Gage R&R With Proportions - Advisable Approach or Not?

[AndrewRSundaresan]

Hi all,

I have an automated visual Gage where many (say 20k) individual die are tested on 'platters'.

There is a proportion of fail (e.g. say 35%) of the individuals. I have 3 runs and 3 proportion values for the same Tester (call it Tester A). I intend to collect 3 more runs for two different platters. So for Tester A I'll have 3 runs for 3 different platters.

Tester B is the older model, also with y-variable as proportion fail. I was thinking of 3 runs on 3 different platters.

Is this a valid MSA approach, and is this nothing but a 2-way ANOVA GR&R (2 "Testers" ans 3 Parts, (3 runs))?

And is it ok to use proportion data as continuous data? I'm unsure of the impact of this.

Any and all sage advice would be much appreciated.

(And no, there are no continuous variable y variables which are measurable here.)

[Stijloor]

A Quick Bump!

Can someone help?

Thank you very much!!

[Barbara B]

An attribute gage result can be used as a continuous response, but first I would recommend that you use more than 3 platters. The recommended number of parts is 10 and the minimal number of deviations or ranges is 15 (=number of operators * number of parts), see MSA 4 p.104. If you only compare the results of 3 platters (=3 parts) for 2 testers (=2 "operators"), you only have 6 different deviations instead of at least 15. Chances are high that you won't get a good evaluation of your measurement system, because you miss some vital causes for variation or a relevant part of your process spread.

Back to your original question: The common statistical approach for go/no-go or pass/fail results is to analyze the probability of failure instead of the proportion itself (binary logistic model). Therefore the proportions have to be transformed before the MSA/variance component calculations can be made. There are two common transformation functions for proportions p_i (e.g. p_i = proportion of tester A, platter 2, run 1):

1. y_i* = ln( p_i / 1-p_i ) with ln being the natural logarithm (logit transformation)
2. y_i* = arc sine ( sqrt ( p_i ) )

But if this model / approach reflects the structure within your data well should be checked (e.g. using residual analysis, goodness of fit like R², R²(adj), and so on) additionally to the usual variance component analysis which will provide percentages for measurment uncertainty (EV%, AV%, GRR%, etc.)