
3.23. In Example 3.14, another design offers two pumps in parallel in the pipe. As in the example, each
has a mean time to failure of 1000 hr governed by an exponential density. State any assumptions, and
calculate the probability that both pumps will survive the first 200 hr of operation.
Solution: In Example 3.14, we found that the probability that one pump will fail in 200 hours is 0.1813.
The probability that the same pump will survive the first 200 hours is 1 −0.1813 = 0.8187. The probability
that both pumps, assuming that one pump does not affect the other, will survive the first 200 hours is
0.8187
2
= 0.6703.
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