Reliability Estimation Model Research Articles

Estimation of structures reliability for non-precise limit state models and vague data

This paper suggests some improvement of reliability estimation in the framework of the Stress-Strength Inference Theory, essentially based on a limit state model. The general purpose is to develop the reliability estimation models more closely corresponding to the real state in nature. Two different methods of improvement are studied. The first method assumes that the limit state model has an error which reflects actual imperfection of an applied physical theory. The error is considered to be uncertain. According to the second method, test data used for the estimation are studied to be vague. Two approaches to describing uncertain variables and non-precise data are used and compared in this paper. The first approach is a combination of the so-called fuzzy numbers method and the Bayesian one, using the former to describe the data vagueness and the latter as a basis for estimation under uncertain parameters. The second approach is exclusively based on the Bayesian approach. Both prior procedures and posterior ones are worked out using these approaches. Application and numerical examples are given to illustrate the results. This representation shows clearly how the two approaches relate to each other.

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.