Comparing a Failure Probability to an Acceptability Criterion: Decision Theory Rationale and a Space Shuttle Application

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. Based on decision theory principles, selection of the failure probability value should be separate from determination of the acceptable failure probability criterion. Selection of the failure probability value considers the losses, or impacts, from underestimating or overestimating the actual value of the failure probability. Selection of the acceptable failure probability criterion considers the consequences of the occurrence of the event. An example application is given for selection of the failure probability value and definition of an acceptability criterion for Composite Overwrap Pressure Vessels (COPVs) on the Space Shuttle. This paper is useful in showing how basic decision theory paradigms can be applied in a practical risk management framework