In order to increase the lifetime of the system, the engineers have a choice between replacing component A with one whose lifetime is distributed Exp(l/2), or replacing component B with one whose lifetime is distributed Exp(l/3).
a. Generate, by simulation, a large number (at least 1000) of system lifetimes under the assumption that component A is replaced.
b. Generate, by simulation, a large number (at least 1000) of system lifetimes under the assumption that component B is replaced.
c. If the goal is to maximize the mean system lifetime, which is the better choice? Explain.
d. If the goal is to minimize the probability that the system fails within a month, which is the better choice? Explain.
e. If the goal is to maximize the 10th percentile of the system lifetimes, which is the better choice? Explain.
(a,b) Answers will vary.
(c) Replacing B results in a longer mean system lifetime (? 3.25 compared with ? 3.0).
(d) Replacing A results in a smaller probability that the system fails within a month (? 0.15 compared with? 0.18).
(e) Replacing A results in a greater 10th percentile (? 0.76 compared with ? 0.68).
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