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my level of stats is kind of restricted to some undergraduate courses. Anyhow I received some data from a planned experiment. Basically it is about to test the shear strength (interval scale) for electronic devices.

The experiments should look for differences in different materials and process parameters. So I factors A, B, C and another factor D as well as a response R2. Anyhow my problem is related to factor D which is a multilevel factor and describes the time (in cycles) the device spent in an accelerated aging chamber before it was removed for destructive testing. The test destroys the device and measures thereby the shear strength. When seeing the data of the response (shear strength) it looks like a multi modal distribution. During the shear test a failure mode (R1) was assigned to each measurement describing the part of the device that failed. With changing cycle times the ratio of failure modes changes. The response variable for the most frequent failure mode at a specific cycle time is kind of normally distributed.

The problem is as follows. For one specific cycle time I get only one or two sufficient failure modes. But the response (shear strength)is dependent on the failure modes. So for the factor cycle time I get heavily imbalanced data regarding the failure modes. The questions is what would be a suitable statistical procedure to analyze the data. I think I cant use ANOVA since the response is not normally distributed for all factor combinations. If I restrict the results for one failure mode several factor levels of the cycle time do have too few data points. Can someone give me some advices which methods or concepts might help if there are any? I certainly can get some implications out of the categorical response R1 by logistic regression but then I would discard the additional information from the metric measurements from R2 wouldn't I?

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