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Designing for System Reliability

Designing for System Reliability. Dave Loucks, P.E. Eaton Corporation.

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Designing for System Reliability

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  1. Designing for System Reliability Dave Loucks, P.E. Eaton Corporation

  2. “Reliability is achieved through sound design, the proper application of parts, and an understanding of failure mechanisms. It is not achieved by estimating it or calculating it. Estimation and calculation are, however necessary to help determine feasibility, assess progress and provide failure probabilities and frequencies to spares calculations and other analyses.” US Army TM 5-698-1 B-1

  3. Reliability ABCs Gold Book (IEEE Std. 493-1997) • Annual Risk - The calculated financial losses of production due to an electrical system failure divided by the frequency (MTBF) of the failure. • Availability - A ratio that describes the percentage of time a component or system can perform its function. • Failure - The termination of the ability of an item to perform a required function. • Failure rate - The mean number of failures of a component per unit exposure time.

  4. Reliability ABCs cont’d • Forced downtime - The average time per year a system is unavailable in between failures and expressed in hours per year. • Lambda - Failure Rate () - The inverse of the mean exposure time between consecutive failures. Lambda is typically in either years per failure or millions of hours per failure. • MTBF - The mean exposure time between consecutive failures of a component or system in either failures per year or failures per million hours. For some applications measurement of mean time between repairs (MTBR) rather than mean time between failures may provide more statistically correct information.

  5. Designing for Reliability • Sound Design • Proper Application of Parts (Components, Systems) • Understanding of Failure Mechanisms

  6. What Reliability Is Seen At The Load? • For example, if power flows to load as below: • Assume outage duration exceeds battery capacity Utility UPS Breaker Load

  7. Series Components • For example, if power flows to load as below: • Assume outage duration exceeds battery capacity Utility UPS Breaker Load 99.9% 99.99% 99.99%

  8. Series Components • For example, if power flows to load as below: • Assume outage duration exceeds battery capacity Utility UPS Breaker Load 99.9% (8.7 hr/yr) x + 99.99% (0.87 hr/yr) x + 99.99% (0.87 hr/yr) = = 99.88% (10.5 hr/yr) • Overall reliability is poorer than any component reliability

  9. Series Components • For example, if power flows to load as below: • Assume outage duration exceeds battery capacity Utility UPS Breaker Load 99.9% (8.7 hr/yr) PF* = 0.1% x + + 99.99% (0.87 hr/yr) 0.01% x + + 99.99% (0.87 hr/yr) 0.01% = = = 99.88% (10.5 hr/yr) 0.12% * PF = probability of failure • PF = (1 – Reliability) = 1 – R(t)

  10. Series Components • For example, if power flows to load as below: • If outage duration less than battery capacity UPS Breaker Load 99.99% (0.87 hr/yr) 0.01% x + + 99.99% (0.87 hr/yr) 0.01% = = = 99.98% (1.74 hr/yr) 0.02%* PF = • Batteries Depleted  99.88% reliable • Batteries Not Depleted  99.98% reliable

  11. Parallel Components • What if power flows to load like this: • Assume outage duration exceeds battery capacity UPS Utility Static ATS Load UPS

  12. Parallel Components • What if power flows to load like this: • Assume outage duration exceeds battery capacity UPS Utility 99.99% Static ATS Load 99.9% UPS 99.99% ?? % 99.99%

  13. Parallel Components • What if power flows to load like this: • Assume outage duration exceeds battery capacity UPS Utility 99.99% Static ATS Load 99.9% UPS 99.99% ?? % 99.99% PF* = 0.1% + PF(a or b) + 0.01% = ?? %

  14. Parallel Components • What if power flows to load like this: • Solve each path independently UPSa UPSa 99.99% 99.99% 99.99 % 99.99 % UPSb UPSb 99.99% 99.99% PF(a or b) = 0.01 % x 0.01% = 0.000001 % R(t) = 1 - PF(a or b) = 99.999999%

  15. Parallel Components • Multiply the two Probabilities of Failure, PF(a) and PF(b) and subtract from 1 UPSa or UPSb Utility Static ATS Load 99.9% 99.99% 99.89 % 99.999999% PF(total) = PF(u) + PF(a or b) + PF(s) = 0.1% + 0.000001% + 0.01% = 0.110001%

  16. Parallel Components • Multiply the two Probabilities of Failure, PF(a) and PF(b) and subtract from 1 UPSa or UPSb Static ATS Load 99.99% 99.99 % 99.999999% PF(total) = PF(a or b) + PF(s) = 0.000001% + 0.01% = 0.010001%

  17. Summary Table Comments?

  18. Value Analysis Is going from this: Utility UPS Breaker 99.88% (only battery) 99.89% to this 0.01% difference UPS Utility Static ATS 99.89% (only battery) 99.99% UPS worth it?

