Question

One supply company, Falcon Carbon Fiber (FCF) has developed a carbon fiber 3 D printer that you are evaluating as a system for making critical replacement components at the Mars refueling station. Based on information FCF collected during the product development process for their 3D printers, the company estimates that 95% of new components produced using their 3D printers will perform satisfactorily (event 'S'= 'satisfactory'). To assess if produced components are satisfactory, a test procedure has been developed by your design department, which has an additional cost. If the component passes the test (event 'P') then the decision is to accept the component; any component that does not pass the test (event '∼P') will be rejected. Your design team has evaluated this test procedure and determined that when the component is satisfactory (event 'S') the test gives the result 'P' nine out of ten times. If the component is unsatisfactory (event'∼S'), the test gives the result '∼P' four out of five times.

(a) Show that these probabilities are correct:

P[∼S|∼P]=8/27 and P[∼S|P] = 2/173.

(b) The consequences of the state of the component are measured on a monetary scale for gain or loss, as indicated below. Construct a decision tree, showing two possible strategies, as follows.

Action1:{do not test; accept the product}. The consequences, in this case, are +$4,000 if the product is satisfactory, –$25,000 if unsatisfactory.

Action2: {test ; accept the product if the test result is positive (event 'P'); reject the product if the test result is negative ('~P')}. The consequences, in this case, are: +$4000 if the product is satisfactory; ‐$25000 if the product passes the test and is unsatisfactory; ‐$750 if the product is rejected (whether it is actually satisfactory or not)

These values should be adjusted to reflect the cost of testing where appropriate. The test costs $500. Draw a decision tree and solve the decision problem, (calculate the maximum expected profit and determine which action produces this maximum expected profit).

Answer 1