I need to build a statistical model to predict the time of assembly of a machine. Those predictions should be updated during the assembly on a daily basis. I have some variables which for each machine built do not change in time such as the machine model and others, and some variables time-dependent such as the number of missing parts required to make the machine, the number of days spent on the machine so far and so on.

So in the dataset for each machine made in the last years (about 100 of them) I have a number of rows equal to the number of days spent to build that machine, in which the response variable is always the same (known at the end of the assembly), while some of the predictor variables changes.

How can I model this kind of data? I think is not a repeated measures analysis because for each machine the response is always the same, only some predictors changes, I just make predictions several times over time because I expect to improve my forecast approaching the end of the assembly. Of course I can change the response variable to be the number of days remaining to finish assembly instead of the total number of days of assembly.

Is there a Bayesian solution to model this type of problem telling the model via the machine id which observations refer to the same machine on different days?