(Texas Tech University, 2000-05) Chollar, George W

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Statistical analysis methods are integrated with systems engineering to provide improvements in requirement definition and flowdown. A Method of Moments approach that supports the calculation of a response probability of noncompliance (PNC) based on system properties and variables is developed. To achieve this result, the statistical properties for each system parameter are combined with system characteristics to predict the response and its statistical properties. This statistical analysis approach supports the allocation of variance for each system parameter when required or desired levels of response PNC are provided.
The necessary relationships for calculating system response uncertainty and allocating variability are developed. A deterministic equation for a system requirement is used as the base model for the statistical analysis approach. A pseudo-model in the form of a second-order Taylor series expansion is created. Basic rules of statistics are applied to develop relationships for parameter variance allocation and the first four statistical moments of the system response. The resulting moment equations require the definition of counterpart statistics for the system variables (or parameters) along with the definition of appropriate probability density functions. The family of empirical Johnson distributions is used to support the analysis objectives for the system parameters and response. Allocation of parameter variance and optimization of other statistical properties follow from calculations for the system response variance and PNC.
In the development and application of the Method of Moments approach, system models with independent, correlated, and non-normally distributed random variables are considered. Comparison with established Monte Carlo methods indicate that the developed statistical-analysis approach provides comparable results. The methods developed in this research provide an anal5d:ical alternative to conventional empirical statistical-analysis methods used for predicting the statistical properties of a system response.