Your limits are claims. The record can check them.

The consequence

A tolerance, a control limit and a change interval each say that the process stays inside a line someone drew. Most plants hold the measurements that would confirm or refute that and have never put the two side by side. On the 2 public data sets audited here, 3 things appeared: a limit the process never meets, limits it can never fail, and a quoted range narrower than the errors it is supposed to contain.

What the forge specimen found

81 forged parts, 18 measured dimensions, 5 production days on a research testbed.

1. One limit is missed by every part. The inner diameter at 55 mm averages 29.568 mm with a standard deviation of 0.008 mm, against limits of 29.7 to 30.3. 81 of 81 parts are outside. The process is steady. The specification does not describe it.

2. Length runs at its upper limit. 9 of 81 parts exceed 237 mm on at least one of 4 measurements. On the worst measurement 6 of 81 are over, a 95% interval of 3.4% to 15.2%.

3. 8 of 18 limits were never tested. The nearest limit is more than 6 standard deviations from the mean. A pass rate averaged over all 18 would be dominated by limits that cannot fail.

4. The usual range is too narrow. A 90% range around a prediction of length, built from the model's own training errors, covered 73% of parts [62%, 81%] on days it had not seen. Built from held-out days it covered 94% [86%, 97%] and was 2.4 times as wide. The tool-wear paper found the same pattern on 16 milling inserts: 68.5% [54.7, 82.4] against a stated 90%.

In money, at your rates

The audit supplies counts. Shipping every part unchecked lets 11.1 over-limit parts through in every 100. Checking every part spends 88.9 checks in every 100 on parts that were fine. Which is cheaper depends on 2 numbers only you hold: what a check costs, and what an over-limit part costs once it has shipped. The specimen has a control where you enter both. Its starting values are an illustration, not an estimate.

3 questions to put to your own records

1. For each stated limit, how far is the process mean from it in standard deviations? More than 6 means the record tests nothing about that limit.
2. Is there a limit that every part misses by the same amount? That is a specification question, and it is cheaper to settle than a process change.
3. When a system quotes a range, were its errors measured on parts, batches or days it had never seen? If not, the range is narrower than it should be.

What this does not support

The forge is a research testbed, 81 parts over 5 days, and its tolerances may not be a customer's. The milling data is 16 inserts on a 1990s machine. Neither says anything about your scrap rate, and neither shows that monitoring does not work. The intervals on the forge treat parts as independent, which parts made on one day are not. No cost in either data set is real.

If you want it run on your records

The Process Calibration Audit is this review on your own measurements, with a data-structure check on day 2 that tells both of us whether the records can support it. Reference price: fixed, set by the size of the record set. About EUR 6,500 for one line with 2 years of records. Timing: 2 weeks from data receipt. One paragraph describing the limit and the records is enough to start: matthew@mtanti.com.

Code and reproduction steps: forging-tolerance-audit and tool-wear-calibration. Forging data: Tachtatzis, Gourlay, Andonovic and Panni, University of Strathclyde, doi:10.5281/zenodo.3405265, CC BY 4.0.