c3-8(analymeth)

8/7/2019 C3-8(AnalyMeth)

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Module 8Module 8

UNIT IIIUNIT III

"Copyright 2002, Information Spectrum, Inc. All Rights Reserved."

HOW TO PERFORM RCMHOW TO PERFORM RCM

HOW TO PERFORM RCMHOW TO PERFORM RCM

ANALYTICAL METHODSANALYTICAL METHODS



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Module Preview:Module Preview:

Module Preview:Module Preview:

IntroductionIntroduction


Interval CalculationsInterval Calculations




Cautions and WarningsCautions and Warnings

Cautions and WarningsCautions and Warnings

Review and SummaryReview and Summary

Review and SummaryReview and Summary

Cost CalculationsCost Calculations

Cost CalculationsCost Calculations

Spreadsheet ExerciseSpreadsheet Exercise

Spreadsheet ExerciseSpreadsheet Exercise




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Module Objective:Module Objective:

Module Objective:Module Objective:

This module will provide information onThis module will provide information on

different analytical methods that may be useddifferent analytical methods that may be used

in RCM analysis:in RCM analysis:

1.1. Introduce some methods of determining taskIntroduce some methods of determining task

intervalsintervals

2.2. Demonstrate the cost equations used by theDemonstrate the cost equations used by the

IRCMS softwareIRCMS software

3.3. Discuss limitations and cautions associatedDiscuss limitations and cautions associated

with these methodswith these methods






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Inspection Interval (I) (Ref: NAVAIR 00Inspection Interval (I) (Ref: NAVAIR 00--2525--403):403):

I = PF/nI = PF/n

Where:Where:

PFPF = interval from potential failure to functional failure= interval from potential failure to functional failurenn = number of inspections during PF interval= number of inspections during PF interval

Where:Where:

Using Pacc (safety or nonUsing Pacc (safety or non--safety)safety)

n = ln (Pacc) / ln (1n = ln (Pacc) / ln (1--theta)theta)

Using Cost optimization (nonUsing Cost optimization (non--safety)safety)n =n = ln [ (ln [ (--MTBF*Ci/PF)/((CnpmMTBF*Ci/PF)/((Cnpm--Cpf)*ln(1Cpf)*ln(1--theta)) ]theta)) ]nn

ln(1ln(1--theta)theta)

OnOn--condition Task:condition Task:





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Derivation:Derivation: n = ln (Pacc) / ln (1n = ln (Pacc) / ln (1--theta)theta)

ThetaTheta = probability of detecting a Potential Failure in= probability of detecting a Potential Failure in

one inspection assuming it existsone inspection assuming it exists

(1(1--theta)theta) = probability of not detecting a Potential= probability of not detecting a PotentialFailure in one inspection assuming it existsFailure in one inspection assuming it exists(1(1--theta)theta)nn = probability of not detecting a Potential Failure= probability of not detecting a Potential Failure

in n inspections assuming it existsin n inspections assuming it exists

Goal of inspection isGoal of inspection is (1(1--theta)theta)nn < Pacc< Pacc

Longest inspection meeting this criteria wouldLongest inspection meeting this criteria would

occur atoccur at (1(1--theta)theta)nn = Pacc= Pacc

Solving for n:Solving for n:

n = ln (Pacc) / ln (1n = ln (Pacc) / ln (1--theta)theta)






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If an inspection may require deferral of theIf an inspection may require deferral of the

corrective action when found the inspectioncorrective action when found the inspection

interval should allow for the deferral time (Tc)interval should allow for the deferral time (Tc)

Applicable in continuously operatingApplicable in continuously operatingequipment or processes or where repairequipment or processes or where repair

deferred and use continuesdeferred and use continues

Mathematically:Mathematically:I = (PF/n)I = (PF/n)--TcTc

where:where:

Tc = Time needed to perform corrective actionTc = Time needed to perform corrective action






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LIMITATIONSLIMITATIONS

Method is conservativeMethod is conservative

Based on assumption that potential failure alwaysBased on assumption that potential failure alwaysexistsexists

If more precise interval is desired, actualIf more precise interval is desired, actual

failure rate and distribution needs to befailure rate and distribution needs to be

considered in more detailconsidered in more detail

As more precision is pursued, loss of conservatismAs more precision is pursued, loss of conservatismmust be weighed against confidence in the datamust be weighed against confidence in the data

sources to ensure adequate levels ofprotectionsources to ensure adequate levels ofprotection

OnOn--condition Task:condition Task:OnOn--condition Task:condition Task: Interval CalculationsInterval CalculationsInterval CalculationsInterval Calculations

ANALYTICAL METHODSANALYTICAL METHODSANALYTICAL METHODSANALYTICAL METHODS


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Interval CalculationsInterval CalculationsInterval CalculationsInterval Calculations

n =n = ln [ (ln [ (--MTBF*Ci/PF)/((CnpmMTBF*Ci/PF)/((Cnpm--Cpf)*ln(1Cpf)*ln(1--theta)) ]theta)) ]nn

ln(1ln(1--theta)theta)

Where:Where:CiCi = Cost of one inspection= Cost of one inspection

CnpmCnpm = Cost of No PM= Cost of No PM= Cost of Corrective Maint + Cost Lost Op time= Cost of Corrective Maint + Cost Lost Op time

