Attribute
measurement systems (abbreviated as AMS in the rest of this article) are systems
which differentiate the measured parts into some categories, such as OK and NG,
instead of characterizing them with variable data. For the convenience of
discussion, this article will further divide AMS into two types:
Type 1: AMS for
characteristics which can also be evaluated with variable measurement systems. An
example of such AMS is the system with a pin gauge. It differentiates the
measured parts into two categories: OK or NG, but the diameter of the hole can
also be measured with a variable measurement system such as CMM.
Type 2: AMS for
true attribute characteristics which cannot be evaluated with variable
measurement systems (abbreviated as VMS in the rest of this article). An
example of such AMS is the manual visual inspection system on products
appearance. The spec of appearance is often not defined with variable data.
In AIAG’s MSA
manual (4th edition), four approaches are introduced for the MSA of AMS,
as listed below:
1.
Gauge performing curve
2.
Signal detection theory
3.
Attribute control charts
4.
Hypothesis test analysis
None of the
above approaches can assess all the five types of variability of a measurement
system, i.e. bias, linearity, stability, repeatability and reproducibility. They
all have certain limitation as explained below:
The 1st
approached is an analytical method which gives good quantitative assessment on
the measurement system. But it is only good to study the bias and repeatability.
Also, it is only good for Type 1 AMS, as the reference value of the samples
used in this study must be available in quantitative data. Readers may refer to
AIAG’s MSA manual (Chapter III, Section C) for how to establish the gauge
performing curve a measurement system. It is quite clearly illustrated there.
Same as the 1st
approach, the 2nd approach can only be used for Type 1 AMS too. It can
be used to assess the GRR and GRR only of the measurement system. It also gives
a quantitative result, but it is an estimated one. The estimation becomes
better with the increase of sample size. As this approach gives only an
estimation of GRR, it should be approved by the customers before it is used.
The
3rd approach is only briefly mentioned in the MSA manual (P.145, 4th
edition). This approach is only good for stability study. Same as the stability
analysis of a VMS, one needs to follow the below steps: pick a sample,
establish the control charts and then study the control charts (please refer to
this article for stability study of VMS). Picking sample for stability study of
AMS is much more critical than the stability study of VMS. It is probably the
key for a good stability study of AMS. In AIAG’s manual (please refer to the
footnote in P.145, 4th edition), it’s noted that for the chosen
sample, np must be greater than 4, i.e. if the sample is measured ten times,
there are at least 4 times this sample is categorized as NG. So the sample
should not be an OK sample which is far away from the spec limit, otherwise
there is a low chance of getting an NG result from measurement. It should not be
an NG sample which is far away from the spec limit either, otherwise, UCL and
LCL are same and the control charts makes no sense (please refer to formula of
UCL and LCL of p charts and np charts in the SPC manual). So the sample must be
close to the spec limit in the gray area of the below image, with a chance of
having both OK and NG results.
In principle, this approach can be used for
both Type 1 and Type 2 AMS, but if AMS involves human judgement, this approach may
not work well, because the appraisers can remember the past judgements and it
can influence the upcoming judgements. So this approach is good if the
equipment makes the judgement, but not suggested if the appraisers make the
judgement.
The 4th
approach can be used for both Type 1 and Type 2 AMS. But unfortunately, the
kappa value obtained with this approach can only assess the agreement between
different appraisers and does not yield any quantitative assessment of any type
of variation of the measurement systems. One cannot really tell how big the
variation of the measurement system is with this approach. Therefore it should
approved by the customers if an organization plans to use it.
As a summary,
below is the table which lists up the possible MSA approaches for AMS. Please
be noted that the agreement analysis in the last column does not belong to the
five types of MSA defined in the MSA manual.