Why a process can post an excellent Cp and still be quietly manufacturing a pile of defective parts.
Cp and Cpk both get reported as "process capability," get plotted on the same dashboard, and get quoted in the same breath — so it's easy to assume they're measuring roughly the same thing. They aren't. Cp only ever asks whether a process's natural variation is narrow enough to fit inside the tolerance window. Cpk asks the question that actually predicts defects: narrow enough, andsitting where it's supposed to. A process can ace the first question and badly fail the second.
Cp (process capability)compares the width of the specification tolerance to the width of the process's natural variation, usually taken as ±3 standard deviations (6σ total):
That single number tells you whether the process is inherently capable of holding the tolerance — ifit were perfectly centered on the target. It says absolutely nothing about whether the process is actually centered there. Cp is blind to location entirely; shift the whole distribution ten units to the right and Cp doesn't move.
Cpk (process capability index) accounts for both the spread and how far the process mean has actually drifted from the target, by taking the smaller — worse — of two one-sided calculations:
Cpk deliberately takes the worseside because that's the side that actually determines defect rate. A process shifted toward the upper limit produces more scrap on the upper side no matter how tight its overall spread is — and Cp, which only ever looks at total width, never sees that coming.
Cp measures a single quantity: total spread against total tolerance width, with no reference point for where that spread sits. Cpk measures the distance from the mean to whichever spec limit is nearer — the one-sided distance that actually determines how much of the distribution's tail spills outside the spec. When the mean sits exactly at the midpoint, the two one-sided distances are equal, so Cpk equals Cp. The moment the mean drifts toward one limit, that side's distance shrinks while the far side's distance grows — and since Cpk always takes the smaller of the two, it can only fall as centering gets worse. That's exactly why Cpk, not Cp, is the number that tracks real-world defect rate: defects come from parts crossing the nearestlimit, and a one-sided calculation is the only one that's looking at the right distance.
False, or at best incomplete. Cp only tells you whether the process's inherent variation is narrow enough to theoretically fit inside the tolerance window if it were perfectly centered — it says nothing about whether the process actually is centered. A process can carry an excellent Cp while its mean has quietly drifted toward one spec limit, and that drift alone — reflected in a much lower Cpk — can produce a real, significant defect rate, exactly as in Case 2 above. If the real question is "how many defective parts is this process actually producing," Cpk is the number to check, not Cp. It also points straight at the fix: when Cpk is poor but Cp is good, the fastest lever is usually re-centering the process on target (adjusting the machine setpoint, offset, or aim) rather than trying to squeeze out more variation the process may not even have to spare.
Cp and Cpk are both called 'process capability' indices, but they answer different questions. Cp compares the width of the specification tolerance to the width of the process's natural variation (typically ±3 standard deviations), assuming the process were perfectly centered on target. Cpk accounts for both that spread and how far the process mean has actually drifted from target, using the worse of two one-sided calculations. A process can have an excellent Cp — plenty of room within spec if centered — while having a poor Cpk and producing real defects, because its mean is shifted toward one spec limit. Cp and Cpk are equal only when the process is perfectly centered; Cpk is always the metric that tracks actual defect rate.
Cp = (USL − LSL) / 6σ compares total tolerance width to total process spread (±3σ, 6σ overall), with no reference to where the distribution sits. Cpk = min[(USL − mean)/3σ, (mean − LSL)/3σ] takes the smaller of the two one-sided distances from the process mean to each spec limit, expressed in units of 3σ. Cpk can never exceed Cp; the two are equal only when the mean sits exactly at the midpoint between LSL and USL, so that both one-sided distances are equal.
It happens whenever a process's variation (spread) is tight relative to the tolerance window, but the process mean itself has shifted away from the target — a machine setpoint that drifted, a fixture that wore, a raw-material lot with a different nominal dimension, a setup that was never centered to begin with. The spread hasn't changed, so Cp hasn't changed, but the one-sided distance to the nearer spec limit has shrunk, so Cpk has dropped. Because defects are generated by parts crossing the nearest limit, not by total spread in the abstract, Cpk — not Cp — is what actually predicts the real-world defect rate.
This distinction is central to Six Sigma and SPC (statistical process control) work: a process index reported as "capable" using Cp alone can be dangerously misleading if nobody also checks Cpk. It also points to the correct corrective action — a poor-Cpk-but-good-Cp process is usually fixed fastest by re-centering (adjusting machine offset, tool wear compensation, or process aim) rather than by chasing further variation reduction, since the process already has more than enough spread margin; a poor-Cp process, by contrast, genuinely needs its variation reduced, since no amount of re-centering can fix a distribution that is simply too wide for the tolerance window.
No. Cpk is mathematically bounded above by Cp — Cpk = Cp only when the process mean is exactly centered between LSL and USL. Any shift away from center makes Cpk smaller than Cp, never larger, because Cpk always uses the nearer (smaller) one-sided distance.
Conventions vary by industry, but 1.33 is a common minimum threshold and 1.67 or higher is often required for safety-critical or highly regulated processes (e.g., automotive, aerospace, medical device). A Cpk below 1.0 generally indicates the process is producing a non-trivial fraction of out-of-spec output even though it may look fine on a Cp-only report.
Re-center the process. Since the spread (σ) is already comfortably within the tolerance window (that is what the good Cp is telling you), the fastest and usually cheapest fix is adjusting the process mean back toward the target — a machine offset, tool compensation, or setup aim — rather than trying to further tighten variation the process does not need reduced.
Not necessarily. Cp and Cpk are both computed from a snapshot of process data and assume the process is stable (in statistical control). A process that is drifting, has special-cause variation, or was sampled from an unrepresentative window can show a healthy Cpk on paper while still being unstable in practice — which is why capability indices are normally interpreted alongside control charts, not in isolation.
Typically as the standard deviation of the process output, estimated either from a sample of measured parts (using an unbiased estimator) or, in an SPC context, from the average of subgroup ranges/standard deviations on a control chart. Using the wrong estimate of σ — for example, blending in an out-of-control shift as if it were routine variation — will distort both Cp and Cpk.
Try our Industrial & Systems Engineering Studio
More calculators, simulators, and guides for this discipline.