Reliability, risk and uncertainty analysis using generic expectation functions

In engineering design and analysis, mathematical models that generally invo lve a number of uncertain parameters are frequently employed for decision m aking. Over the years, a number of techniques have been developed to quanti fy model output uncertainty contributed by uncertain input parameters. Typi cally, the methods that are easy to apply may give inaccurate estimates of model output uncertainty. Other methods that reliably produce very accurate results are either difficult to apply or require intensive computational e ffort. This paper describes the development of generic expectation function s as a function of means and coefficients of variation of input random vari ables. The generic expectation functions are straightforward to develop, an d apply to problems related to reliability, risk, and uncertainty analysis. Several expectation functions based on commonly used probability distribut ions have been developed. Using them, any order of moment can be estimated exactly. It is found that if exact moments of the model output are availabl e, one can find a good estimate of reliability, risk, and uncertainty of a system without knowing its model output distribution exactly. This techniqu e is applicable when an output variable is a function of several independen t random variables in multiplicative, additive, or combined (multiplicative and additive) forms. A practical example is presented to demonstrate the a pplication of generic expectation functions.