Contents

The Space Shuttle Challenger O-Ring Blow Out and Temperature Risk

The O-rings in the booster rockets on a space shuttle are designed to expand when heated to seal different chambers of the rocket so that solid rocket fuel is not ignited prematurely. According to engineering specifications, the O-rings need to expand by 5% to ensure a safe launch. When an O-ring does not expand by at least this amount there is a risk of a “blow-out” failure where fuel leaks out and may ignite outside the booster shell and very likely cascade into an explosion. This was estimated to occur 1 out of 1000 times when the expansion of the O-rings is less than 5%.

O-ring degradation during flight was a known risk. What was unknown was the relationship between temperature and O-ring degradation. The table below shows data on the number of O-rings that failed to expand more than 5% (an “incident”) and the temperature at launch.

Learning Objectives:

• Relevant Ranges
• Applying Information Responsibly

Statistics Needed:

Scatter Plot
Linear Regression Model
Adjusted R-Squared

Data Source:

Temperature	Issues	Incident
53	11	1
57	4	1
58	4	1
63	2	1
66	0	0
67	0	0
67	0	0
67	0	0
68	0	0
69	0	0
70	4	1
70	0	0
70	4	1
70	0	0
72	0	0
73	0	0
75	0	0
75	4	1
76	0	0
78	0	0
79	0	0
81	0	0

Tasks:

Answer the questions below to determine the likelihood of an O-ring blowout during launch at 29 degrees. Based on the results make a recommendation on if the shuttle should be launched in those conditions. Use the 6 steps of the business analytics process as a framework for answering the questions and then write a report to make that recommendation to executives at NASA.

Step 1. Recognizing the problem

• What are the limitations of the data?
• Describing the relationship between temperature and O-ring incidents

Step 2. Defining the problem

• What questions do I need to ask to describe the temperature-incident relationship?
• What would sufficient answers look like?
• How many variables need to be accounted for?

Step 3. Structuring the problem

• How can we predict failure at certain temperatures?
• How far can we assume outside of given temperature ranges?
• Will incidents scale linearly?
• What are our constraints?

Step 4. Analyzing the problem

• What models and techniques are needed to address the questions?
• What are the assumptions we need to make?
• Are the assumptions reasonable?
• How will they affect our models?

Step 5. Interpreting Results and Making a Decision

• How confident can we be in our results?
• What assumptions were made and how do they affect these results?
• Should we launch based off the results?

Step 6. Implementing the solution

• What is the reasoning behind the choice of launching or not?
• What resources or limitations do we need to consider?

Questions to answer:

1. Prepare a scatter plot of the data. Does there appear to be a linear relationship between these variables?

2. Obtain a simple linear regression model to estimate the amount of O-ring incidents as a function of atmospheric temperature. What is the estimated regression function? Is temperature a significant predictor of incidents?

3. Interpret the R2

4. Suppose that NASA officials are considering launching a space shuttle when the temperature is 29 degrees. What number of O-ring incidents should they expect at this temperature, according to your model?

5. On the basis of your analysis of these data, determine the risk of a blow out. You can assume O-ring blowouts are independent. You want the probability of at least one blow out in N incidents. So consider the probability of no blowouts in N incidents. P(at least one blowout in N incidents) = 1 – P(no blowout in N incidents). Would you recommend that the shuttle be launched if the temperature is 29 degrees? Why or why not?

Report

Write a professional report (as if you were a hired consultant or employee) for the director of NASA. The report should be to the point and give specific, actionable advice or solutions based on the data and analytics. Avoid technical aspects and terms that are non-essential and any speculations not substantiated by the data. This report should be concise without lengthy explanations being necessary to understand it.

There is no min or max page limit as charts and tables can take up a highly variable amount of space. However, any charts or tables included need to be understandable to a layman at first glance (labeled and captioned if needed). The particular models you use, interpretations, and advice given are your choice and you should be prepared to explain or defend this if needed!

Use this as an outline for the report:

A. Description of the business problem

• What are the key decisions that need to be made to ensure a successful launch? Indicate specifically what the options are (or give examples of options).
• What are the overall goals, objectives and drivers for these decisions?
• What are the important factors to consider for making the decisions?
• What questions will be answered and how do these explicitly help address the decisions?

B. Data, methods, and models and results

• At a high-level, discuss the basic approach, analytics used, and data and any concerns about the integrity and quality of the data used. For example, “There is concern about incidents at temperature x because it was not part of the data set. There is insufficient data to apply this assumption to other temperatures x,y, and z.”
• Describe the models used (put the formula, tables, graphs, etc. here) indicating what they are used for (do not detail how they were developed or any technical details) e.g. “This calculation determines the reliability of our results with x% confidence”
• Provide detailed answers to the decision questions using the models
• Indicate all “important” assumptions made and why you think they are reasonable. An assumption is important if you cannot get a result without it e.g. “To make a decision whether or not to launch a rocket, we must assume that temperature of the outside air affects the temperature of the O-Ring”. It is also important if the assumption is wrong or invalid your results would be affected significantly. For example, the assumption “A 5% increase in O-ring size will result in no accident” if wrong or invalid would significantly affect what temperatures would be safe to launch.
• Do not list technical assumptions used for statistical analysis e.g. “We assume the data is normally distributed.”

C. Decision making

• Explain specifically how the models and results are used to make your recommendation. This may be literal results such as “Never launch under 67 degrees because O-rings will always fail.”
• Detail special considerations or issues to watch out for e.g. “There is not enough data to accurately predict O-ring behaviors in extreme temperatures.”
• Describe how the improvements or benefits from using the results for making the decisions can be measured or observed. i.e. Does past and will future launch data support the recommendations made.