Quantifying uncertainty in reliability block diagrams
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| Title: | Quantifying uncertainty in reliability block diagrams |
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| Authors: | Yu, Bea |
| Committee Members: | Wearing, Helen; Helen Wearing; James Auby Ellison; Curtis B. Storlie |
| Summary: | Reliability analysis yields statistically derived technical system performance estimates. Traditional reliability analysis employs classical statistical techniques predicated upon asymptotic properties of large data sets. Not uncommonly, however, medium to small data sets constrain analysis efforts for high risk systems characterized by significant danger or cost. This paper outlines a general reliability analysis paradigm to contend with small to medium data sets. Preliminary sensitivity analysis using scatter plots and tests for non-randomness reveals component-level drivers in system-level performance measures. Comprehensive data collection efforts targeting all available, high-quality information sources decrease and allow analysts to estimate uncertainty in model parameters describing driving component performance. Bayesian analysis accumulates these data into posterior distributions summarizing all available performance knowledge about driving components. Sampling-based uncertainty propagation methods then transform component-level posterior distributions into system-level parent and sampling distributions. Reliability metric point-estimates and credible intervals estimate the system reliability and benchmark the quality of the estimates, respectively. An operational reliability assessment of the B-2 Radar Modernization Program (B2-RMP) modernized radar system demonstrates the mechanics of the analysis paradigm applied to real data. Results from analysis including uncertainty explicitly modeled in all B-2 RMP components benchmark results from analysis including uncertainty modeled for driving components only. |
| URL: | https://digitalrepository.unm.edu/math_etds/56 |
| Database: | OpenDissertations |
| Abstract: | Reliability analysis yields statistically derived technical system performance estimates. Traditional reliability analysis employs classical statistical techniques predicated upon asymptotic properties of large data sets. Not uncommonly, however, medium to small data sets constrain analysis efforts for high risk systems characterized by significant danger or cost. This paper outlines a general reliability analysis paradigm to contend with small to medium data sets. Preliminary sensitivity analysis using scatter plots and tests for non-randomness reveals component-level drivers in system-level performance measures. Comprehensive data collection efforts targeting all available, high-quality information sources decrease and allow analysts to estimate uncertainty in model parameters describing driving component performance. Bayesian analysis accumulates these data into posterior distributions summarizing all available performance knowledge about driving components. Sampling-based uncertainty propagation methods then transform component-level posterior distributions into system-level parent and sampling distributions. Reliability metric point-estimates and credible intervals estimate the system reliability and benchmark the quality of the estimates, respectively. An operational reliability assessment of the B-2 Radar Modernization Program (B2-RMP) modernized radar system demonstrates the mechanics of the analysis paradigm applied to real data. Results from analysis including uncertainty explicitly modeled in all B-2 RMP components benchmark results from analysis including uncertainty modeled for driving components only. |
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