Cpk definition takes the worse of the two distances from the process mean to each specification limit, divided by three standard deviations. Balancing rarely needs both halves. Residual unbalance is a magnitude — it cannot go below zero, and a part with less unbalance than required is not defective. There is only an upper limit.
So the calculation reduces to:
Cpk = (Balance tolerance − Average outgoing unbalance) / (3 × Sigma)
Three numbers, and each one has to be measured honestly.
Balance tolerance is the permissible residual unbalance from the part specification. If your specification doesn’t include one, it’s usually derived from a balance quality grade — our ISO 21940-11 balance tolerance guide explains how that derivation works.
Average outgoing unbalance is the mean residual unbalance actually measured on finished parts, after correction. Not the target. Not the acceptance limit. What the machine is really leaving on parts.
Sigma is the standard deviation of that outgoing unbalance across the sample. This is the number people get wrong most often, and it is the number that decides the answer.
Reading the result
| Cpk | What it means in practice |
|---|---|
| Below 1.00 | The process is producing out-of-tolerance parts right now. Sorting is the only thing keeping them in. |
| 1.00 – 1.33 | Inside tolerance with no margin. Any drift in tooling, fixturing or material puts you below 1.00. |
| 1.33 – 1.67 | The most commonly specified requirement in automotive and general manufacturing. |
| 1.67 – 2.00 | Strong margin. Typical target where the consequence of an escape is high. |
| Above 2.00 | Very capable. Worth asking whether the tolerance is tighter than the application needs, or looser. |
Worked example
A driveshaft is specified to 100 g·mm permissible residual unbalance. Over a sample of finished parts, average outgoing unbalance measures 40 g·mm with a standard deviation of 10 g·mm.
Cpk = (100 − 40) / (3 × 10) = 60 / 30 = 2.00
A Cpk of 2.00 is a genuinely capable process. Now change one number: hold the same average but let sigma rise to 20 g·mm, which is what happens as a correction tool wears.
Cpk = (100 − 40) / (3 × 20) = 60 / 60 = 1.00
The average did not move. The process is now marginal. This is the entire argument for measuring spread rather than watching averages.
Where the number goes wrong
Sigma calculated from too few parts. A handful of parts produces an unreliable estimate of spread, and it is usually optimistic. The sample needs to span the variation the process actually sees — different shifts, different material lots, different points in tool life.
Sigma calculated on a sorted population. If out-of-tolerance parts were removed before the data was collected, the distribution has been truncated and the resulting Cpk is fiction. It describes the parts that survived, not the process.
An unstable process. Capability indices assume the process is in statistical control. If the mean is drifting or the spread is changing, a single Cpk is a snapshot of a moving target and tells you very little about tomorrow.
Non-normal distribution. Residual unbalance after automatic correction is often not normally distributed — correction routines tend to pile parts up just under the limit. The parts-per-million estimate in the calculator assumes normality and should be treated as indicative rather than exact.
Measurement variation counted as process variation. The spread you measure includes the variation of the measuring system itself. If the balancer's own repeatability is a significant fraction of the tolerance, some of the sigma in your calculation belongs to the machine, not the process.
Improving a low Cpk
Only two levers exist, and they are not equally available.
Reduce the mean. Correcting closer to zero rather than to just-inside-tolerance raises the numerator directly. This is often a matter of the correction routine's target and stopping criteria rather than the hardware. It is usually the cheaper fix.
Reduce sigma. Spread comes from fixturing repeatability, part-to-part seating, drive coupling, correction resolution and the measurement system. Reducing it is real engineering work, but it is the lever that actually protects you from drift.
A third option — widening the tolerance — is sometimes legitimate and more often a way of moving a problem downstream. If the tolerance came from a balance quality grade rather than a functional requirement, it may genuinely be tighter than the part needs. If it came from a vibration limit the assembly has to meet, it does not.
Frequently asked questions
Why is there no lower specification limit?
Residual unbalance is a magnitude with a floor of zero, and being further below the limit is never a defect. There is nothing to be capable against on the low side.
What is the difference between Cp and Cpk?
Cp measures whether the spread would fit inside the tolerance if the process were perfectly centered. Cpk measures where the process actually sits. With a one-sided specification the distinction largely collapses, which is why balancing capability is normally quoted as Cpk alone.
What about Ppk?
Cpk conventionally uses a within-subgroup estimate of sigma; Ppk uses the overall standard deviation of the whole dataset. Over a long, stable run they converge. If they differ substantially, the process is shifting between subgroups, and that is the finding worth acting on.
How many parts do I need?
Enough to represent real variation rather than one good afternoon. More important than the raw count is that the sample spans shifts, operators, material lots and tool condition. Thirty parts from one hour tells you less than thirty parts from a week.
Can a machine be bought to a guaranteed Cpk?
Capability is a property of a process, not of a machine alone. It depends on the part, the fixture, the correction method, the incoming variation and the tolerance. What can be established is acceptance criteria agreed on your parts, in writing, before the build — which is how we scope every machine.
Related resources
ISO 21940-11 balance tolerance · GD&T symbols reference · Balancing machines · Dimensional gaging systems
