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Designing for System Reliability. Dave Loucks, P.E. Eaton Corporation. - PowerPoint PPT Presentation
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© 2002 Eaton Corporation. All rights reserved.
Designing for System Reliability
Dave Loucks, P.E.Eaton Corporation
“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
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.
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.
Designing for Reliability
Sound Design Proper Application of Parts (Components,
Systems) Understanding of Failure Mechanisms
What Reliability Is Seen At The Load?
Utility UPS Breaker Load
For example, if power flows to load as below: Assume outage duration exceeds battery capacity
Series Components
Utility UPS Breaker Load
99.9% 99.99% 99.99%
For example, if power flows to load as below: Assume outage duration exceeds battery capacity
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)
99.99%(0.87 hr/yr)
99.99%(0.87 hr/yr)
x+
x+
==
99.88%(10.5 hr/yr)
Overall reliability is poorer than any component reliability
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%
99.99%(0.87 hr/yr)
0.01%
99.99%(0.87 hr/yr)
0.01%
x++
x++
===
99.88%(10.5 hr/yr)
0.12%
PF = (1 – Reliability) = 1 – R(t)* PF = probability of failure
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%
99.99%(0.87 hr/yr)
0.01%
x++
===
99.98%(1.74 hr/yr)
0.02%*PF =
Batteries Depleted 99.88% reliable Batteries Not Depleted 99.98% reliable
Parallel Components What if power flows to load like this:
Assume outage duration exceeds battery capacity
Utility
UPS
StaticATS
Load
UPS
Parallel Components
Utility
UPS
StaticATS
Load
UPS99.9%
99.99%
99.99%
99.99%
?? %
What if power flows to load like this: Assume outage duration exceeds battery capacity
Parallel Components
Utility Load
99.9%
99.99%
99.99%
99.99%PF* = 0.1% PF(a or b)+ + = ?? %
?? %
UPS
StaticATS
UPS
0.01%
What if power flows to load like this: Assume outage duration exceeds battery capacity
Parallel Components
99.99%
99.99%PF(a or b) = 0.01 % x = 0.000001 %
99.99 %
UPSa
UPSb
0.01%
What if power flows to load like this: Solve each path independently
99.99%
99.99%
UPSa
UPSb
99.99 %
R(t) = 1 - PF(a or b) = 99.999999%
Parallel Components
Utility Load
99.9% 99.99%
99.999999%
99.89 %
UPSa
orUPSb
StaticATS
Multiply the two Probabilities of Failure, PF(a) and PF(b) and subtract from 1
PF(total) = PF(u) + PF(a or b) + PF(s)= 0.1% + 0.000001% + 0.01% = 0.110001%
Parallel Components
Load
99.99%
99.999999%
99.99 %
UPSa
orUPSb
StaticATS
Multiply the two Probabilities of Failure, PF(a) and PF(b) and subtract from 1
PF(total) = PF(a or b) + PF(s)= 0.000001% + 0.01% = 0.010001%
Summary Table
Configuration ReliabilitySingle UPS system (long term outage) 99.88%
Single UPS system (short term outage) 99.98%
Redundant UPS system (long term outage) 99.89%
Redundant UPS system (short term outage) 99.99%
Comments?
Value AnalysisIs going from this:
Utility UPS Breaker
Utility
UPS
StaticATS
99.89%(only battery) 99.99%
UPS
99.88%(only battery) 99.89%
to this
worth it?
0.01%difference
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?
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
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) – $30000
TEVD = $430120 – $30000 = $400120
Reliability Tools
Eaton Spreadsheet Tools IEEE PCIC Reliability Calculator Commercially Available Tools Financial Tools (web calculators)
Web Based Financial Analysis www.eatonelectrical.com search for “calculators” Choose “Life Extension
ROI Calculator”
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
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
Normal Distribution of Probabilities
From absolutely certain to absolutely impossible to everything in between
AbsolutelyCertain
100%
0%AbsolutelyImpossible
Most likely value
Distribution System Reliability How do you predict when something is going to
fail? One popular method uses exponential curve
AbsolutelyCertain
37% of them are working
50% of them are working
69%
50%
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:
368011
.)(
eeetRt
MTBFt
The ‘mean time’ between failures when 37% devices are still operating
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%
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.
Reliability versus MTBF
Assume at time = 0 Reliability equals 100% (you left it running)
At time > 0, Reliability is less than 100%
tMTBFt eetR
1
)(
Converting MTBF to Reliability
Unknown Reliability = ?
Known MTBF (40000 hrs) t (8760 hrs = 1 year)
tMTBFt eetR
1
)(
UPS
%.
)(
.
380
21908760
400001
1
ee
eetRt
MTBFt
Availability
Increase Mean Time Between Failures (MTBF) Decrease Mean Time To Repair (MTTR)
%100
MTTRMTBF
MTBFAi
i
i
AAMTBF
MTTR)(
100
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0 10 20 30 40 50 60 70 80 90 100
MTTR (Hours)
Avai
labi
lity
1000 hrs800 hrs600 hrs
400 hrs
200 hrs
MTBF
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0 10 20 30 40 50 60 70 80 90 100
MTTR (Hours)
Avai
labi
lity
1000 hrs800 hrs600 hrs
400 hrs
200 hrs
MTBF
10.5 21.1 31.6 42.1 52.6