An analysis and modeling method of the diagnostic characteristics for electro-mechanical systems is presented. Diagnosability analysis is especially relevant given the complexities and functional interdependencies of modern-day systems, since improvements in diagnosability can lead to a reduction of a system’s life-cycle costs. Failure and diagnostic analysis leads to system diagnosability modeling with the failure modes and effects analysis (FMEA) and component-indication relationship analysis. Methods are then developed for translating the diagnosability model into mathematical methods for computing metrics such as distinguishability and No Fault Found. These methods involve the use of matrices to represent the failure and replacement characteristics of the system. Diagnosability metrics are extracted by matrix multiplication. These metrics are useful when comparing the diagnosability of proposed designs or predicting the life-cycle costs of fault isolation.
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Family genealogy, which can be analyzed both bottom-up and top–down in “tree” diagrams, is a good analogy to FMEA and the fault tree. A bottom-up family tree will identify parents, grandparents, and great-grandparents, while a top–down family tree will identify brothers and sisters, aunts and uncles, and cousins. Together, like the FMEA and FTA, the two family models present a complete understanding of all family relationships.
Note that this is a different definition of distinguishability from Clark (1996). While it remains a similar system measure, this new D is specifically a probability of removal rather than an arbitrary index value.
Removing a failed component is justified. Removing a working component is unjustified.
Conditional probability of event A given that event B has occurred: P(A|B) = P(A∩B)/P(B). If P(B) = 0, then P(A|B) is defined as zero.
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Appendix: matrix and metric computations
Appendix: matrix and metric computations
See Table 8.
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Henning, S., Paasch, R. Designing mechanical systems for optimum diagnosability. Res Eng Design 21, 113–122 (2010). https://doi.org/10.1007/s00163-009-0078-1
- Failure Rate
- Failure Probability
- Fault Tree
- Diagnosability Model
- Fault Isolation