USACE Asset Management Risk and Reliability Workshop

Using CI Ratings as an Estimate of Failure

Probability

Allen C. EstesUnited States Military Academy

• Strength-based reliability–Miter gate example

• Serviceability-based reliability–Spillway gate system example

• Strengths and limitations

AgendaAgenda

• Probabilistic Approach to Design and Analysis

• Corps of Engineers requires for major rehabilitation projects

• Used for life-cycle analysis– Probability of failure– Deterioration model– Hazard functions

• Reliability requires lots of data

Reliability MethodsReliability Methods

Strength-Based ReliabilityStrength-Based ReliabilityMiter Gate: Lock and Dam #12Miter Gate: Lock and Dam #12

MomentDiagram

Upper PoolElevation

Low er PoolElevation

VerticalGirder

M m ax

Hydrostatic Forces on Vertical GirderHydrostatic Forces on Vertical Girder

Reliability of Miter Gate on Lock 12Reliability of Miter Gate on Lock 12

Actual Stress

)( 2

max

dAII

A

Ayy

IkyM

NANA

NA

NAsNAactual

Yield Stress]48.3,8.34[Ny

Reliability yactual Pr

As time passes and corrosion ensues

0

0.01

0.02

0.03

0.04

0.05

0.06

140 160 180 200 220 240 260

Pro

bab

ility

Den

sity

Dis

trib

uti

on

S tress (MPa)

Yield StressActual Stress

Year 0

Actual StressYear 20

Actual StressYear 40

Deterioration Model

Atmospheric Zone

ctC log65.04.23loglog

ctC log903.05.148loglog

Splash Zone

C = Thickness loss due to corrosion (micrometers)

t = time (years)

c = uncertainty factor ( mean = 0; Std. Deviation 0.099/0.219)

Level Description

0 New

1 Minor surface scale

2 Moderate pitting

3 Severe pitting

4 Obvious thickness reduction

5 Holes due to thickness reduction 5

Condition Index Description: CorrosionCondition Index Description: Corrosion

Condition State GuidesCondition State Guides

Can I use this to update reliability?

NO

Well, what would it take?

•Quantify the condition levels

•Segment-based inspection

Corrosion Levels Quantified

Level Description Thickness Loss (m)

0 New 0

1 Minor surface scale 0-200

2 Moderate pitting 0-500

3 Severe pitting 0-1000

4 Obvious thickness reduction 1000-3000

5 Holes due to thickness reduction >3000 5

Corrosion Levels QuantifiedCorrosion Levels Quantified

Corrosion Condition State DistributionsCorrosion Condition State Distributions

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 500 1000 1500 2000 2500 3000 3500 4000

Change in Bar Diameter (micrometers)

Pro

ba

bil

ity

De

ns

ity

CS1: LN [100, 51]

CS2: LN [250, 128]

CS3: LN [500, 255]

CS4: N[2000, 510]

CS5: N[4500, 1531]

Thickness Loss Due to Corrosion (micrometers)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

1930 1950 1970 1990 2010 2030

Th

ickn

ess

Lo

ss (

mic

rom

eter

s)

Year

Level 5Level 0 Level 4

Level 2Level 1

Level 1 Level 2 Level 3

AtmosphericCorrosion

Splash ZoneCorrosion

Projected Condition State Deterioration

0

1000

2000

3000

4000

5000

6000

7000

8000

1940 1950 1960 1970 1980 1990 2000 2010 2020 2030

tim e (year)

thic

kne

ss lo

ss (

C)

in m

icro

me

ters

C =148.5 t0.903

C =10.23t0.903

C =4.22t1.13

1998 2008C ond ition Index Inspection :

Revised Splash Zone Corrosion ModelRevised Splash Zone Corrosion Model

CI Limitations

• Not designed to accommodate reliability• Based on subjective judgment of inspector• Not enough information to quantify in

probabilistic terms• CI rating based on condition of the worst

element• Not conducted regularly -- no knowledge of

condition state transition

Strength-BasedConclusions

• Visual inspection information can be used to update reliability analyses– in some cases– with some modification

