As you have learned from your reading, knowing when a part or system will fail is important for a company. Mean time between failures $($MTBF$)$ is the expected time between failures of a part, process, or system and is a common matrix for a firm to use to understand how often a failure will occur.

Assume that you are the manager of a production line and are responsible for keeping the machines running $24$ hours per day, $365$ days per year. When a machine breaks, it must be repaired and put back onto operation as soon as possible. The problem is that your machines are always breaking down, and you really do not have a good understanding of how often a machine breaks down.