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Inspection Decisions including Condition-Based Maintenance
Andrew K S JardineCBM Laboratory
Department of Mechanical & Industrial EngineeringUniversity of Toronto
August 2006
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“Inspection Decisions including Condition-Based Maintenance”
Reliability Improvement through Inspection Decisions
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“Inspection Decisions including Condition-Based Maintenance”
Inspection Problems
1. Inspection frequencies for equipment which is in continuous operation and subject to breakdown.
2. Inspection intervals for equipment used only in emergency conditions. (Failure finding intervals)
3. Condition monitoring of equipment: Optimizing condition-based maintenance decisions.
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“Inspection Decisions including Condition-Based Maintenance”
System Failures
Inspections &Minor Maintenance
Decreasing system failures
Increasing inspection frequency
Component 2
Component 1
Component 5
Component 3
Component 4
Inspection Problems
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“Inspection Decisions including Condition-Based Maintenance”
MTTF(0)
System failure distribution when no inspections occur
System failure distribution when 2 inspections/unit time occur
f(t)
t
Inspection Frequency versus MTTF
MTTF(2)
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“Inspection Decisions including Condition-Based Maintenance”
Optimal Inspection Frequency: D(n) Model
Total Downtime versus Inspection Frequency
Inspection Frequency (n)
Tota
l Dow
ntim
e (D
)
Downtime due to Inspections and Minor Maintenance
Downtime due to System Failures
Optimal inspection frequency minimizes total downtime, D(n)
Total Downtime, D(n)
inn +=
µλ )(D(n)
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“Inspection Decisions including Condition-Based Maintenance”
Optimal Inspection Frequency: D(n) Model
• In practice, the difficulty is to determine the relationship between system failure rate and inspection policy
• In practice, this may be obtained by:
1. Experimentation
2. Co-operation
3. Simulation
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“Inspection Decisions including Condition-Based Maintenance”
D(n) = downtime due to failures + downtime due to inspections
Where:
• λ(n) is the arrival rate of system failures as a function of inspection policy
• 1/µ is the mean repair time
• n is the # of inspections per unit time
• 1/i represents the mean downtime due to inspection and associated minor maintenance
inn +=
µλ )(D(n)
Optimal Inspection Frequency: D(n) Model
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“Inspection Decisions including Condition-Based Maintenance”
D(n) Model: Numerical ExampleAssume:
λ(n) = k/n, and k=3, n≥1
1/µ = 0.033 months (24 hours)
1/i = 0.011 months (8 hours)
D´(n) = 0 gives:
= 3 inspections/month011.0
033.0*3* ==µ
ikn
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“Inspection Decisions including Condition-Based Maintenance”
Inspection Frequency to Minimize the Total Downtime per Unit Time of Buses at an Urban Transit Authority
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“Inspection Decisions including Condition-Based Maintenance”
Montreal’s Transit Commission’s Bus Inspection Policy
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Km (1000)X
X
X
X
X
X
X
X
Inspection Type“A” “B” “C” “D”
X
X
X
X
X
X
X
XTotal 8 4 3 1 Σ = 16
R 0.5 0.25 0.1875 0.0625 Σ = 1.0
Where:Ri = No. of type i inspections / Total No. of inspections i = A, B, D, or D
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“Inspection Decisions including Condition-Based Maintenance”
Mean Distance to Failure versus Inspection Interval
Mean time between failures (km)
Inspection interval (km)
Actual
Predicted
4500 5500 6500 7500 8500
2000
5000
4000
6000
3000
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“Inspection Decisions including Condition-Based Maintenance”
4000 5000 6000 7000 8000 9000
Downtime(% of totalbus-hours/year)
repair
inspection
total
3.5
3
2.5
2
1.5
1
0.5
0
Downtime As a Function of the Inspection Frequency
Interval Between Inspections (km)
Optimal Inspection Interval
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“Inspection Decisions including Condition-Based Maintenance”
Failure Finding Intervals for Protective Devices
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“Inspection Decisions including Condition-Based Maintenance”
Maximizing Availability• The problem is to determine the best interval between
inspections to maximize the proportion of time that the equipment is in the available state
• Two possible cycles of operation are:
Ti
0
Inspect
ti
Inspect
ti
Cycle 1
Good Cycle
Cycle 2
Failed Cycle
Ti Tr
0
Where: Ti = time required to effect an inspection, Tr = time required to effect a repair or replacement, and ti = interval between inspections
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“Inspection Decisions including Condition-Based Maintenance”
Numerical ExampleProblem: A protective device with a normally distributed MTBF = 5
months (and standard deviation = 1 month) has:• Ti = 0.25 month• Tr = 0.5 monthFind the optimal inspection interval, ti, to maximize availability.
