Suppose we are concerned only with the initial failure of a component. That is, once the component has survived past a certain time t = α, we treat the component (for all practical purposes) as if it never failed. In this situation it is reasonable to use the hazard rate

a. Use the result of Exercise 17.45 to find expression for f(t), F(t), and R(t).

b. Show that the probability of initial failure, i.e., the probability that the component fails before time t = α, is 1 - e^-αβ/2.

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