QUESTION 1 

It has been determined that a component is critical to plant operations and you have been given the task of determining a time-based replacement policy. 

Figure: Failure time relative frequency plot. Note that relative frequency is a probability already, not a density. for example, the probability that the asset fails between 0 and 0.2 weeks is 1%.

Answer the following: 

a. Compute the expected failure times under age-based replacement for t p = 0,0.2,...1 using Δt = 0.2 weeks. 

b. If the cost of a preventive replacement is $100 and the cost of a failure replacement is $250, what is the optimal replacement age, t*p? 

c. It turns out that you overestimated the cost of failure by $75. What is the new optimal replacement age?