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

A

AndrewRSundaresan

#1
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.:thanx::cfingers:

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

Barbara B

#3
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.)
 
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