Obviously, we are most interested how probability of failure relates to temperature, and other quantities known before a flight. Given our data, it is not immediately obvious what response variable we should be looking at. For example, should we look at the number of failures of O-rings in a flight, or just the fact that an O-ring failed? These might lead to different results (but fortunately for us they can be looked at using the same analyses).
We have in the past looked at models for count data that were of the form
Although these loglinear models did not require discrete (categorical) predictors, the only examples we saw were of that form. The current data can also be modelled using the standard loglinear model, but an equivalent and more natural approach is to set up the model as a logistic regression.
In this case, allow 
to be the probability of failure given the
temperature t. If one wanted to be really careful, one might write
this as
but the shorthand notation will probably suffice.
A first approach is to consider that the failures are a binomial process with the probability of failure dependent on t, but with the events themselves independent. Thus using the first form of the data (where we explicitly model the number of O-rings that failed) we are assuming that
The second assumption is more tenable than the first, but even the first seems quite reasonable. In order to fret about the first assumption, we will also analyze a version of the data that just records whether there was a failure or not.