Estimation from Zero-Failure Data

When performing quantitative (or probabilistic) risk assessments, it is often the case that data for many of the potential events in question are sparse or nonexistent. Some of these events may be well-represented by the binomial probability distribution. In this paper, a model for predicting the binomial failure probability, P , from data that include no failures is examined. A review of the literature indicates that the use of this model is currently limited to risk analysis of energetic initiation in the explosives testing field. The basis for the model is discussed, and the behavior of the model relative to other models developed for the same purpose is investigated. It is found that the qualitative behavior of the model is very similar to that of the other models, and for larger values of n (the number of trials), the predicted P values varied by a factor of about eight among the five models examined. Analysis revealed that the estimator is nearly identical to the median of a Bayesian posterior distribution, derived using a uniform prior. An explanation of the application of the estimator in explosives testing is provided, and comments are offered regarding the use of the estimator versus other possible techniques.