A batch of color readings answers three questions at once: how far the readings sit from the reference on average, how much they spread, and how often they cross the limit the specification sets. Paste one batch into the tool above and it returns all three – plus a Cp/Cpk-style capability index and a control chart you can export into a report.
What this tool checks
The tool reads a list of ΔE values – each one already the difference between a sample and its reference – and judges them against a single upper limit. A color tolerance is one-sided: a reading well below the limit is not “too good”, so only the upper side counts. It reports:
- the verdict: FAIL when any reading is over the limit, PASS when the batch sits comfortably inside it, and PASS – MARGINAL or AT RISK when it fits today with little room left;
- the mean and the sample standard deviation (SD) of the batch;
- the observed pass rate (the readings that passed) and the predicted pass rate (the share a process with this mean and SD would produce over time);
- a Cp/Cpk-style capability index for the one-sided limit;
- an individuals control chart with the mean, the ±3 SD band and the tolerance limit, exportable as SVG and CSV.
The inputs are ΔE readings, not L*a*b* values. If your batch is still in raw L*a*b* pairs, calculate the ΔE for each sample first with the ΔE Calculator, then bring the numbers here.
Mean and standard deviation
The mean is the center of the batch; the SD is its spread. The two fail in completely different ways. A batch averaging 1.40 with an SD of 0.05 against a limit of 1.50 passes today and drifts over tomorrow. A batch averaging 0.60 with an SD of 0.50 contains both easy passes and clear failures. The mean alone approves both.
The SD here is the sample standard deviation, dividing by n − 1, which is the right choice for readings that are a sample of ongoing production. Below about ten readings it is itself quite uncertain, so treat any index calculated from a tiny batch as indicative rather than contractual.
Small batches flatter themselves
A batch of five readings can easily contain no failures while the process behind it rejects one in ten. Both the predicted pass rate and the capability index widen their uncertainty as n falls. Raise the sample size before relaxing the limit.
Observed pass rate vs predicted pass rate
The observed pass rate is simply the share of readings at or below the limit. It is a fact about this batch. The predicted pass rate estimates what the process would deliver over time, assuming the readings scatter around the mean in a normal distribution: it is the area of that distribution below the limit, Φ((limit − mean) / SD).
The two diverge in exactly the situations that matter. A small batch can show 100% observed while predicting less, because the tail it cannot see still exists. A skewed batch – a run drifting slowly toward the limit, for example – can predict more than it delivers. When they disagree, believe the observed number for this batch, and investigate the process before believing the prediction.
The Cp/Cpk-style index for a ΔE limit
The index used here is (limit − mean) / (3 × SD): the distance from the batch mean to the limit, measured in units of three SD. Because the SD is the overall batch standard deviation, it is strictly a Ppk-style index; with a stable process estimated from subgroups it would be Cpk. The interpretation is the same.
| Index | Reading | What it usually means |
|---|---|---|
| 1.33 or higher | Capable | The limit sits four SD or more above the mean. Comfortable margin against ordinary batch-to-batch variation. |
| 1.0 to 1.33 | Marginal | The batch passes, but drift or a slightly wider run will start producing over-limit readings. |
| Below 1.0 | Not capable | The spread already reaches close to the limit. Expect over-limit readings soon even though this batch contains none. |
| Below 0 | Centered over the limit | The batch mean is itself outside tolerance. No amount of consistency rescues it – the aim has to move. |
An index of exactly 1.0 puts the limit three SD above the mean, which a normal process still breaches about 0.3% of the time. The 1.33 convention is a margin against drift, measurement uncertainty and the fact that real color data is never perfectly normal. It is a starting point for a capability conversation, not a contract.
Reading the control chart
The chart plots the readings in the order they were measured, with three reference lines: the batch mean, the mean ± 3 SD band that describes ordinary scatter, and the dashed red line of the tolerance limit. It is an individuals chart – one point per reading – which is the right form when each reading is a single measurement rather than an average of a subgroup.
What to look for: a run of points creeping upward is process drift long before anything crosses the limit; a single point close to the limit is a sample worth re-measuring; points that all sit on one side of the mean suggest the aim has shifted. The pass rate cannot see any of this – it only counts crossings.
Export the chart as SVG for a batch report, and the readings as CSV for a spreadsheet or SPC system. Both exports are generated in your browser from the numbers you pasted.
