Where to Set the Acceptance Limit When the Laboratory Is Not Certain

How to read this sheet

The sheet will not tell you to ship outside the specification. On a mill where downgrading a good lot costs more than a complaint does, the arithmetic will always prefer an acceptance limit set a little outside the customer's limit, and that is not an optimisation, it is shipping known non-conforming goods. The search is therefore held at the specification and what that costs is reported separately - as a figure to take to the buyer when asking for the limit to be widened, which is a legitimate conversation, rather than as something to do quietly. Read the two error columns together or not at all. Tightening an acceptance limit trades one for the other at a fixed exchange rate set by the laboratory spread, and every quality meeting that has ever been held about one of them without the other has been half a meeting. A mill that knows only its rejection rate cannot tell an unlucky process from an unlucky instrument, and they need opposite work. Replicates are the cheapest lever on the sheet and the last one anybody reaches for. Averaging four tests instead of one halves the laboratory spread for the price of three tests, and on a lot worth six figures three tests are nothing. It is the only lever here that needs no capital, no supplier and no argument - and on the seeded mill three properties out of four want more replicates than they get. Why a steadier process usually beats a sharper laboratory. The laboratory can only ever be worth the lots it misclassifies. The process is worth the conformance itself: a lot that is genuinely outside the limit costs money however perfectly it is measured. So unless the laboratory spread is a large fraction of the process spread the process wins, and the sheet says which by how much rather than leaving it to whoever is loudest. What is not modelled. Both distributions are taken as normal, which is fair for most physical properties and poor for anything bounded at nought - shade difference in particular is not normal near zero and the sheet is optimistic about it. Properties are treated as independent, so a lot that fails two of them is counted twice - which is why the two headline figures are given per hundred lots rather than as a percentage of them, and why they can exceed a hundred on a badly measured book; where two properties share a cause, price them as one row. Sampling within a lot is not modelled at all: this sheet assumes the specimen represents the lot, and where it does not, the true spread is larger than the number you entered.