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A repairable components fails at times t = 3, 4, 6, 9, 11.No further failures are observed during the observation period which ends at t = 19.Determine (to 3 decimal places) the standard deviation of the time between failures.

Question

A repairable components fails at times t = 3, 4, 6, 9, 11.No further failures are observed during the observation period which ends at t = 19.Determine (to 3 decimal places) the standard deviation of the time between failures.

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Solution

The standard deviation of the time between failures can be calculated by first finding the times between each failure, then calculating the standard deviation of these times.

The times between failures are:

4 - 3 = 1, 6 - 4 = 2, 9 - 6 = 3, 11 - 9 = 2.

So, the times between failures are 1, 2, 3, and 2.

Next, calculate the mean of these times:

(1 + 2 + 3 + 2) / 4 = 2.

Then, calculate the variance, which is the mean of the squared differences from the mean:

[(1 - 2)^2 + (2 - 2)^2 + (3 - 2)^2 + (2 - 2)^2] / 4 = 0.5.

Finally, the standard deviation is the square root of the variance:

sqrt(0.5) = 0.707.

Therefore, the standard deviation of the time between failures is 0.707 (correct to 3 decimal places).

This problem has been solved

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