• Case studies show– Works well for external corrosion– Moderately well for internal corrosion– Poorly for fatigue

• Potential exists to use visual inspection data to update deterioration on many structures

• People who design visual inspections and the people who use the data need to talk

• The information is already there – we should use it

• Serviceability issues typically drive repair and rehabilitation decisions

• Periodic inspection results are best measure of overall structural condition– The Corps has developed condition index rating systems

for many structures– Condition index ratings are deterministic, have lots of

variables, and are tough to quantify– AND, they currently have no data

• Can we use the condition index ratings to quantify the risk to a structure for purposes of repair and replacement?

Serviceability-BasedServiceability-BasedReliabilityReliability

Spillway Gates on DamsSpillway Gates on Dams

Level 2:Dam SafetyFunctions

Level 3:Type of

Gate

Level 4:Operational

Systems andEquipment

Level 5:Systems

Level 6:Sub-systems

Level 7:Components

Operations

Equipment

Gatherinfor-

mation

DecisionProcess

Access &Operation

Electrical

Hoist/Gate

System

PowerSupply

Cables &Controls

OvertopDesignFlood

SupportStructure

.30

.70

.40

.60

.35

.55

.10

.60

.40

Hoist/Gate Sub-

systemHoist

Gate

.95

.05

a

b

c

d

e

g

h

f

Great Falls DamGreat Falls Dam

Level 6:Sub-systems

Level 7:Components

Cables &Controlse

Support.Structuref

PowerSupplyd

Freq. &Voltage

EngineTemp/OilPressure

StartingSequence

Insulation

C.25

C.24

Noise &Vibration

Funct.Test

Fuel

Termin-ations

Batteries

BatteryCharger

Alternator

LocalEmergen.Generator

Dielectric

Insulation Tank

Windings

Lubri-cation

CoolingSystem

Intake &ExhaustSystem

Insulation

Termin-ations

Test(TransferSwitch)

Test(ManualSwitch)

Under-groundCables

PowerFeederCables

Trans-former

PowerTransferSystem

LiftingDevice(Steel)

LiftingDevice(Conc.)

Cracks

Distortion

Disp./Deter-ioration

AnchorBolts

Corrosion

Missing/LooseParts

C.61

C.64

C.27

C.26

C.25

.08

.08

.08

.08

.08

.08

.08.08

.08

.08.08

.08

1.0

.25 .25

.25.25

.25

.25

.25

.25

.50

.50

.50

.50

.50

.50

.50

.50

.17.17.17

.17.17.17

Great Falls DamGreat Falls Dam

Hoist Brake Function To arrest motion of gate and hold gate in any position Excellent Can arrest motion at any position, not seized Failed Cannot arrest motion at any position, seizing of brake Indicator 0-9 10-24 25-39 40-54 55-69 70-84 85-100 Score Comments Can arrest motion at any position, not seized

x

Limited slippage without impacting operation; no slip but vibration

x x x

Limited slippage that impacts operation

x x

Continuous slippage, seizing of brake

x

Typical Component Condition TableTypical Component Condition Table

Serviceability: Condition Index

CI Value Condition Description Zone Action85-100 Excellent; no noticeable defects

1Immediate Action not required

70-84 Very good: minor deterioration only

55-69 Good: some deterioration or defects evident

2

Economic analysis of repair alternatives recommended40-54 Fair: moderate deterioration;

function still adequate

25-39 Poor: serious deterioration; function inadequate

3

Detailed evaluation required to determine need for repair, rehabilitation or reconstruction

10-24 Very Poor: extensive deterioration, barely functional

0-10 Failed: no longer functional

• Risk is product of Probability of Failure and Consequences

• Condition Index is the random variable• Random variable assumptions

– Normally distributed– Independent

• Probability of failure (repair/replacement action)

• Structural systems are a function of– Component condition– Component importance

