A Summary of MSA Approaches for Attribute Measurement Systems

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 (4^th 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 1^st 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 1^st approach, the 2^nd 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 3^rd approach is only briefly mentioned in the MSA manual (P.145, 4^th 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, 4^th 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 4^th 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.