Decision tree analysis | Statistics homework help

MicroProducts, Incorporated (MPI), manufactures printed circuit boards for a major PC manufacturer. Before a board is sent to the customer, three key components must be tested. These components can be tested in any order. If any of the components fail, the entire board must be scrapped. The costs of testing the three components are provided in the following table, along with the probability of each component failing the test: 

Component   Cost   of Test  Probability   of Failure 

X                    $1.75                        0.125 

Y                    $2.00                        0.075 

Z                    $2.40                         0.140 

a. Create a decision tree for this problem that could be used to determine the order in which the components should be tested to minimize the expected cost of performing the tests. Draw this tree by hand and include it along with your submission. 

• Do not put any numbers (probabilities, costs, etc.) on your drawing. 

• The tree should show the structure and logic of the decision process. 

• Distinguishing between decision and chance nodes, and naming the various nodes and branches, is critical. 

• Create a tree that is as general as possible – do not eliminate certain branches from consideration because of the specific values of the inputs as presented in the case. 

• Recall that the key to success is determining what decision/event happens first, and then building out the tree in sequential order.

b. Implement your tree from part a in Precision Tree. Print the tree out in a single page and include it along with your submission. 

c. State the optimal decision strategy regarding the order in which the components be tested? 

d. What is the expected cost of performing the tests in this sequence?