  19. Value Analysis • 99.98% x 8760 = 8752 hours on and 8 hours off • 99.99% x 8760 = 8759 hours on and 1 hour off • With the second solution you are on 7 more hours per year • What is 7 hours worth? • What is the second UPS worth?

  20. Breakeven Analysis • Total Economic Value (TEV) • Simple Return (no time value of money) • TEVS = (Annual Value of Solution x Years of Life of Solution) – Cost of Solution • Assume 1 hour of downtime worth $10000 • Assume cost of solution is $30000 • Assume life of solution is 10 years

  21. Breakeven Analysis • Total Economic Value (TEV) • Simple Return (no time value of money) • TEVS = (Annual Value of Solution x Years of Life of Solution) – Cost of SolutionTEVS = (($10000 x 7) x 10) – $30000TEVS = $700000 - $30000 = $670000 Discounting cash flow at 10% cost of money • TEVD = NPV($70000/yr, 10 yrs) – $30000TEVD = $430120 – $30000 = $400120

  22. Reliability Tools • Eaton Spreadsheet Tools • IEEE PCIC Reliability Calculator • Commercially Available Tools • Financial Tools (web calculators)

  23. www.eatonelectrical.com search for “calculators” Choose “Life Extension ROI Calculator” Web Based Financial Analysis

  24. Web Based Financial Analysis • Report provides financial data • Provides Internal Rate of Return • Use this to compare with other projects competing for same funds • Evaluates effects due to taxes, depreciation • Based on IEEE Gold Book data

  25. Uncertainty – Heart of Probability • Probability had origins in gambling • What are the odds that … • We defined mathematics resulted based on: • Events • What are the possible outcomes? • Probability • In the long run, what is the relative frequency that an event will occur? • “Random” events have an underlying probability function

  26. Normal Distribution of Probabilities Absolutely Certain 100% • From absolutely certain to absolutely impossible to everything in between Most likely value Absolutely Impossible 0%

  27. Distribution System Reliability • How do you predict when something is going to fail? • One popular method uses exponential curve Absolutely Certain 50% of them are working 50% 37% of them are working 69%

  28. Mean Time Between Failures • The ‘mean time’ is not the 50-50 point (1/2 are working, 1/2 are not), rather… • When device life (t) equals MTBF (1/), then: • The ‘mean time’ between failures when 37% devices are still operating

  29. MTBF Review • Remember, MTBF doesn’t say that when the operating time equals the MTBF that 50% of the devices will still be operating, nor does it say that 0% of the devices will still be operating. It says 37% (e-1) of them will still be working. • Said another way; when present time of operation equals the mean (1/2 maximum life), the reliability is 37%

  30. Exponential Probability • Assumes  (1/MTBF) is constant with age • For components that are not refurbished, we know that isn’t true. • Reliability decreases with age ( gets bigger) • However, for systems made up of many parts of varying ages and varying stages of refurbishment, exponential probability math works well.

  31. Reliability versus MTBF • Assume at time = 0 • Reliability equals 100% (you left it running) • At time > 0, • Reliability is less than 100%

  32. Converting MTBF to Reliability • Unknown • Reliability = ? • Known • MTBF (40000 hrs) • t (8760 hrs = 1 year) UPS

  33. Availability • Increase Mean Time Between Failures (MTBF) • Decrease Mean Time To Repair (MTTR)

  34. MTBF 1000 hrs 800 hrs 600 hrs 400 hrs 200 hrs

  35. MTBF 1000 hrs 800 hrs 600 hrs 400 hrs 10.5 21.1 31.6 42.1 52.6 200 hrs

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