Reliability, Risk, and Uncertainty Analysis Using Generic Expectation Functions

In engineering design and analysis, mathematical models that generally involve a number of uncertain parameters are frequently employed for decision making. Over the years, a number of techniques have been developed to quantify model output uncertainty contributed by uncertain input parameters. Typically, 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 effort. This paper describes the development of generic expectation functions as a function of means and coefficients of variation of input random variables. The generic expectation functions are straightforward to develop, and apply to problems related to reliability, risk, and uncertainty analysis. Several expectation functions based on commonly used probability distributions 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 available, one can find a good estimate of reliability, risk, and uncertainty of a system without knowing its model output distribution exactly. This technique is applicable when an output variable is a function of several independent random variables in multiplicative, additive, or combined (multiplicative and additive) forms. A practical example is presented to demonstrate the application of generic expectation functions.