We have a process which generates a number of different visual defects. The visual observations are not be visually apparent in the final product, but are thought to result in a local hole with extended operation.
Overall, I am wondering how to determine the correlation of the defects to the failure and then specify the severity of the defects. I have not been able to convince the test team to give me a continuous measurement of the degree of failure nor the length of time until the failure. I will just get an answer that the point did or did not correspond to a failure location.
Since I have an attribute defect and an attribute response, it seems that the best is to do a Chi-square contingency table. An excel file calculating it is attached for details.
I am wondering if this is appropriate because the fact that I do see a microscopic failure at the microscopic location (I can see the initial defect and the hole it caused in the layer below it by SEM) seems that it is highly correlated, but the analysis would indicate otherwise. Even the likelihood that an area without a defect would not have local failure has a confidence interval of 88%.
@lausto – I’m not sure of your question. Are you looking to evaluate whether the hole appears in a specific spot more than other locations? If so, then Chi-Sq would be one method.
I think that you need to focus on the defect that leads to the hole. Since you likely can’t apply the SEM to every product and every location on each, you will want to determine what is causing the defect and take measures to eliminate that cause.
We are losing a lot of money scrapping every defect and working to eliminate them from occurring. The question came up “are these really defects?”. We don’t really know they are a problem.
So I did do the Chi-Square method, but none of the defects were above the critical Chi-Square value. Even when I checked the hypothesis that a spot without a defect will not have a hole. I am concerned that I did not do the calculation correctly.
I appreciate your reply and see that you may not be notified of my previous response since I did not use your screen name.
@lausto – From your description, I would imagine that your table was 2×2, defect/no defect on one axis, and hole/no hole on the other. Observed counts should be in each of the 4 cells. If this is what was evaluated, then your analysis was set up the way that I would have set it up.
Are you evaluating all the components, or sampling? If sampling, are you sure it is a random sample?
Do you have data in each of the 4 cell positions? Chi-Sq loses significance when one or more cells is empty, particularly with so few variables.
If you post your data, I can look at it more closely and give you better feedback.
Thank you for helping because I did not organize my data that way, but I see now how I should have done it. I had attached my original chi-square calculation in the first post, but I am attaching a second pass where I did a 2×2 matrix instead.
For some extra clarity: I had 20 units which had various defect types (labeled 1-6 for confidentiality). I approximated that we would correlate the end of life hole to the beginning of life location within 0.06 cm2 and the unit was 6 cm2. So there were 100 opportunities per cell. A cell with 3 defects would then have 97 areas of no defect.
Since this completely changes the analysis from no correlation to 99% correlation, I would really appreciate your review! I was incorrectly going to advise that there was no need to remove these defects before.