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Fundamental Reliability Concepts

Fundamental Reliability Concepts. Reliability Measure. Mean time to failure ( MTTF ) for nonrepairable system; for repairable system mean time between failure ( MTBF ) Reliability (survival) function R(t) and Cdf F(t)=1-R(t) Mean residual life ( MRL )

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Fundamental Reliability Concepts

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  1. Fundamental Reliability Concepts

  2. Reliability Measure • Mean time to failure (MTTF) for nonrepairable system; for repairable system mean time between failure (MTBF) • Reliability (survival) function R(t) and Cdf F(t)=1-R(t) • Mean residual life (MRL) • Failure rate (hazard rate) function l(t)

  3. ABC Module MTTF v.s. MTBF • MTTF: • MTBF:

  4. 1 2 R(t) 1 Time t 0 Reliability Function and Cdf • Definition: Another way to look at it: let 2 is better than 1?

  5. Mean Residual Life - MRL • Definition: Consider an item is put into operation at time t=0 and is still functioning at time t. the probability that the item of age t survive an additional time period x is

  6. f(t) Time t 0 t t+Δt Meaning of Pdf • Probability density function of T is:

  7. F(t) f(t) t 0 Distribution of Failure Time • Area under pdf is 1. • Example – what “a” should be? • Area under pdf to the left of t is Cdf, • Area under pdf between t1 and t2 is

  8. Median and Mode Mode Median Mean f(t) t 0

  9. l (t) Time t 0 Failure Rate Function • Definition • Consider conditional probability

  10. Failure Rate Function • Increasing failure rate (IFR) v.s. decreasing failure rate (DFR) • Increasing failure rate average (IFRA) v.s. decreasing failure rate average (DFRA)

  11. 1 3 Constant Failure Rate Region 2 Early Life Region Wear-Out Region ABC Module Bathtub Curve (Big Smile) Failure Rate 0 Time t

  12. Example - Bearing

  13. 1 Early Life Region Related Topics (1) • Burn-in: • According to MIL-STD-883C, burn-in is a test performed to screen or eliminate marginal components with inherent defects or defects resulting from manufacturing process. Failure Rate 0 Time t

  14. Supplier 1 1 MTTF=5000 hours Supplier 2 2 Motivation - Old Example Revisit • Improve reliability using “cull eliminator”

  15. Use of Burn-in • One of environment stress screening (ESS) techniques • Example: given

  16. 3 Wear-Out Region Related Topics (2) • Maintenance: • An important assumption for effective maintenance is that component has an increasing hazard rate. • Why? Hazard Rate 0 Time t

  17. Important Relationships Each one of the functions is enough to determine others.

  18. Example 1 • Consider a component with

  19. Example 2 • Consider a component with

  20. Example 3 – Calculation Issue (for large sample) • Given n0 test units, test to fail

  21. Example 3 – Calculation Issue (for large sample) • Good rule of thumb for the number of classes – Sturges’ rule:

  22. Example 3 – Calculation Issue (for large sample) • Given n0 test units, test to fail

  23. Example 3 – Calculation Results • Calculation results

  24. Thank you for your visit Please direct your comments and questions to: Haitao.liao@wichita.edu

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