January 28, 1986 was a sad day for many people around the world, particularly in the United States. At the Kennedy Space Center in Florida seven crewmembers were getting ready to participate in a shuttle mission. It would end up being one of the most horrific days in American and NASA history.
The Challenger mission that was to take place on January 28 was considered routine. Two payloads were to be launched from the aircraft and some experimental work was going to be done inside the shuttle while in flight. Still, all of America was waiting for the launch. The Challenger had been scheduled to depart earlier and was postponed six times due to unsatisfactory weather conditions and some mechanical problems. NASA did not want to delay the launch any longer, despite the cold weather. The Challenger was launch that cold day in January, and exploded just 73* seconds into the mission flight, killing all of the seven crewmembers on board.
Through an investigation, it was concluded that the accident was caused by the failure of the O-rings on the rocket booster. The shuttle was equipped with two rocket boosters that send the rocket into orbit. The boosters are fastened together by field joints and the O-rings seal the joints. The seals then restrain the burning fuel from leaking out of the rocket boosters. If the temperature is too cold, the O-rings will not seal properly. The engineering team was aware of the possible failure of the O-rings under extreme temperatures, but this was considered an acceptable flight risk and the command was given to launch.
We can consider some mathematical principles of probability about the reliability of the O-rings and field joints on the shuttle.
Consider the probability of one field joint and its O-ring working together successfully as P = .977
One booster has three field joints, so the probability of each field joint working effectively becomes P = (.977)3
There are two boosters on each shuttle, giving a final probability of
P = ((.977)3 )2 = (.977)6 = .87
|A damaged O-ring found after the Challenger explosion.
Image reproduced with permission of Great Images in NASA
This means that the probability of all the field joints and O-rings working together successfully is only .87. This is a fairly low rate of success, considering what was in jeopardy. The O-rings had been tested and the results showed that the O-rings could lift off their seal for several seconds at 75°F (23°C) and may lift off for more than 10 minutes at 50°F (10°C). On the day of the launch, the temperature was a record low of 36°F (2°C). The cold weather caused the O-rings to lift off their seals. This caused the burning fuel to leak from the rocket boosters, creating the explosion that shattered the Challenger.
After the shuttle accident, investigations were conducted to find the cause of the explosion. The cause of the accident was determined: the failure of the O-rings to properly seal. Recommendations were given to NASA to improve the design of the rocket boosters. It was suggested that NASA improve the field joints so they had a higher rate of success. NASA created newer and better field joints. These recommendations were made to increase the reliability of the O-rings, the field joints, and the rocket boosters themselves. Reliability is similar to probability as they both show the rate of success of something. This is the mathematical relation. The higher the probability that something will work, the more reliable it is. We use terms of reliability and probability in everyday life. When we can understand the math behind these terms, we are able to understand risk.
An earlier version of this page had the time of the explosiion as 0.678 seconds into the mission flight. In 2021 Jennifer Forgit sent Math Central a note to say this should be 73 seconds and gave a reference. Checking Natasha's notes she has a reference which contains the sentence "Just after liftoff at .678 seconds into the flight, photographic data shows a strong puff of gray smoke was spurting from the vicinity of the aft field joint on the right solid rocket booster." This was the first indication that there was a problem but this is not the time when the explosion happened.