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Which option should we select? The table gives the cost if successful, the cost if the improvement fails, and the expected values of both the cost and net savings. By numbers alone, we would select option B with an expected savings of $197 million. However, reasonable and valid cases can be made for both A and C. In option A, we risk only $35 million, and, therefore, are minimizing the total cost if the improvement succeeds or if it fails. In fact, the $600 million cost of failure for option B may be too much for the system to bear, no matter the expected savings. Option C provides a net savings of "only" $100 million, but its success is virtually certain. Although savings for this option are less dramatic, it does provide major savings while minimizing risk. In this case, we may assume the cost to be a fixed $400 million, with failure being so unlikely that we can discount it Option B, of course, balances cost and risk to maximize the expected savings.

Suppose, however, that option A had an 80% probability of success as shown in A', rather than the original 70% probability. In this case, the expected savings of A' would increase to $205 million, and would make it the preferred approach in pure expectation terms. However, most individuals or groups faced with decisions of this sort are unlikely to change from option B to A' based solely on the increase in estimated probability to 80%. Their decisions are more likely to depend on perceived risk or on minimizing losses. Using nonmathematical criteria does not make the decisions incorrect or invalid, nor does it make the numerical values unimportant We need quantitative information to choose between options but we do not have to base our decisions exclusively on this information.

As a second example, we can apply the results of utility analysis to concept selection for FireSat In particular, the number of satellites strongly drives the cost of a constellation. If we select the low-Earth orbit approach for FireSat, how many satellites should the operational constellation contain? More satellites means better coverage and, therefore, reduces the time from when a fire starts until it is first detected. Consequently, one of our key parameters is the time late, that is, the time from when a fire starts until the system detects its presence and transmits the information to the ground. Figure 3-5 plots the hypothetical time late vs. the number of satellites for

FireSat. The details of such plots will depend on the latitude under consideration, swath coverage, altitude, and various other parameters. However, the characteristic of increasing coverage with more satellites eventually reaches a point of diminishing returns. This will normally be true irrespective of the coverage assumptions.

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