Lines( 30 : 81, plogis(lower), lwd = 3, lty = 3, col = 2)Īpproximate 95% confidence intervals based on asymptotic normality are included to assess the reliability of the results. Pr <- predict(fm, ame(Temperature = 30 : 81), se = T) Points(nFailures / 6 ~ Temperature, data = nofailed, pch = 19, cex = 1.2, col = 4)ģ0 : 81, predict(fm, ame(Temperature = 30 : 81), type = 're'), Main = 'NASA Space Shuttle O-Ring Failures',
Plot(nFailures / 6 ~ Temperature, data = failed, The function to be called is glm() and the fitting process is not so different from the one used in linear regression as shown below. R makes it very easy to fit a logistic regression model. To link p(t) to t, a logistic regression model is used: The model assumes that at temperature t each of the six O-rings would suffer damage independently with the same probability. There are six O-rings on the shuttle, so during each launch, the number of distress events, is modeled as binomial with parameters p = p(t) and n = 6. A statistical model appropriate for this data, conditional on temperature, t, is the binomial model. We can do this by fitting a binomial linear logistic model. For a possible total of three damage incidents in each rocket, a graph of the proportion of failure incidents by temperature range would have illustrated an increase in the proportion of damaged O-rings with lower temperatures.Īlternatively, we might be interested in modelling the effect of treatment on the probability of O-ring failure. A simple bar chart could have focused on the proportion of O-rings exhibiting damage. The vast amount of information in censored observations is contained in the proportions at which they occur. By including all recorded data, the Commission indicated that the pattern was a bit more striking. The Commission produced a modified graph, were they added back in the censored values. However, as noted by the Roger’s Commission, the graph had one major flaw-flights where damage had not been detected were deleted. There were few data and what data were available, did not show a clear relationship between temperature and the number of O-ring failures. Charts displaying outlines of rockets labelled with temperatures of O-ring damage, organized by launch date were presented to NASA.įaxes sent to NASA on January 27th, the night before the launch, presented a graph of damage incidents to one or more rocket O-rings as a function of temperature.Įvidence given in the figure seemed inconclusive to NASA managers. Rocket tests had previously shown evidence of thermal stress in O-rings when temperatures were 65☏ and colder no data were available for the low temperatures predicted for launch time. Engineers of the booster rockets’ manufacturer expressed concern that at cold temperatures, the O-rings would harden and not seal the joints against the hot ignition gases. On the afternoon of January 27, 1986, the eve of the launch, the weather forecast predicted unusually cold weather for Florida during the early hours of January 28.
The Commission further noted that there were organizational problems with NASA that contributed to the catastrophe. Rocket fuel exploded after escaping through an opening left by a failed O-ring. Two rubber O-rings, which had been designed to separate the sections of the rocket booster, had failed due to cold temperatures on the morning of the launch. They found that the immediate cause of the accident was the failure of a key structural component of the shuttle’s rockets. Presidential Commission on the Space Shuttle Challenger Accident (also known as the Roger’s Commission) was established to ascertain the cause of the accident. Let’s examine how statistical science could have provided valuable input to the launch decision process. He argues that not having the data presented in an easily readable format led to the tragedy as well.
It also shows how group think can have dire consequences.Įdward Tufte, a well-known statistician and data visualization expert presents the tragedy in a different perspective. The accident illustrates the potentially disastrous consequences of poor organizational culture, illustrating the need for proper organizational structure. There are many lessons to be learned from this tragedy. The disaster claimed the lives of all seven astronauts aboard, includingĬhrista McAuliffe, a teacher from New Hampshire who would have been the first civilian in space. On Januthe space shuttle Challenger disintegrated 73 seconds after liftoff from Kennedy Space Center. About Blog Project Space Shuttle Challenger Disaster
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