How to show that variation between parts on different tools is intrinsic to the part and not caused by the tool?

Question

All,

I have the following problem I would like some help with:

I have a population of parts each installed in their respective tool. There is some parameter that is measured on the part prior to the installation on the tool (:InspectionValue) and also the same parameter measured on that part while it was installed in the tool (:CurrentValue).

The task is the following - I need to show that the variations between parts is intrinsic to the parts themselves, rather than comes from it being installed on a specific tool. What would be the statistically correct way of showing that based on the provided data?

So far my idea is to compare two values:

:InspectionValue - :CurrentValue - this is my difference between inspection and on tool results

:CurrentValue - Mean(:CurrentValue) - This is how current value differs from tool to tool.

But they are roughly on the same scale. Visually I can see that tools do not affect the values of the parts, and differences are intrinsic to the parts, but I'm not sure how to show that statistically. Anything ideas?

shampton82 · Answer

Sounds like you want to show that the output of the parts condition your measuring is due to the tools they are ran in and not incoming part to part variability.  I would say you need to look at running a OLS model where the parts are nested in the tools being used.

I would set it up like this: one column named "part #" (for each part used 1 to n), one named "measurement time" (prior and current), one column named "die used"(die1, die2, etc) and one column named "measurement value" (with the measured values).  You'll have two rows for each part due to the before after measurements.  Then make the model with y= "measurement value" and X's = "Part #" nested in "die used" & random, "die used", "measurement time" and the interaction between measurement time and die used.  If the terms with die in it are not significant than the tools is not making a difference.

Hope this helps!

Mark_Bailey · Answer

I recommend that you visit the JMP Help entry for Measurement System Analysis for some background knowledge.

statman · Answer

My thoughts with the limited description of the situation. I apologize if I've completely misunderstood your inquiry.

You have a measure on a part before assembly and after assembly in a tool.  Do you know the precision of the measurement device?  Is the measurement on the same location on the part?  If you have not studied and separated these components, then the components of all of the variation in your study is a combination of part-to-part, tool-to-tool, within part and measurement (and associated variables at each layer). You do potentially have multiple measures within tool, but those are confounded with the assembly process variables.

Ways to look at your data include:

1. Multivariate Methods>Multivariate

2. Control charts with a subgroup size of 2 (the before and after measures).  This would put the part-to-part, within part and measurement variability within subgroup and then plot the averages (due to tools).

3. Graph Builder...many options to show what you might want (dependent on the user).

4. Fit Model for some quantitative analysis