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# The Challenger Disaster Revisited

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The Challenger Disaster Revisited The Challenger Disaster On January 28 1986 the space shuttle Challenger had a catastrophic failure due to burnthrough of an O ring seal at a joint in one of the solid fuel rocket boosters This was the 25th shuttle flight Of the 24 previous shuttle flights 7 had incidents of damage to joints 16 had no incidents of damage and 1 was unknown The data comes from recovered solid rocket boosters the one that was unknown was not recovered The question we wish to examine is Could an estimate of the probability of an O ring failure be created from the results of previous launches Damage to Booster Rocket Field Joints Below are data from the Presidential Commission on the Space Shuttle Challenger Accident 1986 The data consist of the flight temperature at the time of launch F and whether or not there was damage to the booster rocket field joints No 0 Yes 1 Flight STS 1 STS 2 STS 3 STS 4 STS 5 STS 6 STS 7 STS 8 Temp 66 70 69 80 68 67 72 73 Damage NO YES NO NO NO NO NO Flight STS 9 STS 41 B STS 41 C STS 41 D STS 41 G STS 51 A STS 51 C STS 51 D Temp 70 57 63 70 78 67 53 67 Damage NO YES YES YES NO NO YES NO Flight STS 51 B STS 51 G STS 51 F STS 51 I STS 51 J STS 61 A STS 61 B STS 61 C Temp 75 70 81 76 79 75 76 58 Damage NO NO NO NO NO YES NO YES The temperature when STS 51 L Challenger was launched was 31 F Figure18 Plot of Incidence of Booster Field Joint Damage vs Temperature Using the techniques of this section we can fit a logistic model to the Challenger data We will regroup the data by temperature into intervals of 5 degrees using the midpoint of each interval for the independant variable We also adjust the probabilities a bit replacing 0 with 0 01 and 1 with 0 99 so we can take logarithms for the logit fit Thus we have the following data Interval Temp Prob Logit 51 55 53 0 99 4 595 56 60 58 0 99 4 595 61 65 63 0 99 4 595 66 70 68 0 20 1 386 71 75 73 0 25 1 099 76 80 78 0 01 4 595 81 85 83 0 01 4 595 The graph of the transformed data with

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