Repeatability/Reproducibility with One Part and Multiple Operators

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    I was given data for a Gage R&R done in our lab for measurements. We had 4 operators measure 4 different products 3 times each. I need to get repeatability within product and operators. I’m using Minitab for the analysis.

    The problem is that the 4 different products that were measured are 4 completely different products (different specification ranges), so when I do the typical gage R&R, all the difference is in part to part variation, which makes sense since the parts are completely different. I’m used to part being the same product across the specification range, not completely different products. Would this still be a valid Gage R&R?

    I’m thinking in order to get the repeatability I’m looking for, I should do something looking at 1 part, measured 3 times, with 4 different operators. I would wind up with 4 different reports, but if they all have similar results, it should be okay. What would be the best way to do this type of study? I tried Type 1 study, but there are too few measurements I believe




    Robert Butler

    If the measurements within an operator for each part are independent measures and not repeated measures then you could take the results across parts for each operator and regress the measurements against part type (you would have to construct a dummy variable for parts to do this).  The variability of the residuals from this regression would be a measure of the variation within each operator.

    If you then reversed the process and took all of the measurements for a single part across operators and did the same thing with operators as the predictor variable the variation of the residuals for that model would be a measure of the variability within a part.

    If you wanted to get an estimate of the process variation controlling for part type and operator you would take all of the data and build a regression with part and operator as the predictor variables.  The variation of the residuals would be an estimate of ordinary process variation with the effect of operators and parts removed.

    In all of these cases you would want to do a thorough graphical analysis of the residuals.  Since you would have the time stamp of each measurement you would want to include a plot of residuals over time as part of the residual analysis effort.  If you’ve never done residual analysis then I would recommend taking the time to read about how to do it.  My personal choice would be Chapter 3 of Draper and Smith’s book Applied Regression Analysis – 2nd edition – you should be able to get this book through inter-library loan.

    The big issue is that of operator measurements on the same part.  You can’t just give an operator a part and have him/her run a sequence of three successive measurements – these would be repeated measures not independent measures and the variation associated with them would be much less than the actual variation within an operator.  You would need to space the measurements of the parts out over some period of time and so that each measurement of a given part by each operator has some semblance of independence.

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