# Returning to Problem 13.6, the

Returning to Problem 13.6, there is another way in which we could have expanded the analysis from this point. In fact, the systems engineers and stakeholders have to determine whether the system is acceptable after these tests are over and the test results are in; that is, they have to make a decision. In addition, going into the test, they are not sure whether the system has acceptable performance for the stakeholders. If the system does, and it is accepted, then there should be relatively few and inexpensive fixes needed relative to the case where the system’s performance is unacceptable, but the decision is made to accept the system.

So we have two decision nodes: which test site to choose and whether to accept the system for use by the stakeholders.

The weather has two states and associated probabilities as in Problem 13.8.

The ability of the three sites to reproduce good versus poor test conditions in the weather conditions is as it was in Problem 13.8.

Now we must introduce our prior probabilities on the acceptability of the system’s performance. Suppose we start with only two possibilities (acceptable and unacceptable) with probabilities of 0.8 and 0.2.

We must also introduce our uncertainty that the test will say the system is ‘‘acceptable.’’ This uncertainty is dependent on the system’s actual performance and our ability to reproduce the test condition. The table below describes this probability distribution.

The quality engineers are called in to help us determine what the relative value of accepting a system is given it is or is not acceptable, over the life time of the system. These engineers conduct an analysis over the 10-year life time of our system and present the net present value (NPV) to our organization for the following conditions:

Which site should we choose? Remember the rental cost of each site. What is the expected value of perfect information on the weather?

Problem 13.6

You have been tasked with providing a recommendation for a test site at which an acceptance test will be conducted. There are three possible test sites (A, B, and C). Site A is the preferred site during good weather. Site C is the least preferred. Unfortunately, there is a long-range weather forecast for 3 months from now when the test needs to be conducted. The weather forecasters described the possibilities for weather as ‘‘good,’’ ‘‘fair,’’ and ‘‘poor.’’ These possibilities have been defined very carefully and their forecast for the time period of the test is: 0.3 for good, 0.6 for fair and 0.1 for poor.

You have tried to find a way to reserve site A for a long enough period of time that the weather will certainly be good. However, site A is used by many people, and management has determined that the project cannot afford to rent site A for this extended time period. The cost at which the sites can be reserved for the time period in question is \$1000 for site A, \$700 for site B, and \$400 for site C.

Usage of each of these sites has varying positives and negatives for being able to analyze the results and recommend that the system be accepted. You have queried your colleagues to determine how much they would be willing to pay to change a specific site in the different weather conditions to the preferred site A and weather condition. These relative dollar values do not include the cost of renting the site for the needed time period. The relative dollar value equivalents for sites and weather conditions are shown below:

That is, site A in good weather is worth \$1000 more dollars in terms of test performance than it is in poor weather. Similarly, site A in good weather is worth \$500 more than site C in good weather.

a. Draw the influence (or decision) diagram for this problem.

b. Draw the decision tree for the problem.

c. Compute the expected values for the three sites to determine which site should be recommended.

d. What is the value of perfect information for weather? Show the influence diagram and decision tree for computing the value of perfect information.

e. Using the following u curve, what is the best expected utility decision?

Where  is the total monetary value associated with using the site in question.

f. What is the value of perfect information using the above  curve?

Problem 13.8

Consider Problem 13.6. The first paragraph holds except we will drop the fair weather condition. The probability of good weather is 0.3; the probability of poor weather is 0.7.

We are now going to enhance this model to address the need to test our system under a specified test condition. The weather affects the ability of each site to provide the necessary elements (e.g., terrain, visibility) that define the test condition. Our test experts visit each site and return with probabilities that each site can do a ‘‘good’’ versus ‘‘poor’’ job of reproducing the needed test condition. Assume that we have definitions of good and poor that meet the clairvoyant’s test. (Note we could have defined more than two categories if we felt we needed to achieve more accuracy.)

The test engineers have determined that they would be willing to pay \$10,000 to move from a test site providing a poor version of the test condition to a test site providing a good version of the test condition. Which site should we choose? Remember the rental cost of each site. What is the value of perfect information on the weather?

Problem 13.6

You have been tasked with providing a recommendation for a test site at which an acceptance test will be conducted. There are three possible test sites (A, B, and C). Site A is the preferred site during good weather. Site C is the least preferred. Unfortunately, there is a long-range weather forecast for 3 months from now when the test needs to be conducted. The weather forecasters described the possibilities for weather as ‘‘good,’’ ‘‘fair,’’ and ‘‘poor.’’ These possibilities have been defined very carefully and their forecast for the time period of the test is: 0.3 for good, 0.6 for fair and 0.1 for poor.

You have tried to find a way to reserve site A for a long enough period of time that the weather will certainly be good. However, site A is used by many people, and management has determined that the project cannot afford to rent site A for this extended time period. The cost at which the sites can be reserved for the time period in question is \$1000 for site A, \$700 for site B, and \$400 for site C.

Usage of each of these sites has varying positives and negatives for being able to analyze the results and recommend that the system be accepted. You have queried your colleagues to determine how much they would be willing to pay to change a specific site in the different weather conditions to the preferred site A and weather condition. These relative dollar values do not include the cost of renting the site for the needed time period. The relative dollar value equivalents for sites and weather conditions are shown below:

That is, site A in good weather is worth \$1000 more dollars in terms of test performance than it is in poor weather. Similarly, site A in good weather is worth \$500 more than site C in good weather.

a. Draw the influence (or decision) diagram for this problem.

b. Draw the decision tree for the problem.

c. Compute the expected values for the three sites to determine which site should be recommended.

d. What is the value of perfect information for weather? Show the influence diagram and decision tree for computing the value of perfect information.

e. Using the following u curve, what is the best expected utility decision?

Where  is the total monetary value associated with using the site in question.

f. What is the value of perfect information using the above  curve?

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