Worked example
Ten readings from one batch of molded parts, measured in sequence against a tolerance of ΔE ≤ 1.50:
| Reading | ΔE | Against the limit |
|---|---|---|
| 1 | 0.82 | Within tolerance |
| 2 | 1.05 | Within tolerance |
| 3 | 0.94 | Within tolerance |
| 4 | 1.21 | Within tolerance |
| 5 | 0.77 | Within tolerance |
| 6 | 1.34 | Within tolerance |
| 7 | 0.98 | Within tolerance |
| 8 | 1.12 | Within tolerance |
| 9 | 0.88 | Within tolerance |
| 10 | 1.09 | Within tolerance |
Readings (n)
10
One batch, measured in sequence
Mean ΔE
1.02
Where the batch centers
SD
0.18
Sample standard deviation
Minimum
0.77
Lowest reading
Maximum
1.34
Highest reading
Range
0.57
Maximum minus minimum
Observed pass rate
100%
0 of 10 over 1.50
Predicted pass rate
99.7%
Normal approximation
Cp/Cpk-style
0.90
(1.50 − 1.02) / (3 × 0.18)
The batch mean is 1.02 with an SD of 0.18, and no reading crosses 1.50, so the observed pass rate is 100%. The predicted pass rate is 99.7% and the Cp/Cpk-style index is (1.50 − 1.02) / (3 × 0.18) = 0.90, below 1.0. This is the pattern the index exists to catch: a batch with no failures that is still running too close to the limit. The verdict is AT RISK – the aim or the process spread has to move before the next batch is this lucky.
Sample size for color QC
How many readings a batch needs is a question about two different risks: estimating the mean precisely enough to compare batches, and seeing the bad parts at all.
To estimate the mean, use n = (z × s / h)², where s is the expected SD from a pilot batch, h is the margin of error you can tolerate on the mean, and z is 1.96 for 95% confidence. With s = 0.25 and h = 0.10 that is 25 readings.
To catch defects, use n = log(0.05) / log(1 − p): the readings needed for a 95% chance of seeing at least one reading from a defect rate p. At a 5% defect rate that is 59 readings; at 1% it is 299. Ten readings find a bad batch only when it is badly bad.
Both calculations are built into the sample-size helper inside the tool above.
Where to take the readings
Sample size only helps if the readings are representative. Spread them across the batch – different positions, times, cavities or rolls – rather than repeating one spot. Ten readings from one point measure the instrument; ten readings across the batch measure the batch.
Color QC FAQ
What is a pass/fail color tolerance?
A pass/fail color tolerance is a maximum acceptable ΔE between a production sample and an agreed reference, written into the product specification. Any reading at or below the limit passes; anything above fails. The limit is only meaningful with its measurement conditions named alongside it: instrument, geometry, illuminant, observer and the ΔE formula used.
What does the Cp/Cpk-style index mean for ΔE readings?
It measures how much room the batch leaves below the limit, in units of the batch's own spread. An index of 1.0 means the limit sits three standard deviations above the batch mean; 1.33 gives four. Higher means more margin against variation. It describes the process rather than any single reading, and says nothing about the cause of a failure.
Why do the observed and predicted pass rates differ?
The observed pass rate counts the readings that passed. The predicted pass rate estimates the long-run share that would pass if the process continued with the same mean and spread, assuming a normal distribution. Small batches and skewed data separate the two quickly, so use the observed rate for the batch in hand and the predicted rate as an early warning about the process.
How many readings should one batch have?
Enough to see both the average and the bad tail. Around 10 to 30 readings spread across the batch is a common working range for routine QC; below about 10, the mean and standard deviation are both too uncertain to judge the margin. To have a 95% chance of catching a defect that affects 5% of output you need 59 readings – the sample-size helper in the tool calculates this for any rate.
What does the control chart show that the pass rate does not?
Order. The pass rate treats the batch as a bag of numbers; the chart shows the sequence they were measured in. Upward drifts, step changes and isolated spikes are visible on the chart while the batch is still passing, and they are the early warnings that stop the next batch from failing.
Does this tool send my measurements anywhere?
No. The calculation runs entirely in your browser with JavaScript. Nothing is uploaded to this site, nothing is stored in your browser, and the batch is not written into the page address, so the numbers stay in the tab where you entered them.