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Designing mechanical systems for optimum diagnosability

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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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Fig. 2


  1. 1.

    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.

  2. 2.

    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.

  3. 3.

    Removing a failed component is justified. Removing a working component is unjustified.

  4. 4.

    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.


  1. Bahr NJ (1997) System safety engineering and risk assessment: a practical approach. Taylor & Francis, Washington, DC

  2. Clark GE, Paasch RK (1996) Diagnostic modeling and diagnosability evaluation of mechanical systems. J Mech Des 118(3):425–431

  3. Eubanks CF, Steven K, Kosuke I (1996) System behavior modeling as a basis for advanced failure modes and effects analysis. In: Proceedings of the 1996 ASME computers in engineering conference

  4. Eubanks CF, Steven K, Kosuke I (1997) Advanced failure modes and effects analysis using behavior modeling. In: Proceedings of the 1997 ASME design theory and methodology conference

  5. Fitzpatrick M, Paasch R (1999) Analytical method for the prediction of reliability and maintainability based life-cycle labor costs. J Mech Des 121(4):606–613

  6. Heckerman D, John SB, Koos R (1994) Troubleshooting under uncertainty,” technical report MSR-TR-94-7, Microsoft Research, September 1994

  7. Henning S, Robert P (2000) “Distinguishability analysis for fault isolation in mechanical systems. Proceedings of the 2000 ASME design theory and methodology conference, Baltimore, MD

  8. Kmenta S, Kosuke I (1998) Advanced FMEA using meta behavior modeling for concurrent design of products and controls. In: Proceedings of the 1998 ASME design engineering technical conferences

  9. Kościelny JM, Michał B, Paweł R, Jose Sá da C (2006) Actuator fault distinguishability study for the DAMADICS benchmark problem. Control Eng Pract 14(6):645–652

  10. Kurki M (1995) Model-Based fault isolation diagnosis for mechatronic systems. Technical Research Centre of Finland, Espoo

  11. Leitch RD (1995) Reliability analysis for engineers: an introduction. Oxford University Press, Oxford

  12. Murphy MD, Paasch RK (1997) Reliability centered prediction technique for diagnostic modeling and improvement. Res Eng Des 9(1):35–45

  13. Ruff DN, Paasch RK (1997) Evaluation of failure diagnosis in conceptual design of mechanical systems. J Mech Des 119(1):57–64

  14. Sen S et al (1996) Simulation-based testability analysis and fault diagnosis. In: Proceedings of the AUTOTESTCON’96 conference, pp 136–148

  15. Simpson WR, Sheppard JW (1994) System test and diagnosis. Kluwer, Boston

  16. Stone RB, Tumer IY, Wie MV (2005) The function-failure design method. J Mech Des 127(3):397–407

  17. Trave-Massuyes L, Escobet T, Olive X (2006) Diagnosability analysis based on component-supported analytical redundancy relations. IEEE Trans Syst Man Cybern Part A Syst Hum 36(6):1146–1160

  18. Wong B (1994) Diagnosability analysis for mechanical systems and human factors in diagnosability, M.S. thesis, Department of Mechanical Engineering, Oregon State University, Corvallis, Oregon

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Author information

Correspondence to Robert Paasch.

Appendix: matrix and metric computations

Appendix: matrix and metric computations

See Table 8.

Table 8 Component-indication failure rate matrix for example problem

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Henning, S., Paasch, R. Designing mechanical systems for optimum diagnosability. Res Eng Design 21, 113–122 (2010).

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  • Failure Rate
  • Failure Probability
  • Fault Tree
  • Diagnosability Model
  • Fault Isolation