System reliability: System reliability is concerned with how long a system will
ID: 3128285 • Letter: S
Question
System reliability: System reliability is concerned with how long a system will operate before it breaks down and repairs are required. In this problem the system is an electric power plant consisting of four generators. These generators operate simultaneously to generate power. We will assume that each generator operates independently of all the others. Suppose the probability that a generator fails in the k^th month is given by a geometric probability mass function with probability of failure equal to 0.1. Thus, its probability mass function is: What is the probability that none of the four generators fails in the first month of use? Suppose there is only one generator. What is the probability that it doesn't fail in the first 12 months? Now, use part (b) to find the probability that three out of four generators will be working after 1 year.Explanation / Answer
Ans: a) The probability that none of the 4 generators fail in the first month of use is (9/10)^4.
b) In case of only one generator, the probability of a generator does not fail in the first 12 months is (9/10)
c) The probability that three out of the four generators wil be working after 1 year = (1/10) (9/10)^3
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