Result:
ti 1 2 3 4 5 6
A(ti) 0.8000 0.8905 0.9173 0.9047 0.8366 0.7371
Therefore, the optimal inspection interval is 3 months
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“Inspection Decisions including Condition-Based Maintenance”
Inspection Interval vs. Availability
0
20
40
60
80
100
0 1 2 3 4 5 6
Inspection Interval (Months)
% A
vaila
bilit
y
Where:
A(ti) = availability per unit time
R(ti) = reliability at an inspection interval of ti
f(t) = density function of the time to failure of the equipment
Ti , Tr , and ti have been defined in the previous slide
In this case, Ti = 0.25 month and Tr = 0.5 month
Optimal Interval
( )( ) ( )
( )[ ]irii
ii
i tR-1TTt
tfttRttA
×++
×+×=
∫∞−
itdt
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“Inspection Decisions including Condition-Based Maintenance”
F.F. Interval vs. Availabilty:Moubray (Horton) Model
I = 2(1-A)M
Where:
A = AvailabilityM = MTBF I = Failure Finding Interval
Source: Moubray, RCM II, pp. 177
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“Inspection Decisions including Condition-Based Maintenance”
An Example Using the Moubray ModelProblem: Brake lights on motorcycles
• MTBF = 10 years • FFI = 10% of MTBF of 10 years = 1 year
Result: Availability = 95.0%
Problem source : Moubray, RCM II., 1999, pp. 175-176
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“Inspection Decisions including Condition-Based Maintenance”
Example Using Moubray (Horton) Model
Problem: A protective device has a MTBF = 10 years. Determine the FFI which will yield an Availabilty = 99%.
Answer: FFI = 10 weeks (roughly)
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“Inspection Decisions including Condition-Based Maintenance”
Example for FFI (Failure Finding Interval) for a Protective Device
Pressure safety valve
1000 valves in service
Inspection interval = 12 months
Time to inspect = 1 hour
Time to repair a defective valve = 1 hour
10% of valves found defective at inspection, therefore
MTTF = (1000x 1) / 100 = 10 years.
What is valve availability for different inspection intervals?
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“Inspection Decisions including Condition-Based Maintenance”
Failure Finding Pressure Valve
Interval (Weeks) Availability (%)
1 99.9
5 99.5
10 99.0
15 98.5
21 98.0
54 95.0
104 90.0
Answer
Pressure Valve Availability Chart
889092949698
100102
0 20 40 60 80 100 120
Replacement Interval (Weeks)
Avai
labi
lity
(%)
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“Inspection Decisions including Condition-Based Maintenance”
Condition Monitoring Decisions
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“Inspection Decisions including Condition-Based Maintenance”
Condition monitoring:
85% visual inspection
15% vibration monitoring, oil analysis etc
A Recent Statement
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“Inspection Decisions including Condition-Based Maintenance”
“world class companies often devote up to 50% of their entire maintenance resources
to condition based monitoring and the planned work that is required as a result
of the findings”
Source: December 2003 issue of Maintenance Technology, page 54, Terrence O'Hanlon
Another Statement
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“Inspection Decisions including Condition-Based Maintenance”
Optimising Condition Based Maintenance (CBM) (Section 3.5)
Objective is to obtain the maximum useful life from each physical asset before taking it out of service for preventive maintenance...
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“Inspection Decisions including Condition-Based Maintenance”
RCM Methodology Logic
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“Inspection Decisions including Condition-Based Maintenance”
While much research and product development in the area of condition based maintenance focuses on data acquisition and signal processing, the focus of the work at the CBM Lab in Toronto is the third and final step in the CBM process – optimizing the decision making step
CBM Research
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“Inspection Decisions including Condition-Based Maintenance”
WorkingAge
Normal < 200ppm
Warning > 200ppm
Alarm > 300ppm
• Simple to understand
• Limitations:– Which
measurements?– Optimal limits?– Effect of Age?– Predictions?
