NASA's Challenger Crash, as explained by Logistic Regression

-
On January 28th 1986, NASA's Challenger spacecraft launched skyward from Cape Canaveral Florida. Approximately 73 seconds later, the ship began to break apart in what appeared to be an explosion as seen from land. This chain of events that eventually destroyed the ship initiated when an o-ring in the right rocket booster failed shortly after takeoff.

After each previous NASA launch, the rocket boosters that fall from the ship, typically into the Atlantic Ocean, are retrieved for analysis. The same structural o-rings that proved to be Challenger's downfall were assessed and assigned a damage level. This information can be paired with the respective outside temperature at time of launch. That data set is available today, and we hope it can help us comprehend factors that led to this crash:

We will assess the damage field as binary; any damage level=Failure. No damage=No Failure. That assumption is used throughout this analysis. With failure being either true or false, we get an initial look at the relationship between temperature and o-ring failure:


Put simply, lower temperatures appear to increase the likelihood of o-ring failure. A convenient tool to utilize here is a logistic regression. This regression model converts our binomial output of "Failure" and "No failure" to a probability of failure between 0 and 1 when paired with a continuous variable. In our case the continuous variable used is temperature in degrees Fahrenheit. Essentially a logistic regression will use Euler based logarithms to convert our Failure/Non-failure measure to odds of failure and finally to a probability of failure. When this model is created, our output can be visualized as such: 

Each black point is a fitted value from our regression, and the blue line is a visual aid for the model's behavior overall. We can now use this model to extrapolate fitted values outside of our original data set. If we assign this formula to each temperature from 30°F to 80°F at .5° intervals we get the following:


Next, we can add our original Failure and Non-failure elements back in. I have assigned o-ring failure as red and non-failure as green.



Again, the relationship between temperature and failure is clear. Our model predicts almost certain failure for any temperature below 45°F. This observation makes the next element addition even more striking:



The red triangle is the actual temperature at time of takeoff 1/28/86. The unusually cold weather that morning unfortunately played a critical role in the ultimate failure of the o-ring and the disaster that occurred seconds later.  

Comments

Post a Comment

Popular posts from this blog

Using a Neural Network to Predict Pneumonia From X-Ray Images

-
Image
According to the American Lung Association , ' Pneumonia is an infection of the lungs that may be caused by bacteria, viruses, or fungi. The infection causes the lungs' air sacs (alveoli) to become inflamed and fill up with fluid or pus. That can make it hard for the oxygen you breathe in to get into your bloodstream. The symptoms of pneumonia can range from mild to severe, and include cough, fever, chills, and trouble breathing.' Pneumonia Infographic Patients with pneumonia could have the following symptoms: Cough that produces phlegm or sometimes blood Fever Shortness of breath or difficulty breathing Chills or shaking Fatigue Sweating Chest or muscle pain If a person is suspected of having pneumonia, a doctor will begin by asking the patient about their medical history and symptoms. Next will be a physical exam, so the doctor can listen to the patient's lungs. In checking for pneumonia, a doctor will listen for abnormal sounds like crackling, rumbling or wheezing. I
Read more

Using a Neural Network to Classify Lego Figures

-
Image
 The efficacy of image classification has grown leaps and bounds in recent years with the advent of neural networks. Without going into too much detail, an artificial neural network consists of a series of layers through which inputs flow becoming output predictions. Each layer is composed of a predetermined number of neurons, and each neuron feeds information to the next layer of neurons via weighted connections. These weights are real numbers that flow from layer to layer eventually reaching an output layer, producing a numerical prediction.  For the purposes of image classification, the inputs are pixels. These pixels are converted to numeric inputs by gray-scale figures or color codes (RBG, hex, etc). The output is the neural network's prediction of what that image contains. The neural network learns using a dataset of labeled images; recording correct predictions and attempting to grasp what elements of a picture correspond to which labels.  This abstract concept can be intui
Read more

Why are people leaving Illinois?

-
Image
  Illinois is famous for being one of the very few states in the country with negative population growth.   The goal of this analysis is to i dentify the key reasons for the declining population by extracting  meaningful insights   from unstructured text. The raw text used for this project is in the form of roughly 300,000 news articles and titles scraped from the web that reference Illinois, Chicago, or Springfield. This project was completed in Python & Pyspark with several Natural Language Processing packages. 
Read more