It is known that the time of failure, in months, of a certain spare part for a pump follows a distribution of p.d.f

f(t) = 0.2 for 0

f(t)= 0.1 for 2

A failure replacement cost $200 while a preventive replacement costs $100. Using age-based replacement model find the following:

(a) The optimal replacement age (consider values of tp= 2,4,6,8 months) and cost

(B) The expected number of spare parts that need to be ordered for such 50 pumps over a period of one year and a half

For a constant interval replacement policy where failure between preventive replacements are handled with a minimal repair that costs $150, find the following

(c) The optimal replacement time (consider values of tp=2,4,6,8 months)

(d) the expected number of spare parts that need to be ordered for 50 such pumps over a period of one year and a half

(e) compare (b) and (d) and explain the difference