If you are using life time data for all of the items, then the items that failed for another reason are treated as censored data. (It is similar to competing cause analysis. You have some items with 'infant death' and others with a 'normal' failure mode.) They survived the failure mode of interest up to the time that they failed for another reason. These observations would be included in the Life Distribution analysis.
If you are using agregate count data of the total units failed at the endpoint in time (i.e., you don't observed items until the final moment, e.g., 3 months), then don't include these observations in the count of failures and delete them from the count unfailed. It is as if you started with a smaller sample. You can't count them as censored data in your Contingency analysis.
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