Construct a decision tree for a posterior and preposterior analysis of the control device situation.

A firm designs and manufactures automatic electronic control devices that are installed at customers’ plant sites. The control devices are shipped by truck to customers’ sites; while in transit, the devices sometimes get out of alignment. More specifically, a device has a prior probability of .10 of getting out of alignment during shipment. When a control device is delivered to the customer’s plant site, the customer can install the device. If the customer installs the device, and if the device is in alignment, the manufacturer of the control device will realize a profit of $15,000. If the customer installs the device, and if the device is out of alignment, the manufacturer must dismantle, realign, and reinstall the device for the customer. This procedure costs $3,000, and therefore the manufacturer will realize a profit of $12,000. As an alternative to customer installation, the manufacturer can send two engineers to the customer’s plant site to check the alignment of the control device, to realign the device if necessary before installation, and to supervise the installation. Because it is less costly to realign the device before it is installed, sending the engineers costs $500. Therefore, if the engineers are sent to assist with the installation, the manufacturer realizes a profit of $14,500 (this is true whether or not the engineers must realign the device at the site). Exercises for Section 18.2 

Before a control device is installed, a piece of test equipment can be used by the customer to check the device’s alignment. The test equipment has two readings, “in” or “out” of alignment. If the control device is in alignment, there is a .8 probability that the test equipment will read “in.” If the control device is out of alignment, there is a .9 probability that the test equipment will read “out.”