Process Capability Calculator
Cp and Cpk from your measurements against a spec: what the process could do spread-wise, what it actually does position-wise, and the gap between the two — the centering bill, priced.
Process Capability Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Cp/Cpk from sample s on entered measurements — no Ppk/pooled long-run forms
- Normality assumed for the conventional readings; the ratios themselves are distribution-free
In short: Bolt spec 9.850000 to 10.150000 (tolerance 0.300000), measurements 10.05, 9.98, 10.12, 9.92, 10.08, 10.00, 9.95, 10.03, 10.14, 9.90: the process runs at μ = 10.017000 with s = 0.081792. Cp = 0.300000/(6×0.081792) = 0.611304 — even perfectly centered, the spread cannot fit the tolerance. Cpk = min(10.133000, 0.167000)/(3×0.081792) = 0.542023, and the Cp − Cpk gap of 0.069281 is the centering bill: the mean sits high, closer to the upper spec, and pays for it. The convention calls Cpk ≥ 1.33 capable — this process is far under both bars, and the arithmetic says so without adjectives.
Formula
Cp = (USL−LSL)/(6s) · Cpk = min(USL−μ, μ−LSL)/(3s)
Cp asks whether the SPREAD fits the tolerance with no opinion about position; Cpk asks whether the process AS IT SITS clears the nearer spec. The difference is pure centering — a Cp − Cpk gap larger than zero means the mean is off-center and paying rent to the nearer limit. s is the sample standard deviation of your measurements.
Worked Example
- Enter the measurements from a stable process — a control chart first, capability second: an unstable process has no capability, only snapshots.
- Enter both spec limits; they come from the customer, not from the data.
- Read Cp (spread vs tolerance) and Cpk (position included) — the gap is the centering bill.
- Use the verdict card, which names the 1.33 convention as a convention.
Defaults: μ 10.017000, s 0.081792, Cp 0.611304, Cpk 0.542023, gap 0.069281 — spread fails and centering makes it worse. Center the mean exactly (drive μ-friendly data) and Cpk climbs toward Cp; halve s and both double.
Strengths & Limits Of This Model
Where this engine is strong
- Cp and Cpk side by side so the centering bill is a number
- Spec inputs kept separate from data — the customer's line is not the process'
Where it stops
- No confidence interval on Cpk (needs far more machinery)
- No non-normal (Pearson/Johnson) capability
Practical Use Cases
Manufacturing
machine capability vs tolerance
Quality audits
the 1.33 conversation, priced
Procurement
supplier processes before the PO
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Process Capability Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does Cpk matter more than Cp?
Cp is the process's potential — the spread grade with the position forgiven; Cpk is the reality — the nearer spec already bites. A Cp of 2 with a Cpk of 0.9 is a well-spread process parked near a wall: the fix is centering, not new tooling. This page prints both so the gap is a number, and the gap is the diagnosis.
Why 1.33 as the capable line?
Convention, and this page names it as one. The classical argument: 1.33 corresponds to roughly 4 sigma from the mean to the nearer spec, which buys low defect rates PLUS a buffer against drift. Some industries demand 1.67; some accept 1.00. The number is a contract between you and the reader — the arithmetic under it is not negotiable, the bar is.
The process is in control — why is Cpk still awful?
Because control and capability are different questions: control asks whether the process is STABLE against its own past; capability asks whether that stable process fits the SPEC. A perfectly stable process centered wrong, or spread wide, produces beautiful charts and awful Cpk. Stability is the prerequisite — capability is the verdict.
What does the Cp − Cpk gap tell me to DO?
It prices the centering bill. Gap near zero: the mean sits mid-tolerance, and capability work means reducing spread. Gap large: move the mean before buying anything — centering is often a setup adjustment, not a capital project. In the defaults the gap is 0.069281 on a Cpk of 0.542023: real money, but the spread problem is bigger.
Why sample s and not a long-run sigma?
This page prices capability from the measurements you enter, with the honest sample s. Long-run capability (Ppk) folds drift and lots together and needs weeks of data — named here as out of scope. The distinction matters: a machine trial s can flatter a process whose weeks drift.
Can Cpk be negative?
Yes, and it means the mean is already outside the specification: the nearer distance is negative. The page prints it without cosmetics — a negative Cpk is not a small problem, it is a sign error in the plant's favor of zero.
Why refuse identical measurements?
A constant series has s = 0 and both ratios divide by zero: no spread, no yardstick, no capability. Usually it means the measurement system is rounding or the data were summarized before entry. The page refuses rather than print a limit that would flatter any spec.
Does Cpk say anything about defects per million?
It implies one under normality — Cpk 1.33 maps to a few parts per million — but the mapping inherits every normality assumption, and real tails lie. This page stops at the ratio and the named convention; a DPMO promise built on a 30-point sample is a forecast wearing a lab coat.