Process Capability Study

What this tool does

CM8-291 turns measured readings and a specification into a capability study: the mean, the standard deviation, Cp, Cpk, Cpu, Cpl, Pp and Ppk, an estimated defect rate in parts per million, a histogram against the limits, a run chart in sample order, and a table showing every calculation. It is both a Cp calculator and a Cpk calculator, because reporting one without the other is how a well-behaved process pointed at the wrong place gets signed off. No account, no upload, no network request.

Capability in one idea

Capability compares the voice of the process — the spread of the readings, and where that spread sits — with the voice of the customer, the distance between the specification limits. An index is the ratio. If the customer allows a window six standard deviations wide and the process fills exactly six, the index is 1.00 and it only just fits. Allow eight and it is 1.33. Allow four and it is 0.67: no care will keep parts inside the drawing, and the process needs changing, not watching.

Cp against Cpk

Cp measures spread and nothing else. Tolerance width divided by six standard deviations, with no regard to where the process sits: "could this fit if it were perfectly centred?" — a statement about potential. Cpk measures spread and position together, taking the distance from the mean to the nearer limit in units of three standard deviations and reporting the worse side: "does this fit where it is now?" — a statement about reality.

That is why they must be read as a pair. Consider a Cp of 2.0 with a Cpk of 0.8. The Cp says the spread is beautiful: the process fills only half the tolerance and, centred, would produce a defect about once in a billion parts. The Cpk says it is making scrap right now. Both are true. It is a well-behaved process pointed at the wrong place — the variation is under control and the setting is wrong. The fix is an offset taking ten minutes and no capital, while a variation-reduction project would be months of work aimed at the one thing that is not the problem. Reverse the pair — Cp 1.05, Cpk 1.02 — and nothing can be adjusted: the only route left is less variation.

So read the gap. Cp minus Cpk is the centring loss — the capability given away by not sitting in the middle. Near zero, Cp is the honest limit of what you have; large, and centring is the cheapest capability you will ever buy.

Every formula

is the standard normal distribution, computed with a published rational approximation. The divisor n − 1 is deliberate: you are estimating a process from a sample. With one limit only, Cp and Pp are not computed — they need a tolerance width — and Cpk is the single one-sided figure, which the summary table states.

Cp/Cpk against Pp/Ppk, and which this tool computes

The formulas are identical; the difference is which sigma goes into them. Cp and Cpk are meant to use the within-subgroup sigma — short-term variation from the average range of rational subgroups. Pp and Ppk use the overall sigma of every reading, which also contains what happened between subgroups: tool wear, temperature, material batches, shift changes, re-settings.

This tool computes the overall sigma, so its headline figures are strictly Pp and Ppk. They are labelled Cp and Cpk on the tiles because that is what nearly everyone calls them; the summary table names them properly. Overall capability is the more conservative and honest number — it is what the customer experienced.

Fill in the optional subgroup column and the tool also estimates the within-subgroup sigma from R ÷ d2 and reports true short-term Cp and Cpk beside the overall pair, labelled "within". Subgroups hold two to five readings, and where sizes differ only the most common is used, because d2 depends on it. A wide gap between the pairs is not an error: it measures the drift between them.

The normality assumption

Every index here, and the parts-per-million estimate above all, assumes the readings come from a roughly normal distribution. Cpk becomes a defect rate by reading the tail area of a normal curve. If the distribution is not normal, that conversion is not slightly wrong — it can be wrong by orders of magnitude.

Skew breaks it in the dangerous direction: characteristics with a natural floor — flatness, roundness, surface finish, contamination counts — pile up against zero with a long tail one way. Two humps usually mean two machines, cavities, operators or batches pooled into one study, and the combined index describes neither. A wall at one end means the parts were sorted before you measured, so you are measuring the inspection.

