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A repairable components fails at times t = 1, 4, 7, 10, 11.No further failures are observed during the observation period which ends at t = 18.Determine (to 3 decimal places) the mean time between failures (MTBF).

Question

A repairable components fails at times t = 1, 4, 7, 10, 11.No further failures are observed during the observation period which ends at t = 18.Determine (to 3 decimal places) the mean time between failures (MTBF).

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Solution

The Mean Time Between Failures (MTBF) is calculated as the total time divided by the number of failures.

In this case, the total time is the time from the first failure to the end of the observation period, which is 18 - 1 = 17 units of time.

The number of failures is the number of times the component failed, which is 5.

Therefore, the MTBF is calculated as:

MTBF = Total Time / Number of Failures MTBF = 17 / 5 = 3.4

Therefore, the mean time between failures is 3.4 (correct to 3 decimal places).

This problem has been solved

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