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I have a dataset which looks like this:

Timestamp           Event       Actions_since_last_maintenance
2016-01-01 12:00    Action      10
2016-01-01 12:01    Action      11
2016-01-01 12:01    ERROR       11
2016-01-01 12:02    Action      12
2016-01-01 12:03    Action      13
2016-01-01 12:04    Maintenance 0
2016-01-01 12:05    Action      1
2016-01-01 12:06    Action      2
2016-01-01 12:07    Action      3
2016-01-01 12:07    ERROR       3
2016-01-01 12:08    Maintenance 0
2016-01-01 12:09    Action      1
2016-01-01 12:10    Action      1
2016-01-01 12:11    Action      3
2016-01-01 12:12    ERROR       3

A machine is performing an action and I count the number of actions since the last maintenance. From time to time an error occurs at the machine. As a first step I want to calculate if there is a relationship between "Actions_since_last_maintenance" and the error. The final goal is to find an optimal maintenance interval for the machine.

It seems simple but I am not sure what is the best way to analyze that relationship statistically.

One thing I am not sure about is the fact that the maintenance intervals are not always the same.

So when I assume that the error is completely unrelated from "Actions_since_last_maintenance" and most of the time the maintenance is done after 3 actions I will find most errors between "actions_since_last_maintenance" 0 and 3 of course and not at values at 10 for example.

I hope the question is clear and someone could give me a hint. Thanks!

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First off: are "actions" always the same? If not, try to put them into relation to your error. This could be done via counting (like your first approach). However, you should try to check if it matters which action followed on which one. E.g., "A1->A2->ERR": maybe errors occur more often if a certain chain of actions followed up on each other. Furthermore: use timestamps: how much time in average lays between errors, how does that relate to the number of performed actions?

What is a "Maintenance"? Is it always the same error?

It is hard to give you proper advise as your problem seems to be very generic..

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