1. Suppose that in problem 3.19 you had only made a two-state model—diode either good or bad, P(xg) c 0.9, P(xb) c 0.1. Would the reliabilities of the three systems have been the same? Explain. 2. A...

1.
Suppose that in problem 3.19 you had only made a two-state model—diode either good or bad,
P(x
g) c 0.9,
P(x
b) c 0.1. Would the reliabilities of the three systems have been the same? Explain.

2.
A mechanical component, such as a valve, can have two modes of failure: leaking and blocked. Can we treat this with a three-state model as we did in problem 3.19? Explain.

3.
It is generally difficult to set up a reliability model for a system with common mode failures. Oftentimes, making a three-state model will help. Suppose
x1 denotes element 1 that is good,
x
c
denotes element 1 that has failed in a common mode, and
x
i
denotes element 1 that has failed in an independent mode. Set up reliability models and equations for a single element, two series elements, and two parallel elements based on the one success and two failures modes. Given the probabilities
P(x1) c 0.9,
P(x
c) c 0.03,
P(x
i) c 0.07, evaluate the reliabilities of the three systems.