Introduction to Reliability of Mechanical Systems

03 5018

Syllabus

Lecture note sections to be covered (links to Lecture Notes below)

  • Robustness and Opportuneness, pp.3-9: statically loaded beam.
  • Robustness and Opportuneness, pp.10-11: Fourier expansion.
  • Robustness and Opportuneness, pp.12-14: geometry of ellipsoids.
  • Robustness and Opportuneness, pp.15-17: statically loaded beam.
  • Robustness and Opportuneness, pp.27-36: vibrating cantilever.
  • Performance vs Robustness of a Cantilever.
  • Two coupled harmonic oscillator example.
  • Heat conduction example.
  • Probabilistic failure models. Time to failure, reliability, MTTF.
  • Probabilistic failure models. Poisson process, exponential and gamma distributions.
  • Probabilistic failure models. Serial and parallel systems.
  • Probabilistic failure models. Pareto distribution.
  • Probabilistic failure models. Weibull, normal, log-normal distributions.
  • Probabilistic failure models. Probabilistic reliability with info-gap uncertainty.
  • Acceptance testing. Thickness measurement.
  • Acceptance testing. Sequential sample.
  • Acceptance testing. Matching 2 dimensions.
  • Acceptance testing. Engine warming.
  • Acceptance testing. Failure rate and chi-square.
  • Acceptance testing. Chi-square test of independence.
  • Acceptance testing. Acceptance sample in large population.
  • Acceptance testing. Sample size for detecting change.
  • Acceptance testing. Tests of the mean.  (through section 9.3).
  • Acceptance testing. Accelerated lifetime testing.

Lecture Notes

Lecture Notes on Performance vs. Robustness of a Cantilever

Lecture Notes on Info-gap Uncertainty

Lecture notes on robustness and opportuneness

Fourier expansion, example

Geometry of ellipsoids, example

Two coupled harmonic oscillator example

Heat conduction example

Lecture notes on probabilistic failure models

Lecture notes on acceptance testing

Lecture notes on censoring and estimation in statistical sampling

Homework

99 problems on Info-Gap Robustness and Opportuneness

12 problems on Acceptance Tests

15 problems on Probabilistic Failure Models

Homework #1: Info-gap robustness and opportuneness, problem 63 a, b. Discussed 3.4.2019.

Homework #2: Info-gap robustness and opportuneness, problem 64 a-c. Discussed 10.4.2019.

Homework #3: Info-gap robustness and opportuneness, problem 66 a-e. Discussed 17.4.2019.

Homework #4: Info-gap robustness and opportuneness, problem 4 a-d. Discussed 1.5.2019.

Homework #5: Info-gap robustness and opportuneness, problem 15 a, b. Discussed 13.5.2019.

Homework #6: Probabilistic Failure Models, problems 1-4. To be discussed 29.5.2019.

Homework #7: Probabilistic Failure Models, problems 10, 13. To be discussed 5.6.2019.

Homework #8: Probabilistic Failure Models, problems 7, 14. Discussed 12.6.2019.

Homework #9: Acceptance Tests, problems 1, 4. Discussed 19.6.2019.

Homework #10: Acceptance Tests, problems 6, 7.