Refer to the electronic switch in Exercise 4-40. 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 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%?