1. Two nickel-cadmium batteries provide electrical power to operate a satellite transceiver. If both batteries are operating in parallel, they have an individual failure rate of 0.1 per year. If one fails, the other can operate the transceiver (at a reduced power output). However, the increased electrical demand will triple the failure rate of the remaining battery. Determine the system reliability at 1, 2, 3, 4, and 5 year. What is the system MTTF?
2. An engine health monitoring system consists of a primary unit and a standby unit. The MTTF of the primary unit is 1000 operating hours, and the MTTF of the standby unit is 333 hour when in operation and 2000 hours while in standby status. Estimate the design life of the system if specifications require a reliability of 0.9. What is the system MTTF?
3. A computerized airline reservation system has a main computer on-line and a secondary standby computer. The on-line computer fails at a constant rate of 0.001 failure per hour, and the standby unit fails when on-line at the constant rate of 0.005 failure per hour. There are no failures while the unit is in the standby mode.
(a) Determine the system reliability over a 72-hour period
(b) The airline desires to have a system MTTF of 2000 hour. Determine the minimum MTTF of the main computer to achieve this goal assuming that the standby computer MTTF does not change.
4. A truck company requires two loading machines to unload a truck in 5 hours. Working together, the two loading machines have a failure rate of 0.05 per hour. However, if one fails while unloading a truck, the other's failure rate increases to 0.2 per hour as a result of the increase in the unloading rate necessary in order to complete the task on time. Compute the probability (reliability) that a truck will be successfully unloaded by a two-machine system. What is the expected time to failure (in working hours) of the two-machine system.