Case Background Consider a machine that can be used for another year. The question has arisen as to whether the machine should be overhauled. The cost to overhaul the machine is $5000 if it is done before the machine fails but if the machine fails while in operation, it will cost $8000. Your engineers have estimated the probability that the machine will fail while in operation. You are very apprehensive since in addition to the extra cost to replace the machine, which is easily quantifiable, other problems will also arise if the machine fails while in operation that you cannot completely quantify. You would prefer to avoid being in that situation if possible. You have been told that there a test can be performed on the machine to help you predict if the machine will fail in the next year. As with any test, it is imperfect, but you want to at least consider it. An eager statistician has put together a decision tree (attached).

Screen Fail means that the screen predicts that the machine will fail. This is considered a positive test.

Screen No Fail means that the screen predicts that the machine will not fail. This is considered a negative test.

Please use the attached decision tree to answer all the questions to follow:

(Enter as percentages rounded to the nearest whole number) 1. What is the prior probability that the machine will fail during operation? 2. What is the probability that the test will predict that the machine will fail? 3. What is the positive predictive value for the screening test? 4. What is the negative predictive value for the screening test?

Multiple Choice

If you choose to screen and it predicts failure, what decision would you make? o Overhaul o No Overhaul o Not enough information was provided

What is the EMV for screening? o -$4800 o -$7440 o -$3370 o -$1120 o Not enough information was provided for the calculation

Based on your analysis of the decision tree would you recommend that your company buy the screening test if the cost

Overhaul ' 5 (5,000.00) $ (5,000.00) Do we overhaul? No Screen 5 [ (4,800.00) Fail 60.0% ' 5 (8,000.00) 5 (8,000.00) N o Overhaul 5 (4,800.00) 40.0% Ma Fail ' 0 $0.00 Do we 5: reen ?