A pass or fail measurement needs a decision rule

A measurement is information about a defined property. A pass or fail is a decision that uses that information. The two should not be collapsed into one unchecked number.

Say what is being measured

JCGM 106:2012 is a guide from the Joint Committee for Guides in Metrology on using measurement uncertainty in conformity decisions. In that guide, a specified requirement often takes the form of one or two tolerance limits around a measurable property. If the property's value lies inside that tolerance interval, it conforms. If it lies outside, it does not.

The guide's procedures apply when three conditions exist. The item is described by one measurable property that can be represented by a single value. An interval of permissible values is specified. The measurement result can be expressed together with its uncertainty.

Many workshop checks sit outside that scope. A visual judgment, a drawing with many features, or a go/no-go feel still needs an agreed method. Those checks are not automatically covered by this measurement guide.

The creator should state the product requirement in plain language and, when a number matters, the property and the permissible values. The maker should confirm that the property can be measured with the tools and method on hand.

Uncertainty means the number can mislead

Because a measurement is uncertain, two mistakes are possible. An accepted item may actually fall outside the requirement. A rejected item may actually fall inside it. The guide calls these the consumer's risk and the producer's risk in this setting.

It therefore separates two intervals. The tolerance interval states permissible values of the property. The acceptance interval states permissible measured values. A decision rule is the documented rule for how measurement uncertainty is taken into account when accepting or rejecting, given the requirement and the result.

One documented option is simple acceptance, also called shared risk. Under that rule, the parties accept an item whose measured value falls in the tolerance interval. The guide says the producer and the user then share the consequences of a wrong decision. It also says that, for a common case with a symmetric single-peaked distribution, a measured value very close to a tolerance limit can leave about a 50 percent chance of an incorrect decision. That figure belongs to that stated case. It is not a universal error rate for every caliper, part, or workshop.