Reliability and risk models based on independent trials

An analysis has been made of the mathematical relationship between two alternative models for reliability and risk estimation under the assumption of mutual independence. In cases where the reliability formulation is expressible as a compound union event, the resultant reliability expressions are analogous to the Bernoulli and Poisson trials processes. Nonparametric inequality relationships aredeveloped that demonstrate that a Bayesian-Bernoulli model always predicts event probabilities that are less than Bernoulli probabilities, which are always less than or equal to probabilities predicted by the finer grained Poisson trials model. An analysis of the maximum relative prediction error indicates when the individual probabilities are less than 0.1, the relative error between the Bernoulli and Poisson models is always less than 5 percent. The results are demonstrated to have utility in system reliability, engineered design lifetime risk analysis, and simulation applications in which the model is based on independent trials.