QUESTION 2 

Through a thorough analysis, your company has identified a critical bearing as a source of costly downtime. You have been tasked with identifying an optimal time-based maintenance strategy. Through analysis of previous failures, it has been found that the bearing failure times (in weeks) are Weibull distributed with n = 10 and B = 6. 

a. The cost of failure has been found to be approximately $17,000, which includes labour, lost production, parts and failures in other components that resulted from the bearing failure. In contrast, the cost of replacing the component prior to failure is $8,000, with most of the savings coming from ensuring proper resources are on hand and prevention of induced failures. Determine the average cost per week of replacing the component every 7 weeks. When computing the expected failures, use (rather large) time steps of one week (Δt = 1). Carry out the computations by hand for this part. 

b. We would like to use smaller intervals so our analysis is more accurate. As you can imagine, this would be quite tedious if we did this by hand. Using the MATLAB function expected_failures.m posted under Learning Resources on Blackboard, compute the expected number of failures for tp = 1,2,...,10 weeks using Δt = 0.1 weeks. 

c. Now that you have the expected number of failures, use your favourite software tool to compute CR(t) at Δt = 0.1 week intervals. What is the best PM time? Provide your code or spreadsheet with your answer. 

d. It turns out that your cost model was wrong. The actual cost of failure turns out to be $20,000. What is the new optimal PM time? (Hint: you need to re-calculate!) 

e. Using your answers from parts c) and d), determine how much money per week your faulty cost model cost the company. Did you still do better than if you ran the component to failure? Justify your answer.