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Hi All,

I'm mulling how to approach a project I've been assigned at my work relating to a manufacturing process. In this process, over some months, there are three kinds of warnings that are flagged. We'll label them by grades of 1, 2, and 3 in this case in order of severity.

What is of interest to stakeholders is if a modeled month-to-month fitted predicted mean trendline in event counts exceeds some absolute threshold. The threshold is different for each severity of error, with the the monthly threshold being lower for Grade 3 events rather than Grade 1 events. So, for example, company leadership wants the process to be flagged if in some month the modeled trendline crosses the thresholds for, say, 100 Grade 1 events, 20 Grade 2 events, or 10 Grade 3 events.

With this being ordinal data, one way I could picture this mentally would be with an ordered logit/probit model. However, as the proportion of events per month is presently less important to the stakeholders than predicted absolute counts of each grade, I was thinking that it may be more appropriate to partition the data by grade into univariate time series and then start by running a Poisson time series regression for each grade. If overdispersion seemed present, I was thinking of opting for a generalized Poisson regression, as the negative binomial interpretation of binary failures and successes does not make sense in light of there being multiple "failure" out comes in the overall process so to speak.

Is this approach appropriate or very misguided? I appreciate your time and input, thank you very much.
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