General ApproachGeneral Approach

)( failureactualf CICIPP

• Initially enter a condition state at the mean value• Inspector correctly identifies condition 95% of the time• Inspector error is equally distributed between high and low• Failure is defined as mean CI = 25; = 12.75

– 0 – 40 is failure range in description– 88 % of failures occur in that range; 10 % in 40 – 50 range– Values will improve with a database established

• Linear transition through condition states based on expected life of structure

• If expected life is exceeded, mean CI remains at lowest value in the condition state

General AssumptionsGeneral Assumptions

Condition Index Assumptions Condition Index Assumptions

Condition Index

Pro

ba

bil

ity

De

ns

ity

InitialMean CI

SmallestMean CI

Range of Condition State

Mean valueshifts over

time

Inspectorerror too high

2 ½%

Inspectorerror too low

2 ½%

Serviceability: Condition Index

CI Value Condition Description Zone Action85-100 Excellent; no noticeable defects

1Immediate Action not required

70-84 Very good: minor deterioration only

55-69 Good: some deterioration or defects evident

2

Economic analysis of repair alternatives recommended40-54 Fair: moderate deterioration;

function still adequate

25-39 Poor: serious deterioration; function inadequate

3

Detailed evaluation required to determine need for repair, rehabilitation or reconstruction

10-24 Very Poor: extensive deterioration, barely functional

0-10 Failed: no longer functional

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Condition Index

Pro

ba

bil

ity

De

ns

ity

CI =0 to 9

CI =25 to 39

CI =10 to 24

CI >55

CI =40 to 54

11.5%0.8%

10.7%

38.5%38.5%

Quantification of FailureQuantification of Failure

= 25

= 12.75

4.5174785

MeanValue

2.293.57

11.227.65

StandardDeviation

x4x3

xxx2xx1

85 - 10070-8455-6940-5425-3910-240-9

Condition Index ScoreCondition

State

Medium Voltage Overhead Wires

4.5174785

MeanValue

2.293.57

11.227.65

StandardDeviation

x4x3

xxx2xx1

85 - 10070-8455-6940-5425-3910-240-9

Condition Index ScoreCondition

State

Medium Voltage Overhead Wires

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 10 20 30 40 50 60 70 80 90 100

Condition Index

Pro

ba

bil

ity

De

ns

ity

CS 1Mean = 85 = 7.65

CS 2Mean = 47 = 11.22

CS 3Mean = 17 = 3.57

CS4Mean = 4.5 = 2.29

FailureMean = 25 = 12.5

Medium VoltageOverhead Lines

Ideal ComponentIdeal Component

Ideal Component

ConditionState

Condition Index Score MeanValue

StandardDeviation0-9 10-24 25-39 40-54 55-69 70-84 85 - 100

1 x 92.5 3.82

2 x 77 3.57

3 x 62 3.57

4 x 47 3.57

5 x 32 3.57

6 x 17 3.57

7 x 4.5 2.29

Ideal ComponentIdeal Component

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 10 20 30 40 50 60 70 80 90 100

Condition Index

Pro

ba

bil

ity

De

ns

ity

Component B

FailureMean = 25 = 12.75

CS 1Mean = 92.5

= 3.82

CS 2Mean = 77 = 3.57

CS 3Mean = 62 = 3.57

CS 4Mean = 47 = 3.57

CS 5Mean =32 = 3.57

CS 6Mean = 17 = 3.57

CS 7Mean = 47 = 2.29

Ideal Component

System Condition Index System Condition Index

BBAAj

n

jjStructure CIICIICIICI

1

Mean Value (Chouinard et.al. 2003) Eqn [4.5]

