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Fundamental Reliability Concepts

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This guide explores fundamental reliability concepts such as Mean Time to Failure (MTTF) for non-repairable systems and Mean Time Between Failures (MTBF) for repairable systems. It delves into the reliability function R(t), the cumulative distribution function F(t), and the mean residual life (MRL). Additionally, it discusses hazard rates, probability density functions, and the bathtub curve, along with real-world applications like burn-in methods and maintenance strategies. Enhance your understanding of these critical reliability metrics and their implications for engineering and manufacturing.

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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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