Abstract
Sometimes a parameter in an aleatory model, such as p in the binomial distribution or λ in the Poisson distribution, can be affected by observable quantities such as pressure, mass, or temperature. For example, in the case of a pressure vessel, very high pressure and high temperature may be leading indicators of failures. In such cases, information about the explanatory variables can be used in the Bayesian inference paradigm to inform the estimates of p or λ. We have already seen examples of this in Chap. 5, where we modeled the influence of time on p and λ via logistic and loglinear regression models, respectively. In this chapter, we extend this concept to more complex situations, such as a Bayesian regression approach that estimates the probability of O-ring failure in the solid-rocket booster motors of the space shuttle.
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Notes
- 1.
As pointed out by [2], inclusion of flights with no incidents of blowholes is questionable. Therefore, the analysis presented here is intended only to illustrate the types of modeling that are possible, and the results should not be interpreted as the output of a validated data set.
- 2.
With the Jeffreys prior, the posterior mean is numerically equal to the MLE.
References
Dezfuli H, Kelly DL, Smith C, Vedros K, Galyean W (2009) Bayesian inference for NASA probabilistic risk and reliability analysis. NASA, Washington, DC
McDonald AJ, Hansen JR (2009) Truth, lies, and O-rings: inside the space shuttle challenger disaster. University Press of Florida, FL
Dalal SR, Fowlkes EB, Hoadley B (1989) Risk analysis of the space shuttle: pre-challenger prediction of failure. J Am Stat Assoc 84(408):945–957
Hamada MS, Wilson AG, Reese CS, Martz HF (2008) Bayesian reliability. Springer, New York
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© 2011 Springer-Verlag London Limited
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Kelly, D., Smith, C. (2011). Bayesian Regression Models. In: Bayesian Inference for Probabilistic Risk Assessment. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-1-84996-187-5_11
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DOI: https://doi.org/10.1007/978-1-84996-187-5_11
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