Standard Deviation

2222

1

22BBAA

n

jjjCI III

Structure

Standard Reliability ReferenceItem Number Importance Mean CI Deviation Index TableLevel 7: ComponentsPower Supply 86.25 2.07 4.74 Local or Emergency Generators 7d 1.00 86.25 2.07 4.74 C.25 Frequency and Voltage 7d.1 0.08 85.00 7.65 4.03 Engine Temperature / Oil Pressure7d.2 0.08 85.00 7.65 4.03 Starting Sequence 7d.3 0.08 85.00 7.65 4.03 Noise and Vibratiion 7d.4 0.08 85.00 7.65 4.03 Functional Test 7d.5 0.08 92.50 3.83 5.07 Fuel 7d.6 0.08 92.50 3.83 5.07 Batteries 7d.7 0.08 85.00 7.65 4.03 Battery Charger 7d.8 0.08 85.00 7.65 4.03 Alternator 7d.9 0.08 85.00 7.65 4.03 Lubrication 7d.10 0.08 85.00 7.65 4.03 Cooling System 7d.11 0.08 85.00 7.65 4.03 Intake and Exhaust System 7d.12 0.08 85.00 7.65 4.03

Cables and Controls 7e 87.94 2.57 4.84 Underground and Encased Cables 7e.1 0.25 85.00 5.41 4.33 C.24 Insulation 7e.1.1 0.50 85.00 7.65 4.03 Terminators 7e.1.2 0.50 85.00 7.65 4.03 Power Feeder Cables 7e.2 0.25 85.00 5.41 4.33 C.25 Insulation 7e.2.1 0.50 85.00 7.65 4.03 Terminators 7e.2.2 0.50 85.00 7.65 4.03 Transformer 7e.3 0.25 89.25 5.69 4.60 C.26 Dielectric 7e.3.1 0.00 N/A N/A N/A Insulation 7e.3.2 0.50 85.00 7.65 4.03 Windings 7e.3.3 0.55 85.00 7.65 4.03 Tank 7e.3.4 0.00 N/A N/A N/A Power Source Transfer System 7e.4 0.25 92.50 3.83 5.07 C.27 Test (Transfer Switch) 7e.4.1 0.00 N/A N/A N/A Test (Manual Transfer Device) 7e.4.2 1.00 92.50 3.83 5.07

Supporting Structure 6e 92.50 2.07 5.22 Lifting Device Structure (Steel) 7f.1 0.50 92.50 1.56 5.25 C.64 Displacement / Deterioration 7f.1.1 0.17 92.50 3.83 5.07 Anchor Bolts 7f.1.2 0.17 92.50 3.83 5.07 Cracks 7f.1.3 0.17 92.50 3.83 5.07 Distortion 7f.1.4 0.17 92.50 3.83 5.07 Corrosion 7f.1.5 0.17 92.50 3.83 5.07 Missing or Loose Parts 7f.1.6 0.17 92.50 3.83 5.07 Lifting Device Structure (Concrete) 7f.2 0.50 92.50 3.83 5.07 C.61

Derived from a Combination of Inspected Items

Directly Measured by Inspection

• Based on the assumptions, a risk-based approach is possible• Structure is described in visible hierarchical format; easy to

include/exclude variables• Inspector is only required to choose the condition state• Range and inspector uncertainty is quantified• Linear transition accounts for effects of aging• Normal, independent assumptions make computations easy• Methodology can be applied to any structure• Any relevant variable can be included• Wrong assumptions are corrected as data becomes available• System CIs provide effective means of comparison between

entire structures

Conclusions: StrengthsConclusions: Strengths

• Not based on any real data; assumptions have not been verified

• System CI proposal is controversial; violates rules of traditional reliability

• Linear transition across condition states needs further analysis

• Not a replacement for a traditional reliability analysis

• Need a red flag provision for component CI scores lower than CI = 40

Conclusions: LimitationsConclusions: Limitations

• Apply methodology to a single class of structures to– develop procedural modifications – verify assumptions – time dependence on real structure – compare with cost-benefit from traditional reliability

• Investigate for other types of structures (i.e., bridges, buildings)

• Corps of Engineers needs to commit to CI inspections– Mandatory for all USACE districts– Centralized consolidation of data– Publish deterioration rates

RecommendationsRecommendations

USACE Asset Management Risk and Reliability Workshop

Using CI Ratings as an Estimate of Failure

Probability

Allen C. EstesUnited States Military Academy

Questions?