Question: 6 State dependent system models Submission date March 10, 2017 1. Two nickel-cadmium batteries provide electrical power to operate a satellite transceiver. If both batteries

6 State dependent system models Submission date March 10, 2017 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 yr. What is the system MTTF? 2. 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/hr, 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-hr period. (b) The airline desires to have a system MTTF of 2000 hr. Determine the (minimum) MTTF of the main computer to achieve this goal assuming that the standby computer MTTF does not change. 3. An alarm system may fail safe (false alarm) or may fail to danger (failure on demand). If the fail-safe failure rate is a constant 0.00034 failure per operating hour and the fail-todanger failure rate is a constant 0.000021 failure per operating hour, what is the design life of the alarm if an operating reliability of 0.99 is desired? What is the probability of a fail-to-danger failure occurring over 1000 operating hours? 4. A contractor must decide between two different sump pump systems to be installed in a new housing development. The option is to install a single 1000 gallon per minute (gpm) system or two 500-gpm pumps. If the two-pump system is used, one pump can carry most of the load in the event the other pump fails. Both of the 500-gpm pumps have an MTTF of 800 hr when working together. Their individual MTTF is 200 hr. The 1000gpm system has a rated MTTF of 700 hr. Which system is preferred on the basis of system MTTF? Which system has the best design life for a reliability of 0.80? 1

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