18. After being repaired, a machine functions for an exponential time with rate A and then fails....
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18. After being repaired, a machine functions for an exponential time with rate A and then fails. Upon failure, a repair process begins. The repair process proceeds sequentially through k distinct phases. First a phase 1 repair must be performed, then a phase 2, and so on. The times to complete these phases are independent, with phase / taking an exponential time with rate ì,, / = 1, ..., A:.
(a) What proportion of time is the machine undergoing a phase / repair?
(b) What proportion of time is the machine working?
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