In the conclusion of the Report of the Presidential Commission on the Space Shuttle Challenger Accident, recommendations are given in order to avert a future similar incident. The importance of knowledge and control is emphasized. Probability can be known, and must be, if it is to be controlled.

The following graph shows the results of a rather complex analysis of how o-rings behave at different temperatures. The analysis used is called logistic regression. Even though you have not covered this technique in class, you can see and understand the probabilities the graph shows. The black curve shows the predicted probability of failure at the low 31 degF temperature at the time of the launch. The red curves show confidence bands for the probability values. These confidence bands show you the region in which you can be 95% certain that the true probability value lies. In following chapters, you will calculate confidence regions yourself.

In situations in which you have little data, the confidence regions are wide. The more data you have, the better confidence you can get that your estimates are true. At low temperatures, you can see that the confidence bands are wide....but look at the estimated probability value. Would you say that is an acceptable level?

Investigating the explosion was Richard Feynman. In Feynman's personal observations he points out that

It appears that there are enormous differences of opinion as to the probability of a failure with loss of vehicle and of human life. The estimates range from roughly 1 in 100 to 1 in 100,000. The higher figures come from the working engineers, and the very low figures from management. What are the causes and consequences of this lack of agreement? Since 1 part in 100,000 would imply that one could put a Shuttle up each day for 300 years expecting to lose only one, we could properly ask "What is the cause of management's fantastic faith in the machinery?"

The following analysis of the data summarizes the influence temperature on the number of O-ring incidents for 24 previous space shuttle flights. The results are presented in this data table. Box plots of the data show graphically the results that there are 17 instances with no O-ring failures, 5 instances with one O-ring failure, 1 instance with two O-ring failures, and 1 instance with three O-ring failures. Would you say that, in general, there seems to be more failures are lower temperatures?