A system is maintained according to policy 7 with a constant repair cost limit c. System lifetime L and repair cost C have the respective distribution functions F(t) and The cost of a minimal repair...

A system is maintained according to policy 7 with a constant repair cost limit c. System lifetime L and repair cost C have the respective distribution functions F(t) and The cost of a minimal repair is R(x). assumed (quite naturally) to depend on c as follows: c_m
= c_m(c) = E(C|C ≤ c).

(1) Determine the corresponding maintenance cost rate via formula (3.85) for any distribution function F(t) and for any distribution function R(x) = P(C ≤ x) with density r(x) and property R(cr) = 1.

(2) Determine the optimal repair cost limit with given by (3.91) and given F(t) R(x) by (3.96)

Note Exercises 3.18 to 3.29 refer to ordinary renewal processes. The functions f(t) and F(t) denote density and distribution function; the parameters μ and μ₂
are mean value and second moment of the cycle length Y. N(t) is the (random) renewal counting function and H(t) denotes the corresponding renewal function.