1. Seven pumps have failure times (in months) of 15.1, 10.7, 8.8, 11.3, 12.6, 14.4 and 8.7. Assume an exponential distribution. Assume the dataset is complete and all units have been operated to failure.

a) Find a point estimate of the MTTF

b) Estimate the reliability of a pump for t = 12 months

c) Calculate the 95% two-sided confidence interval for ?, using the c ² distribution.

, if the distribution is exponential, the distribution of the MTTF can be approximated by the Chi-squared distribution, where r is the number of failures and T is the accumulated hours in a functioning state.

2. A radar system uses 650 similar electronic devices. Each device has a failure rate of 0.00015 per month. If all these devices operate independently, what is the probability that there are no failures in a given year?

P [xy (2r) xi-a/(2r)] 27