• EXAKT extends and enhances the Control Chart technique
Condition-monitoring via Warning Limits
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“Inspection Decisions including Condition-Based Maintenance”
EXAKT Optimal Decision – A New “Control Chart”
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“Inspection Decisions including Condition-Based Maintenance”
Electric wheel motor: Condition monitoring by oil analysis
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“Inspection Decisions including Condition-Based Maintenance”
Warning Limits in ‘ppm’Normal
< 20
<10
<50
<200
<15
Warning
20 - 40
10 - 20
50 - 100
200 - 300
15 - 25
Alarm
> 40
>20
>100
>300
>25
Al
Cr
Cu
Fe
Si
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“Inspection Decisions including Condition-Based Maintenance”
An example: Measurements & Decision
In Operation
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“Inspection Decisions including Condition-Based Maintenance”
Cardinal River Coals• Oil analysis from 50
wheel motors– Twelve covariates
measured– Covariates used: Iron
and sediment– Estimated Saving in
Maintenance Costs: 22% when the cost consequence of a failure replacement was 3 x cost of preventive replacement.
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“Inspection Decisions including Condition-Based Maintenance”
Optimizing CBM Decisions
Three Keys:
• Hazard
• Transition Probabilities
• Economics
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“Inspection Decisions including Condition-Based Maintenance”
( ) ( )1 1
1...( ) n nz t z ttHAZARD t e
βγ γβ
η η
−+ +⎛ ⎞= ⎜ ⎟
⎝ ⎠
Step 1: Hazard Model
Constants estimated from data
0.4830.0518 1.867 0.011831.483
148790 148790Fe Al Mgt e + +⎛ ⎞= ⎜ ⎟
⎝ ⎠
Failures/op.hour Failure/flying hour Failures/km.Failures/tonneFailures/cycleEtc…
Contribution of age to hazard
Contribution of condition information
to hazard
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“Inspection Decisions including Condition-Based Maintenance”
How does data model hazard?
Lead and Silicon are the significant covariates.
EQUIPMENT FAILURE
Age Effect
Sample History History consists of:•Beginning time•Inspection results•Ending time and reason
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“Inspection Decisions including Condition-Based Maintenance”
DATA PLOT
Age
Data
Hazard PLOT
Age
Hazard PHM
Data to Hazard
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“Inspection Decisions including Condition-Based Maintenance”
OPTIMAL POLICY - OPTIMAL HAZARD LEVEL
Optimal Hazard level
Age
Hazard
Hazard
Cost/unit time
Hazard PLOT
COST PLOT
Ignore Hazard
Replace at failure only
minimal cost
optimal hazard
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“Inspection Decisions including Condition-Based Maintenance”
We have created a theory, but in order to
make it work in practice we need a tool
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“Inspection Decisions including Condition-Based Maintenance”
Real world research
Securing Canada's Energy Future
Managing Risk: A CBM Optimization Tool
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“Inspection Decisions including Condition-Based Maintenance”
Research Team
Collaborating ResearcherDr. Xiaoyue Jiang, Assistant Professor
Louisiana State University
Principal InvestigatorProf. Andrew K.S. Jardine
Research StaffDr. Dragan Banjevic, Project DirectorWei Hua (Walter) Ni, Programmer/AnalystDr. Daming Lin, Research AssociateDr. Ali Zuaskiani, Post doctoral FellowNeil Montgomery, Research AssociateSusan Gropp, Research Assistant
Research StudentsDiederik Lugtigheid (Repairable Systems)Darko Louit (Spare Parts Optimization)Jean-Paul Haddad (Research Topic TBA)Andrey Pak (Maintenance & Repair Contracts)
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“Inspection Decisions including Condition-Based Maintenance”
• Transition probabilities for all significant covariates are calculated from all histories
• Probabilities can change over time– e.g. probability of worsening wear can
increase with age.
