Let X(t) be the cumulative repair cost of a system arising in the interval (0, t] (excluding replacement costs) and the corresponding cumulative repair cost rate Assume The system is replaced by an...

Let X(t) be the cumulative repair cost of a system arising in the interval (0, t] (excluding replacement costs) and

the corresponding cumulative repair cost rate Assume

The system is replaced by an equivalent new one as soon as reaches level R(t) r.

(1) Given a constant replacement cost c, determine a level r = r∗ which is optimal with respect to the long-run total maintenance cost per unit time . (Make sure K(r) that an optimal level exists.)

(2) Compare to the minimal long-run total maintenance cost per unit time K(r∗) K(τ which arises by applying the corresponding economic lifetime ∗) τ∗.