A component failed 5 times during a 360-hour test, following an exponential distribution. What is the estimated MTBF in hours?

To estimate the Mean Time Between Failures (MTBF) when a component fails multiple times during a given test period, the formula used is based on the total operational time divided by the number of failures.

In this scenario, the component operated for a total of 360 hours and experienced 5 failures. The formula for MTBF is:

MTBF = Total Operating Time / Number of Failures

Plugging in the numbers:

MTBF = 360 hours / 5 failures = 72 hours

This result indicates that, on average, the component is expected to operate for 72 hours between each failure. Thus, the estimated MTBF of 72 hours signifies the reliability of the component over time, helping to inform maintenance schedules and replacement strategies. Understanding this concept is crucial for quality engineers in assessing product durability and readiness.