Step 2: Transition Probabilities
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“Inspection Decisions including Condition-Based Maintenance”
Very Smooth
Smooth
Rough
Very Rough
Failure
Inspection Interval = 30 days
Transition Probabilities
0.9276720.0521140.0170390.0026960.00048Above 0.37
0.506990.243380.1903980.0474220.0128520.22 to 0.37
0.1997140.2293980.377880.1375830.0554260.15 to 0.22
0.0760020.1374140.3308980.2498180.2058680.1 to 0.15
0.0147310.0405540.1451610.2241810.5753730 to 0.1
Above
0.37
0.22 to
0.37
0.15 to
0.22
0.1 to
0.15
0 to 0.1
VEL #1AAge 0 to 180(Days)
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“Inspection Decisions including Condition-Based Maintenance”
Data to Model: Summary{ }
1.523exp 0.2293* 0.4151*2.523
3402 3402 Pb Sit⎛ ⎞+⎜ ⎟
⎝ ⎠
PLUS
Hazard
Covariate Evolution
Optimal Hazard Level
Cf = Total cost of failure replacement
Cp = Total cost of preventive replacement
AND
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“Inspection Decisions including Condition-Based Maintenance”
Optimal Decision Chart
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Vibration Monitoring Data
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Vibration Analysis Events Data
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Vibration Monitoring Decision
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“Inspection Decisions including Condition-Based Maintenance”
Analysis of Shear PumpBearings Vibration Data– 21 vibration measurements
provided by accelerometer
Using <EXAKT>:– 3 measurements significant
A Check:– Had <EXAKT> model been
applied to previous histories – Savings obtained = 35 %
Campbell Soup Company
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“Inspection Decisions including Condition-Based Maintenance”
EXAKT V 4.0 Released in December 2005
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“Inspection Decisions including Condition-Based Maintenance”
Recent Developments in CBM Optimization
• Marginal Analysis: addressing individual system failure modes
• Remaining Useful Life (RUL): Reporting RUL and standard deviation for selected state of covariates and working age
• Probability of failure in a short interval as a part of decision report
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“Inspection Decisions including Condition-Based Maintenance”
#1. Marginal Analysis: Modeling of Diesel Engines employed on T23 Frigates
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“Inspection Decisions including Condition-Based Maintenance”
Diesel Engines: Failure Modes
Unrelated to oil
readings
Possibly related to
oil readings
12Misc, including cylinder block failures9
14Cylinder Heads8
15Pistons, Articulations and Bearings7
20Valves and Running Gear6
24Cylinder Liners and Rings5
9Accessories4
9Generator3
6Fuel System2
13Cooling System1
3Not Known0
CountType of Failure
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“Inspection Decisions including Condition-Based Maintenance”
Simultaneous decisions for each failure mode of a repairable system
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“Inspection Decisions including Condition-Based Maintenance”
#2. Conditional Density Function & Remaining Useful Life
• Shows the shape of the distribution of the time to failure given current conditions
• Expected time to failure (Remaining Useful Life, or RUL)
• Standard deviation
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“Inspection Decisions including Condition-Based Maintenance”
#3. Pre-2006
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“Inspection Decisions including Condition-Based Maintenance”
2006-
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“Inspection Decisions including Condition-Based Maintenance”
Age Data
Condition-Monitoring Data
Supplied by user
Software engine
Intermediate result
Final result
MaintenanceDecision
Hazard ModelTransition Model
CostModel
RemainingUseful Life
Principle of CBM Optimization using EXAKT
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“Inspection Decisions including Condition-Based Maintenance”
Other CBM Optimization Studies
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“Inspection Decisions including Condition-Based Maintenance”
Risk factors:• Cholesterol level• Blood pressure• Smoking• Lifestyle• Levels of protein
ConstituentHomocysteine
Hazard or Risk = f (Age) + f (Risk factors)
Condition Monitoring – An AnalogyHEART FAILURE
Risk factors:• Oil Analysis (Fe, Cu, Al,
Cr, Pb…..etc.)• Vibration (Velocity and
Acceleration)• Thermography• Visual Inspection
……….………….…………………..
EQUIPMENT FAILURE
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“Inspection Decisions including Condition-Based Maintenance”
Hong Kong Mass Transit Railway Corporation– Had excessive traction
motor ball bearing failures
– CBM to monitor bearing grease colour
– Changed inspections from every 3.5 years to annual
– Reduced failures/yr.. From 9 to 1
– Reduced total costs by 55%
The reality: Failures reduced to 2/yr.
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“Inspection Decisions including Condition-Based Maintenance”
Analysis of Warman-PumpBearings Vibration Data– Total 8 pumps each with two bearings
(16 bearings) analyzed– 12 vibration covariates identified
Using <EXAKT>:– 2 covariates significant– Annual replacement cost savings= 42 %
Feedback:– Model results found realistic by Sasol
plant– Significant vibration covariates identified
by <EXAKT> are agreed as a major problem
Sasol Plant
Vlok, et al, "Optimal Component Replacement Decisions using Vibration Monitoring and the PHM", JORS, 2002.
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“Inspection Decisions including Condition-Based Maintenance”
Open Pit Mining Operation
– Covariates used: Iron, Aluminum, Magnesium
– Saving in Maintenance Costs: 25%
– Average replacement time increase: 13%
– Warranty limit could be increased
CAT 793B Transmissions Oil data analyzed
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“Inspection Decisions including Condition-Based Maintenance”
EXAKT Modeling with MWM Diesel Engine
employed on Halifax Class ships.
