# Converting a Probability to Fail Into a Time to Failure Metric

Getting the most out of your Probability to Fail Models. With predictive maintenance problems, there are two common metrics that represent the health of your asset.

With predictive maintenance problems, there are two common metrics that represent the health of your asset.

The first is a probability to fail. That is, at a given moment in time, what is the probability that your machine will fail. Sometimes, this is represented by a health score. Typically, the health score is one minus the probability to fail times 100.

The second metric is the time until failure. That is, how many days, weeks, months, hours, minutes or seconds do you have until the asset in question stops working.

There are many different ways to calculate these metrics. Probably the most common way to gauge the probability to fail is a machine learning algorithm like logistic regression, random forest or gradient boosted tree (Note, there are many more).

Time to failure models typically rely on some type of survival model. A survival model is a family of techniques based on measuring and predicting expected lifetimes, given certain attributes of an individual or population. For example, will a drug treatment increase or decrease the life of a cancer patient? Or, how much longer will a machine operate if we service it every three months instead of every six months?

What if you have a probability to fail and want to convert it into a time to failure? Is this possible?

Of course it is possible. In fact, there are many ways to do it. In this article, I focus on my favorite technique. Not saying it is the best, just my favorite.

You probably won’t see this in a textbook, but my approach has served me well over the years. My technique is pretty easy and guarantees that your time to failure and probability to fail metrics are perfectly in-synch.

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