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Prove the multinomial criterion

Question:

1. Prove the multinomial criterion (formula 3.55). Assume that L has density Fl

2. A system is maintained according to policy 7 (section 3.2.6.4). The repair cost of a system failing at time t has a uniform distribution over the interval [a, a + bt] with and a ≥ 0 b > 0.

3. Under the same assumptions as in section 3.2.6.4 (in particular assumptions (3.96) and (3.99)), show that every linearly increasing repair cost limit c(t) = c + dt with and a leads to a higher maintenance cost rate than given by (3.105).

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