Maintenance and Diagnostic Data
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“Inspection Decisions including Condition-Based Maintenance”
Condition-based Optimal Replacement Policy
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“Inspection Decisions including Condition-Based Maintenance”
Review
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Inspection DecisionsSYSTEM FAILURES
• Expect Failure Rate to be Constant
• Can Drive Down System Failure Rate By Preventive Maintenance (E.g. Inspections and Minor Maintenance)
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“Inspection Decisions including Condition-Based Maintenance”
Inspection DecisionsSystem Failures
Inspections &Minor Maintenance
Decreasing system failures
Increasing inspection frequency
Component 2
Component 1
Component 5
Component 3
Component 4
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“Inspection Decisions including Condition-Based Maintenance”
OperatingHours
SystemFailureRate Drive Down
Through MorePM, BetterProcedures Etc.
System Failure Rate
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“Inspection Decisions including Condition-Based Maintenance”
Failure Finding Intervals
• Availability Maximization
• Moubray (Horton) model for a single protective device
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“Inspection Decisions including Condition-Based Maintenance”
An Overview of EXAKTEvents Data Inspection Data
Replacement Recommendation© CBM Lab: University of Toronto
EXAKT Modeling Module
EXAKT Decision Module
CBM Model
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“Inspection Decisions including Condition-Based Maintenance”
Additional CBM References1. www.mie.utoronto.ca/cbm (For
information about the CBM research activities at the University of Toronto)
2. www.omdec.com (For information about the EXAKT: CBM Optimization software)
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“Inspection Decisions including Condition-Based Maintenance”
www.omdec.com/articles/p_exaktTutorial.html
www.omdec.com/articles/p_ExaktTutorialComplexItems.html
Learn the fundamentals of EXAKT by going through the EXAKTtutorial for single items, i.e.,components or systems as a whole:
Link to advanced EXAKT tutorial for complex items,e.g., systems consisting of components with differentfailure modes:
Note: Just follow the instructions on the web pages.
EXAKT Tutorials
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“Inspection Decisions including Condition-Based Maintenance”
Problems1) The current maintenance policy being adopted for a complex
transfer machine in continuous operation is that inspections aremade once every 4 weeks. Any potential defects that are detected during this inspection and that may cause breakdown of the machine are rectified at the same time. In between these inspections, the machine can break down, and if it does so, it is repaired immediately. As a result of the current inspection policy, the mean time between breakdowns is 8 weeks.
It is known that that breakdown rate of the machine can be influenced by the weekly inspection frequency, n, and associated minor maintenance undertaken after the inspection, and is of the form λ(n) = K/n, where λ(n) is the mean rate of breakdowns per week for an inspection frequency of n per week.
Each breakdown takes an average of 1/4 week to rectify, while the time required to inspect and make minor changes is 1/8 week.
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“Inspection Decisions including Condition-Based Maintenance”
Problemsa. Construct a mathematical model that could be used
to determine the optimal inspection frequency to maximize the availability of the transfer machine.
b. Using the model constructed in (a) along with the data given in the problem statement, determine the optimal inspection frequency. Also give the availability associated with this frequency.
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“Inspection Decisions including Condition-Based Maintenance”
Problems2) A company monitors the gearboxes on vehicles by
attaching a wireless sensor to each gearbox to take vibration readings. The vibration signals are then analyzed by a digital signal processing toolbox. Two condition indicators showing the health of the gearbox, CI1 and CI2 are extracted from each vibration signal. After running the above condition monitoring on a fleet of vehicles, the company has accumulated a certain amount of data. Now the company manager asks you to apply EXAKT to the data.
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“Inspection Decisions including Condition-Based Maintenance”
Problemsa. The first step for you would be to collect and prepare the data.
What are the two main sources of data required by EXAKT?
b. Now you have obtained the right data and have properly prepared it. You want to establish a PHM for the gearboxes. The usual way for the modeling is to include both indicators in the PHM.
i. If you find one of them, CI1, is significant and the other, CI2, is not, how would you proceed with the modeling? What would you do if both CI1 and CI2 are not significant?
ii. If you find that the shape parameter is not significant (i.e., β = 1), how would you proceed? What does it really mean when you say the shape parameter is not significant?
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“Inspection Decisions including Condition-Based Maintenance”
Problemsc. Assume that the final PHM you get is <insert equation>where h(t, CI2) is the hazard rate and t is the operation hours.
Given the following data from the three gearboxes, estimate the hazard rate of each gearbox (Table 1).
d. You are asked to submit a report regarding the hazard rate ofgearbox 1. How might you explain the value you have obtained and what maintenance action would you recommend within the next 48 hours?
Table 1: Data from Three Gearboxes
Gearbox No. Operation Hours CI1 CI2
1 8550 2 5.5
2 3215 10 2.1
3 9460 12 1.4