## Comparing a Failure Probability to an Acceptability Criterion: Decision Theory Rationale and a Space Shuttle Application## Volume 3, Number 4, October 2007 - Paper 4 - pp. 433 -440## WILLIAM E. VESELYNASA Headquarters, Office of Safety and Mission Assurance 300 E Street SW, Washington, DC 20037, U.S.A.(Received on August 1, 2006) ## Abstract:This paper presents basic decision theory rationale for selecting a particular failure probability value from its uncertainty distribution to compare to a defined acceptability criterion. Since the success probability, or reliability, is one minus the failure probability, the rationale also applies to selecting a particular reliability value to compare to a reliability criterion. The uncertainty in the failure probability estimate is described by a probability distribution which is termed the uncertainty distribution. This is consistent with the Bayesian statistical approach that is commonly used in probabilistic modeling and in quantitative risk assessments. The uncertainty distribution completely characterizes the uncertainty in the estimate, giving all the percentiles, or Bayesian confidence bounds, for the estimate.
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