Problem:

Col. Demgen is leading a technology investment program for the missile defense agency. Five technologies have been proposed:

1. A composite casing for the second stage. It will increase the cost of the stage by $20,000, but the second stage will be lighter, allowing the first stage to be 10% smaller (by mass). The first stage costs $250,000 today.
2. A faster computer can be installed in the onboard tracking system. This will add $250,000 to the cost of each interceptor missile. It will reduce the number of target misses by 5%.
3. An improved maneuvering system. This will increase the probability of hitting a target by 1% (a 0.70 probability of hit will change to a 0.71 probability of success). The cost is $200,000.
4. A commercial inertial navigation package. This will reduce the cost of the missile by $30,000. However, the failure rate of the package is once per 3000 flights, whereas todays navigation package has never failed.
5. An improved prelaunch built-in test system. This costs $350,000 per unit, but one unit services a battery of four interceptors. It is believed that 2 out of every 100 launches is failing because of problems that could have been identified via built-in test.

The current interceptor missile costs $1 million and has a 0.92 probability of destroying an inbound enemy missile.

Which technologies should Col. Demgen pursue, and in what order should the selected technologies be applied to the missile?

Use the value model: worth = cost / ln(1-P_s). Note that worth is always negative, so closer to zero is better. Col. Demgen is risk neutral.

Hint: There are 6 alternatives (5 new technologies and the current interceptor missile. All you need to do is use the value model to compute the worth. By knowing the cost and probability of destroying an inbound enemy missile, the current worth can be calculated. Then, 1: Composite casing of the second stage increases the cost by $20,000. The weight of the first stage is reduced by 10%. No information is given about the relationship between the weight and cost of the first stage, so assume directly proportional. 2: The faster computer increases the cost of the system by $250,000. The number of target misses is reduced by 5%, so the current success rate would be increased by (0.080.05). 3: The improved maneuvering system increases the probability of success by 1%, and increases the cost by $200,000. 4: The commercial inertial navigation package reduces the cost of the system by $30,000. The failure rate of the package is 1/3,000, therefore the current success rate of 0.92 would be reduced by a factor of 2,999/3,000. 5: The improved pre-launch built-in-test system increases the cost of the missile by ($350,000/4). The system reduces the failure rate by 2%. Which Technologies should be pursued (in comparison with the current system)? Which Technologies should not be pursued?