Since neither the production nor measurement processes are perfect, there will always be some dispersion in the observed product value either for repeated measurements of one item or for measurements of a series of items.
Conformity assessment is focused on determining actual product errors: apparent dispersion due to limited measurement capability should normally be small.
The first step is to set tolerances on product:
- Specification limits, USL and LSL, for the magnitude of a characteristic of any entity
- For any entity, the maximum permissible (entity) error, MPE.
For a symmetric, two-sided tolerance interval: MPE = (USL – LSL)/2.
For a one-sided interval: MPE = USL – nominal, for instance.
Note that these specifications are normally set by the producer on the basis not only of what can be practically and economically produced, but also ultimately on what the customer or consumer requires in terms of product characteristics.
A simple example is pre-packaged coffee. Consumer requirements aimed at ensuring a guarantee that each coffee packet is not sold at underweight obliges the producer to test that manufactured coffee packets of, say, nominal mass 500g weigh at least 485g. This one-sided, lower specification limit on the quality characteristic mass per packet has a corresponding MPE of – 15g, as stipulated in current EU legislation for pre-packaged goods.
Typically, a coffee producer might fill about 100000 packets à 0.5 kg a day. Commodity value is typically 10 €/kg when on the market, whilst production costs will be some fraction so that the producer can make a profit. These economic factors can be used to optimise production, by balancing these against the consequence costs associated with dissatisfied customers.
In cases where measurement dispersion is comparable with actual product variation, it can be difficult to separate these.
In order to assess an entity, according to the above product specifications, corresponding measurement specifications are often set. These are of two distinct kinds:
- limits on maximum permissible measurement uncertainty (or, equivalently, minimum measurement capability) when testing product
- limits on maximum permissible error in the indication of the measurement equipment/system intended to be used in the measurements when testing product
Setting limits on maximum permissible error in the indication of the measurement equipment/system intended to be used in the measurements when testing product can be viewed as a special case of general conformity assessment, where the entity subject to assessment is the measurement equipment/system and the quality characteristic can be:
- indication of the display of the measurement instrument
- error associated with the chosen measurement method, operator etc
Setting an MPE on the measurement system is one way of ensuring that, when measurements are actually performed when testing product, requirements on maximum permissible measurement uncertainty (MPU) are likely to be satisfied: Whether they will or not depends not only on instrument specifications but also on the actual metrological performance when measuring.
A well-known example is legal metrology, as covered by the EU Directive Measuring Instrument Directive (MID), where instead of performing conformity assessment of all legally-important measurements in society (fuel, energy, commodities, water, environmental emissions etc), one chooses instead to assess compliance of the measurement instruments and meters in use in society – both by type approval, initial & subsequent verification. Typically, alongside more qualitative attribute requirements, such as inspection of correct instrument labelling and unbroken sealing of instruments, measurement specifications are also set by variable in terms of MPE, both for the main characteristic (e.g. indication of an electricity energy meter) as well as of any influence quantity (e.g. level of disturbing electromagnetic field, in EMC testing) to be tested through quantitative measurement.
- An initial question is: what is an appropriate maximum permissible error, MPE, to be specified for the instrument or measurement system, in relation to the corresponding specification limit on entity error – also an MPE?
The next steps are to fix specifications on the production process and measurement process capabilities needed to make product according to the product specifications.
Limits on both process and measurement capabilities are traditionally set in terms of certain factors – Cp and Cm, respectively – which are fractions of the same product tolerances (specification limits, USL and LSL, for the magnitude of a characteristic of an entity) and maximum permissible product value errors, e.g. USL – LSL.
with standard deviation sp and where Cp = 2 is used the famous ‘six-sigma’ approach to statistical process control (SPC) [Joglekar 2003].
with standard measurement uncertainty um and typically M = 4 (corresponding to a coverage factor, k = 2 and 95% confidence).
Limits on capability factors
In various sectors of conformity assessment, different limits on measurement capability have become established, with Cm,min ranging from typically 3 to 10. A common limit to ensure that measurement quality variations are small is < 30%,
as in Measurement System Analysis (MSA) in the automobile industry, for instance.
But many of these rules have a certain element of arbitrariness and limits vary, often with little motivation as to the actual consequences of incorrect decision-making in conformity assessment. Questions of appropriate rules for decision-making in conformity assessment with due account of measurement uncertainty raise questions which ultimately can be resolved by economic considerations.
A.M. Joglekar 2003, Statistical methods for six sigma in R&D and manufacturing. Wiley, Hoboken ISBN: 0-471-20342-4
- Measurement quality
- Measurement error
- Measurement accuracy
- Specifications of Process and Measurement Capabilities
- Uncertainty in a measurement value
- Estimating measurement uncertainty
- Conformity assessment