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# A Method to Calculate Function and Component Failure Distributions Using a Hierarchical Bayesian Model and Frequency Weighting

[+] Author Affiliations
Bryan M. O’Halloran, Chris Hoyle, Robert B. Stone, Irem Y. Tumer

Oregon State University, Corvallis, OR

Paper No. DETC2012-71003, pp. 727-736; 10 pages
doi:10.1115/DETC2012-71003
From:
• ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
• Volume 7: 9th International Conference on Design Education; 24th International Conference on Design Theory and Methodology
• Chicago, Illinois, USA, August 12–15, 2012
• Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
• ISBN: 978-0-7918-4506-6

## abstract

This paper presents a method to calculate function and component parameter distributions during the design process. Frequency Weighting, a unique style of weighting proposed in this research, is applied to a Hierarchical Bayesian model to account for the number of times a component has solved a function. During the design process, functions are systematically solved by components to transition from a functional model to a physical design. This research contributes to an ongoing effort toward predicting reliability in early design, specifically during functional modeling and concept generation. In general, reliability prediction methods are applied after concept generation. There currently does not exist a statistical method to calculate functional failure rates to aid reliability prediction during and before concept generation. The method presented in this paper also captures uncertainty in the early stages of design. This is important because uncertainty in this stage of the design process can be significant. A description of the process used to calculate the function and component level failure rate distributions is presented. The level of detail provided is meant for reapplication to other examples. Three examples are worked out and graphical results are presented. These results show an effect of the Frequency Weighting on the function level distribution. Changing the occurrence vector, which is used to show the number of times a set of components has solved a function, from (1, 1, 1, 1) to (1, 1, 2, 5) results in the function level distribution mean value shifting from 5.53E−06 to 4.84E−06. In addition, an example is provided to demonstrate how this method can be applied while components are being selected during the design process. A two part reliability goal is generated for the combined failure rate of the design and the probability a design will meet that goal. Function level distributions are used to show which components should initially be selected to maintain reliability values that meet the reliability goal. Combinations of compatible component level distributions are also used to calculate a combined failure rate distribution for each design. A probability is calculated for each distribution to show which designs meet the probability portion of the reliability goal.

Topics: Failure

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