Renewal Processes

A renewal process is a way to model situations where events happen over time, with each event "resetting" the system's schedule. For example, consider machines that break down and are repaired; the times between failures are random but follow a certain pattern. After each failure and repair, the process starts anew, similar to a "renewal." This concept helps analyze the frequency and timing of recurring events, allowing for predictions and planning in areas like maintenance, inventory, and systems management. Essentially, it tracks and predicts when future events are likely to occur based on past occurrences.