Refer to the electronic switch in given Exercise. In order to improve the reliability of a system, three such additional switches are used on a standby basis. This means that only when a switch fails, another is activated, and so on. The system operates as long as at least one switch is operational.
(a) What is the mean life of the system?
(b) What is the standard deviation of the system life?
(c) What is the probability that the system will operate for at least 5000 hours?
(d) What is the minimum number of additional switches, on a standby basis, needed if it is desirable for the system to operate at least 3000 hours with a probability of 40%?
Exercise
An electronic switch has a constant failure rate of 10-3 per hour.
(a) What is the expected life of the switch?
(b) What is the standard deviation of the life of the switch?
(c) Find the probability that the switch will last at least 1200 hours.
(d) What is the probability that the switch will last between 1200 and 1400 hours?