# Logit and Probit Models for O-Ring Failure Data

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Logit and probit models are common binomial models for success or failure probabilities. Following the 1986 Challenger shuttle disaster due to a failed O-ring, the impact of air temperature on the the probability of at least one primary O-ring failure was analyzed from data from previous flights using a logit model. The analysis found that the probability of failure increased dramatically as temperature decreased.

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Contributed by: Darren Glosemeyer (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The logit models have the form . Probit models have the form . The term is called the linear predictor and is linear in the parameters . The linear predictor is . The quadratic linear predictor is .

The data is based on table 5.10 from A. Agresti, *An Introduction to Categorical Data Analysis*, New York: Wiley, 1996.

The original source of the data is table 1 from S. R. Dalal, E. B. Fowlkes, and B. Hoadley, "Risk Analysis of Space Shuttle: Pre-*Challenger* Prediction of Failure," *Journal of the American Statistical Association*, 84(408), 1989 pp. 945–957, in which logistic regression models were used.

## Permanent Citation

"Logit and Probit Models for O-Ring Failure Data"

http://demonstrations.wolfram.com/LogitAndProbitModelsForORingFailureData/

Wolfram Demonstrations Project

Published: March 7 2011