Assignment 4
Due to Wednesday, April 15, 2020
http://www.spacesafetymagazine.com/space-disasters/challenger-disaster/
I’m sure all baby-boomers have a vivid recollection, but for younger readers, here’s some background …
“On the morning of 28 January 1986, the Space Shuttle Challenger, mission 51– L, rose into the cold blue sky over the Cape. To exuberant spectators and breathless flight controllers, the launch appeared normal. Within 73 seconds after liftoff, however, the external tank ruptured, its liquid fuel exploded, and Challenger broke apart.”
What happened?
“The specific failure,” noted the Report of the Presidential Commission on the Space Shuttle Challenger Accident, “was the destruction of the seals that are intended to prevent hot gases from leaking.…”
Investigators quickly focused their attention on a key part of the seals— the rubber O-rings that went in between two sections of the solid rocket motor— the “tang” and the “clevis.”The O-rings on the Challenger needed to be flexible enough to compress and expand, sometimes within milliseconds.But O-ring resiliency “is directly related to its temperature… a warm O-ring will follow the opening of the tang-to-clevis gap. A cold O-ring may not.”
In fact, investigators found that a compressed O-ring is five times more responsive at 75 degrees Fahrenheit than at 30 degrees Fahrenheit. The air temperature at launch was 36 degrees Fahrenheit.
The commission’s report found “it is probable” that the O-rings were not compressing and expanding as needed.The resulting gap allowed the gases to escape, destroying the Challenger.
So why didn’t engineers stop the launch, given the cold temperatures?
They tried.
“We were concerned the temperature was going to be lower than the 50 or the 53 that had flown the previous January, and we had experienced some… erosion on the O-rings… it wasn’t a major concern, but we said, gee, you know, we just don’t know how much further we can go below the 51 or 53 degrees or whatever it was. So we were concerned with the unknown.”
In other words— they didn’t have enough data.
Nobody knew what would happen to the O-rings on a day where the temperature was 15 degrees colder than that of any previous launch.
But not having data below 53 degrees was just one of the issues. The team recognized that they didn’t have data below 53 degrees, and decided to look at all cases where there had been signs of O-ring distress, regardless of temperature. In this case, the data was limited only to incidents of O-ring thermal distress, defined as O-ring erosion, blow-by, or excessive heating) — exactly the question of interest.
The night before the disaster— as engineers tried to convince their managers at Thiokol and NASA not to launch— someone pointed out that there had been signs of O-ring distress on a shuttle that was launched at 75 degrees. It’s true— there had been issues at 75 degrees. And at 70 degrees. And at 63 degrees. In fact, on seven separate missions, there was evidence of O-ring thermal distress. And if you look at the temperature for these launches, you’ll see that there is no easily recognizable pattern.
Observing this data, you could easily be convinced that temperature does not affect O-ring performance.
The conclusion the scientists and engineers drew based on this data was correct.
As the Rogers Commission Report stated, “In such a comparison, there is nothing irregular in the distribution of O-ring ‘distress’ over the spectrum of joint temperatures at launch between 53 degrees Fahrenheit and 75 degrees Fahrenheit.” But, when you conduct a statistical analysis on a sample of the available data, you can induce what in statistics is known as a sample selection problem. Running an analysis on less than the entire data set is not always a problem, but it can lead to mistaken conclusions depending on the question you are trying to answer. The above comparison only looks at data from 7 out of the 24 space shuttle launches up to that point.
In retrospect, the engineers should have looked at all of the data on O-ring performance — not just cases where there were signs of distress.
In this assignment, we will reanalyze the space-shuttle data set with more appropriate modeling approach. Data from Dalal et al. (1989) about O-ring failures in the NASA space shuttle program. The damage index comes from a discussion of the data by Tufte (1997).
Question 1
‘Oring’ data set contains information on the first 24 space shuttle launches of the National Aeronautics and Space Administration’s Space Shuttle program. Information is recorded on six variables and the variable descriptions are as follows; An O-ring is a seal that separates the fuel supply from the combustible gases in the rocket’s exhaust; if it fails to do so perfectly, it will show signs of thermal distress after the launch. In cold weather, O-rings are less resilient and may be more likely to fail.
VARIABLE DESCRIPTION
FlightNumber: Number of space shuttle flight.
Temperature: temperature during start (in degrees F).
Pressure: pressure.
Fail (Response Variable): did any O-ring failures occur? (no, yes).
NFailures: how many (of six) 0-rings failed?.
Damage: damage index.
• Using logistic regression, model the way in which the probability of an O-ring failure depends on temperature.
• What is the problem when you fit the regression model (a straight line on the first plot)? Which pattern revealed in this data set (based on the line on the second plot) (Hint: See the scatterplot)?
• What is the coefficient for Temp?
• Compare the pattern of the logistic regression to the pattern of the logit model.
• Estimate the odds ratio for O-ring failure with a 10 degree decrease in the launch temperature.
• The 25th space shuttle launch, involving the space shuttle Challenger, took place on January 27, 1986. Seventy-three seconds into the flight, the fuel mixed with the rocket exhaust, resulting in an explosion which destroyed the shuttle and killed all seven astronauts on board. The launch temperature that day was 31 degrees. Based on data from the first 24 launches, estimate the probability of a O-ring failure on the Challenger flight.
Question 2
Consider the ‘warpbreaks’ dataset, which is included with R. The dataset gives the results of an experiment to determine the effect of wool type (A or B) and tension (low, medium or high) on the number of warp breaks per loom. Data were collected for nine looms for each combination of settings.
As the response variable breaks is a count, it is best modeled as a Poisson distributed variable.
• Using ‘glm’ function, build the Poisson model using the wool type and wool tension to predict the number of warp breaks (per loom) and interpret the coefficients in this context.
• The model should have terms for the wool type, wool tension and the interaction between the two. Update the main effect model by adding interaction term and interpret the interaction effects.
• Do you think the interaction term is helpful to improve the model? (Hint: See the ANOVA test).