As @dsaxton said, you can build a discrete time model. You set it up to predict p(fail at this day given survived up to previous day). Your inputs are current day (in whatever representation you want) eg one hot encoding, integer,.. Spline... As well as any other independent variables you might want

So you create rows of data, for each sample that survived till time t-1, did it die at time t (0/1).

So now the probability of surviving up to time T is the product of p(don't die at time t given didn't die at t-1) for t=1 to T. Ie you make T predictions from your model and then multiply together.

As @dsaxton said, you can build a discrete time model. You set it up to predict p(fail at this day given survived up to previous day). Your inputs are current day (in whatever representation you want) eg one hot encoding, integer,.. Spline... As well as any other independent variables you might want

So you create rows of data, for each sample that survived till time t-1, did it die at time t (0/1).

So now the probability of surviving up to time T is the product of p(don't die at time t given didn't die at t-1) for t=1 to T. Ie you make T predictions from your model and then multiply together.

I would say the reason its not such an idea to directly predict time to failure is because of the hidden structure of the problem. Eg what do you input for machines that didn't fail. The underlying structure is effectively the independent events: fail at time t given didn't fail up to t-1. So eg if you assume it is constant, then your survival curve becomes an exponential (see hazard models)

Note in you case you could model at 10 minute interval or aggregate up the classification problem up to day level..