So read the histogram before you believe the number — that is why it is the first chart. One hump, roughly symmetrical, tailing off before the limits is what the arithmetic assumes; anything else means the index summarises a shape it does not fit, and you should transform the data, use a non-normal method, or quote the observed out-of-specification count instead — which is why that count sits beside the estimated parts per million.

Stability comes first

An unstable process has no single capability. If the mean walks with tool wear, or jumps at every set-up, the process measured this morning and the one measured this afternoon are different, and an index across both describes a period rather than a process. Prediction is the point of an index, and you cannot predict something that will not sit still. Make the process stable, demonstrate it, then measure capability — stability is a control chart question, the job of the SPC Control Chart tool. The run chart here is the warning: a trend, a step or a long run on one side of the mean.

How many readings

Thirty is the usual working minimum and fifty is better; many customer schemes ask for 100 pieces or 25 subgroups of four. A standard deviation from a small sample is itself uncertain, and it sits in the denominator of every index, so with a dozen readings the true Cpk could be a third either side of what you calculate. Where they come from matters as much: thirty consecutive parts off one bar give a flattering sigma holding none of the between-batch and between-shift variation the customer will meet. Under 25 readings the tool marks the study provisional.

The thresholds are convention, not law

• Cpk — Usual reading — Roughly
• Below 1.00 — Not capable — Producing out-of-specification parts now
• 1.00 to 1.33 — Marginal — Fits, with no room for drift
• 1.33 to 1.67 — Capable — The common contractual minimum
• 1.67 and above — Excellent — Usual for safety-critical work

These are conventions, not laws of nature: a characteristic whose failure is a nuisance and one whose failure hurts somebody should not share a threshold. Set your own minimum in the settings. The defect rates behind them all come from the normal model.

Measurement error eats capability

Every reading contains the variation of the process and of the measurement system. They add as variances, so the sigma here is always larger than the truth and every index lower. If the gauge is a third of the observed spread, a genuine Cpk of 1.33 measures as roughly 1.26; at half, around 1.15 — failing an audit it should have passed. The gauge must also resolve far more finely than the tolerance. Establishing how much of a marginal result is the gauge is a measurement systems analysis, the job of the Gauge R&R tool.

Excluding readings honestly

Occasionally a reading is genuinely not the process — a mis-set gauge, a part measured before an operation finished. Tick exclude and it stays in the register and the report but leaves every index; the tool will not accept an exclusion without a written reason. Be strict: a reading is not abnormal merely because it is out of specification.

The spreadsheet workflow

• Spreadsheet template in the toolbar saves a CSV whose headings are exactly this tool's column labels — study name, characteristic, measurement, sample number, sample date, subgroup, excluded reading, exclusion reason and the rest — with a guidance row showing what each expects.
• Fill it in, then delete the guidance row before saving as CSV.
• Import spreadsheet reads it back, matching columns by heading, so order does not matter and extra columns are ignored. Rows missing a required column, or failing a check, are skipped and reported by number.

Nothing is uploaded and the original file is unchanged. The limits are settings, not columns, so set them once after importing.

FAQ

Cp or Cpk to a customer? Cpk, with Cp alongside. Cp alone describes a process that does not exist unless it is perfectly centred.

My index looks fine but we scrap parts. Usually the process is not stable, or the distribution is not normal so the real tail is fatter than the model, or the study came from a different population than the parts being scrapped.

Several characteristics in one register? Record them, but analyse one at a time — the indices use every non-excluded reading in the filter. Use the search box to isolate one.

Saving your work

Everything goes to this browser's local storage as you type, and that storage belongs to one browser on one computer. Treat Export .json as the real save; Import .json restores it anywhere. Export CSV gives you the filtered readings. Reset asks twice and cannot be undone.

Accuracy & disclaimer

The arithmetic is elementary and performed faithfully. Everything deciding whether the answer is true sits underneath: whether the process was stable, whether the distribution is anything like normal, whether the gauge was capable, and whether the exclusions were fair. A capability index is a model; the histogram and the out-of-specification count are the reality check. When they disagree with the index, trust the data.