12 152 Case Study 25 Case Study 25: Iranian Hostage Rescue Mission\' During the
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12 152 Case Study 25 Case Study 25: Iranian Hostage Rescue Mission' During the spring of 1980, a joint task force consisting of eight RH-53 s Stallion helicopters was launched from the U.S.S. Nimitz in an attempt to rescue the 44 U.S. hostages held in Teheran [Lars 85]. The mission was scrubbed after three of the eight helicopters suffered either electrical or hydraulic malfunctions Six helicopters would have been needed to get all of the hostages out. The aborted mission turned to tragedy when one of the helicopters crashed into a C-130 at the desert landing site. An interesting question to consider is could we have predicted beforehand whether eight helicopters was a sufficient number of helicopters to send if six were needed to successfully complete the mission? Some basic principles of probability and reliability provide some revealing information about the mission The reliability of the RH-53 Sea Stallion helicopter can be estimated from the maintenance records By using some basic descriptive statistics (e.g histograms, frequency distributions on the maintenance data, we could estimate th mean time between failures (MTBF) as well as individual failure times (T) for thi type of helicopter. From this summary data, it could be ascertained that the time to failure (T) was exponentially distributed with l/MTBF. A X2 Goodness-of Fit test could be performed to validate the use of the exponential model. In fact this was actually done after the operation. The analysis revealed that T was indeed exponential with a MTBF of 20 hours. That means that n 1/20. Knowing that the rescue mission will take a total of 14 hours of flying time, one can compute the probability that one RH-53 will successfully complete the mission. That is, we 1/20 /20)14. 4966 .5 Once the probability of a successful mission for one helicopter is calculated, we can now use the binomial distribution to calculate the probability that six o more helicopters will successfully complete their missions. Thus, if the random Most of the data in this case study comes from Buddy Wood's film on Application of the Binomial," USAF Academy, 1982 dep ters n ch is not sould we hav h reveals number of probabil POX 0.8 0.6 0.2Explanation / Answer
Lets calculate the reliability of a helicopter
R(9) = e^(-9/20) = 0.6376
In order to achieve the success rate of 0.9, number of helicopers required are
P(X>=n) = 0.9
Below is the table which gives all possible number of probabilities of success of mission for number of helicopters where minimum 6 should work
From the above table minimum 14 helicopters need to be sent for successful completion of the mission.
number of helicopter sent Probability of success 6 0.0000 7 0.0429 8 0.1516 9 0.3091 10 0.4804 11 0.6356 12 0.7593 13 0.8489 14 0.9093 15 0.9475Related Questions
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