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I want to use hour as a feature in my random forest model. The challenge that I’m facing is that some observations are recorded based on machine operating hour while others are in engine hour. Without a clear cut conversion between the 2 unit of measurements, how can I include hour into a model without creating bias?

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Don't mix the two features together as you say this will create bias. Instead, I would suggest you create two separate features for each of the two units of measurement and leave the field missing when you don't have one or the other. That is, for a sample where you have the engine hour, you would leave the machine operating hour empty, and vice versa.

Random forest models can handle missing values by imputation, that is, the missing value is filled with some median value of the entire training set or an estimate. More theory here.

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