Consider again Mr. Maloy’s decision problem described in Problem 8. Use the PrecisionTree add-in to identify the strategy that minimizes Mr. Maloy’s annual expected total cost. Also, perform sensitivity analysis on the optimal decision and summarize your findings. In response to which model inputs is the expected total cost value most sensitive?

Problem 8

In designing a new space vehicle, NASA needs to decide whether to provide 0, 1, or 2 backup systems for a crucial component of the vehicle. The first backup system, if included, comes into use only if the original system fails. The second backup system, if included, comes into use only if the original system and the first backup system both fail. NASA engineers claim that each system, independently of the others, has a 1% chance of failing if called into use. Each backup system costs $70,000 to produce and install within the vehicle. Once the vehicle is in flight, the mission will be scrubbed only if the original system and all backups fail. The cost of a scrubbed mission, in addition to production costs, is assessed to be $8,000,000.

TABLE 7.10 Distribution of Accident Types and Corresponding Damage Amounts Type of Accident Conditional Probability Damage to Vehicle Minor $200 Moderate $1,000 Serious $4,000 Catastrophic $30,000 0.60 0.20 0.10 0.10