Question

The failure time of a component is believed to be an Exponential random variable. A component life test is performed, with the goal being to make inferences about the mean time to failure. One component is in operation at all times; in the event of failure, the failed component is immediately replaced by a new component. Observation begins at time T = 0 and ends at time T = 1,840 minutes, during which time 14 failures occur. Which is the correct limits of a 95% (two-sided) confidence interval for MTTF (in minutes).

Lower limit = 219.17 Upper limit = 78.33
		Lower limit = 78.33 Upper limit = 219.17
		Lower limit = 220.17 Upper limit = 77.33
		Lower limit = 77.33 Upper limit = 220.17

Answer 1

The MTTF estimate is 1840/14 = 131.428571 minutes

MTTF_lower = 0.5960 (Obtained using Tables of MTBF Confidence Interval Factors. Screenshot attached)
MTTF_upper = 1.8291 (Obtained using Tables of MTBF Confidence Interval Factors. Screenshot attached)

Lower limit of 95%Confidence Interval = MTTF_lower*MTTF

Lower limit of 95% Confidence Interval = 0.5960*131.4286 = 78.33

Upper Limit of 95% Confidence Interval = 1.8291*131.4286 = 240.40

Thus, correct limits of a 95% (two-sided) confidence interval for MTTF (in minutes) are:

Lower limit = 78.33

Upper Limit = 240.40

Please note that the option given are incorrect.