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Fuzzy Statistical Interpretation of Linear Dynamic System Reliability

Salehi, Hojat Allah | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44234 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Sadati, Nasser
  7. Abstract:
  8. Reliability analysis in engineering systems is one of important parts in design stage. Stress-Strength method is a method for reliability analysis in engineering systems. To obtain reliability, stress and strength distribution functions should be known, but these functions depend on design parameters and mostly these parameters are unknown. Usually obtaining exact stress and strength distributions is difficult and there is some uncertainty in distribution functions and their parameters. Also, weakness and uncertainty in data makes it difficult to calculate exact stress and strength distributions. In the case, when data is weak, results in point estimation methods (for example Maximum Likelihood) has lots of errors and as a consequence of this imprecision can the system is harmful. Bayesian method is used to solve this problem. In this approach, unknown parameters are treated as random variables and a prior distribution is considered for these parameters. In this research, Dempster-Shafer (D-S) theory as a generalization of Bayesian theorem is used to calculate a bound for reliability. In this thesis, instead of calculating a deterministic number for reliability, an interval is calculated and the true value of reliability is somewhere in this interval. Local perturbation method is used to express engineer doubt on distribution parameters of Bayesian prior distribution and upper and lower marginal distribution on D-S method. One problem in local perturbation is that; mass is assigned with same confidence to all intervals. Fuzzy theorem is used to solve this problem by attaching a membership function to interval and reliability is then calculated as a fuzzy number. Finally, the method is implemented on a set of real data and results are discussed
  9. Keywords:
  10. Reliability ; Dempster-Shafer Theory ; Bayesian Method ; Nonlinear Dynamical System ; Stress-Strength Model ; Local Perturbation

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