A failing Cpk may describe the gauge rather than the process. The correction is straightforward arithmetic — but the corrected number is not always the one the decision needs.
Variances add. What you observe is the process plus the measurement system:
σ²observed = σ²process + σ²measurement
Because measurement variance adds rather than cancels, observed spread always exceeds true process spread. Capability indices computed from measured data therefore understate capability — and the bias runs in only one direction.
That one-directional bias is useful. An observed capability index is a lower bound on true process capability. A process that passes on measured data has passed conservatively and needs no defending. A process that fails on measured data has not yet been shown to be incapable.
Subtract variances, never standard deviations:
σ²process = σ²observed − σ²gauge R&R
The gauge term has to come from a measurement systems study run on the same parts, operators and conditions as the capability data. Borrowing a number from a study on a different line, or from the manufacturer's specification sheet, imports an assumption that will not survive questioning.
Two consequences follow that are easy to overlook. First, the correction inherits the uncertainty of the gauge study — a variance component estimated from ten parts and three operators is not precise, and that imprecision propagates into the corrected capability figure. Reporting a corrected Cpk to three decimals from a small gauge study overstates what is known.
Second, the subtraction can return a negative number. That is not a computational failure to be clipped at zero and ignored. It says measurement variation is of the same order as everything observed, so the data contain almost no information about the process. The honest response is to say so and fix the measurement system before making any capability claim at all.
Because the relationship is between variances, moderate measurement noise costs less capability than intuition suggests, and severe noise costs more.
If measurement contributes 30% of observed standard deviation, it contributes about 9% of observed variance. Removing it shrinks the standard deviation by roughly 5%, so the capability index rises by about 5%. A process posting 1.28 was really about 1.34 — real, but rarely decisive.
At 50% of observed standard deviation, measurement is 25% of variance. The index rises by about 15%: a process posting 1.15 was really about 1.33. That is the difference between failing and passing a common acceptance threshold, on the same product, from the same data.
The practical rule is that a gauge should be judged against the capability margin available, not against a fixed percentage. A process with capability to spare can tolerate a mediocre measurement system. A process running near its limit cannot, and for that process the gauge is part of the problem whether or not it passes a generic threshold.
Having done the correction, the temptation is to report the corrected figure as the true one and move on. That is right for some decisions and wrong for others, and the distinction matters more than the arithmetic.
For process improvement, use the corrected figure. The question is whether the process needs work and where the variation lives. Measurement noise is not a property of the process and including it points effort in the wrong direction.
For conformance, acceptance and what the customer receives, use the uncorrected figure. Units are accepted or rejected on the measured value, not the true value. A customer receiving product screened by a noisy gauge experiences the consequences of that noise. Reporting corrected capability in an acceptance context describes a process nobody is actually buying from.
The defensible practice is to report both, labeled, with the gauge study attached. A report that presents a single capability number without saying which question it answers invites exactly one follow-up from a competent reviewer, and it is not a comfortable one.
Capability indices describe spread relative to a specification. They say nothing about the probability of a wrong decision on an individual unit — and near a limit, that probability is not small.
A conforming unit can measure out of specification and be scrapped. A nonconforming unit can measure in and be shipped. The rates of both depend on measurement variation relative to the distance between the true value and the limit, which means they are worst exactly where product density is often highest. No capability index reveals this, because none of them is about individual decisions.
Quantifying that misclassification, and choosing deliberately how to split the risk between producer and consumer, is what a guard band does. That is the natural next step once the capability question is settled, and it is a different calculation.
The most common version is a yield or capability investigation that starts with the conclusion already assumed: the process has degraded, so find out what changed. Establishing how much of the observed variation belongs to the measurement system first is cheap, uses records that already exist, and occasionally ends the investigation before any experiment is designed.
That separation was the first step in the first-pass yield investigation described on the Work page, for exactly that reason: knowing where the variability actually sat determined which characterization studies were worth running and which were not.
If you have a failing capability index and a gauge study sitting in the same quality system, the two have probably never been put together. That is usually a few hours of work with data already in hand.
Worse, always. Measurement variance adds to process variance rather than canceling, so observed variation is larger than true process variation and capability indices computed from measured data are biased downward. A process can be genuinely capable and still post a failing Cpk if the gauge is noisy enough. The bias is one-directional, which is useful: an observed capability index is a lower bound on true process capability, so a process that passes on measured data has passed conservatively.
By subtracting variances, not standard deviations. Observed variance equals process variance plus measurement variance, so process variance is estimated as observed variance minus the gauge R&R variance from a measurement systems study. The measurement estimate has to come from a valid study on the same parts, operators and conditions, and its uncertainty propagates into the corrected capability figure. When the subtraction returns a negative number the arithmetic is telling you something real: measurement variation is of the same order as everything you observed, so the data contain almost no information about the process itself.
It depends on the decision, and reporting the wrong one is a common and consequential error. For process improvement — deciding whether the process needs work and where — the corrected figure is right, because it describes the process rather than the process seen through a gauge. For conformance, acceptance and predicting what a customer actually receives, the uncorrected figure is right, because units are accepted or rejected on the measured value and not the true value. The measurement error is part of what the customer experiences. The defensible practice is to report both, labeled, with the gauge study attached.
Because conformance is decided on a measured value that carries error. Near a specification limit, a conforming unit can measure out and a nonconforming unit can measure in, and the rate of both depends on the ratio of measurement variation to the distance from the limit. Capability indices say nothing about this — they describe spread relative to the specification, not the probability of a wrong decision on an individual unit. Quantifying and controlling that misclassification is what a guard band is for.
There is no single threshold, because the answer depends on how much capability you have to spare. The relationship is one of variances, so a measurement system contributing thirty percent of observed standard deviation contributes only about nine percent of observed variance and depresses the capability index by roughly five percent — often tolerable. At fifty percent of observed standard deviation the depression is around thirteen percent, which will fail a marginal process that is actually adequate. Judge the gauge against the capability margin available, not against a fixed number.