CpfCpf = Cost of repairing a PF= Cost of repairing a PF

See NAVAIR 00See NAVAIR 00--2525--403403

OnOn--condition Task:condition Task:OnOn--condition Task:condition Task:



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Interval CalculationsInterval CalculationsInterval CalculationsInterval Calculations

Statistical (Weibull) or empirical (Test orStatistical (Weibull) or empirical (Test or

sampling) methodssampling) methods

Beyond the scope of this courseBeyond the scope of this course

HardHard--Time Task:Time Task:HardHard--Time Task:Time Task:



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Interval CalculationsInterval CalculationsInterval CalculationsInterval CalculationsFailureFinding TaskFailureFinding Task:FailureFinding TaskFailureFinding Task:

Inspection Interval (I) (Ref: NAVAIR 00Inspection Interval (I) (Ref: NAVAIR 00--2525--403):403):

Determine by setting PDetermine by setting Pmfmf= P= Paccacc

WhereWhere::

PPmfmf== PPhiddenhidden xx PPadditionaladditional

PPmfmf == ProbabilityProbability ofof multiplemultiple failurefailure occurringoccurring

PPhiddenhidden == ProbabilityProbability ofof thethe hiddenhidden failurefailure occurringoccurring

PPadditionaladditional = Probability of an additional failure occurring= Probability of an additional failure occurring



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Interval CalculationsInterval CalculationsInterval CalculationsInterval CalculationsFailureFinding Task:FailureFinding Task:FailureFinding Task:FailureFinding Task:

Assuming a constant failure rate for each term:Assuming a constant failure rate for each term:

PP = 1= 1 -- ee--t / MTBFt / MTBF

(1)(1) PPmfmf = P= Phiddenhidden x Px Padditionaladditional= (1= (1 -- ee--t / MTBFt / MTBFhiddenhidden) x (1) x (1 -- ee--t / MTBFt / MTBFadditionaladditional ))

(2)(2) PPmfmf== PPaccacc(t) = (1(t) = (1 -- ee--t / MTBFt / MTBF

acceptableacceptable))



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Combining equations (1) and (2)Combining equations (1) and (2)

(3)(3) (1(1 -- ee--t / MTBFt / MTBFacceptableacceptable) = (1) = (1 -- ee--t / MTBFt / MTBFhiddenhidden) x (1) x (1 -- ee--t / MTBFt / MTBFadditionaladditional ))

Two unknowns: MTBFTwo unknowns: MTBFacceptableacceptable and tand t

To determine MTBFTo determine MTBFacceptableacceptable solvesolve (1(1 -- ee--t / MTBFt / MTBFacceptableacceptable ) for a) for a

known Pacc and tknown Pacc and tFor example using a program established Pacc(at t=1) = .000001For example using a program established Pacc(at t=1) = .000001

Finally Equation (3) can be solved for t which is used for IFinally Equation (3) can be solved for t which is used for I

Note: equation (3) can only be solved iteratively (use theNote: equation (3) can only be solved iteratively (use thespreadsheet)spreadsheet)

For economic/operational consequences, must beFor economic/operational consequences, must be

costcost--effectiveeffective



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LIMITATIONSLIMITATIONS

Method assumes hidden and additional failures areMethod assumes hidden and additional failures are

random andrandom and independentindependent

Assumption of randomness is usuallyAssumption of randomness is usually

conservativeconservative

If failures are dependent method may NOT beIf failures are dependent method may NOT be

conservative!conservative! If hidden failure is not random to a high degreeIf hidden failure is not random to a high degree

another task option such as Hard time may beanother task option such as Hard time may be

more appropriatemore appropriate



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Service/Lube:Service/Lube:Service/Lube:Service/Lube: Cost CalculationsCost CalculationsCost CalculationsCost Calculations

Service/Lube TaskService/Lube Task

SLSLOPOP = Service/lubrication task cost per operating= Service/lubrication task cost per operating

timetime

SLSLOPOP = C= CSLSL/ I/ ISLSL

WhereWhere::

CCSLSL== CostCost OfOf OneOneSLSL TaskTask

== ((MHsMHsto perform task) x (cost per MH) + material costto perform task) x (cost per MH) + material cost

IISLSL == Task IntervalTask Interval



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OnOn--Condition:Condition:OnOn--Condition:Condition: Cost CalculationsCost CalculationsCost CalculationsCost Calculations

OnOn--condition Taskcondition TaskOCOC

OPOP =On=On--condition task cost per operating timecondition task cost per operating time

OCOCOPOP = ((C= ((COCOC / I/ IOCOC) *(L) *(L -- (I(III--IIOCOC)) / L) + C)) / L) + CRR/ MTBF/ MTBF

WhereWhere::

CCOCOC = Cost of oneOC Task (Not including repair costs)= Cost of oneOC Task (Not including repair costs)

(MHs to perform task) * (cost per MH) + cost of materials(MHs to perform task) * (cost per MH) + cost of materials

LL == Item Design LifeItem Design Life

IIII == InitialInitial InspectionInspection IntervalInterval(Inspection(Inspection Threshold)Threshold)

IIOCOC == TaskTask IntervalInterval

MTBFMTBF == MeanMean timetime betweenbetween failuresfailures (both(both potentialpotential andand functionalfunctional withwith

tasktask inin place)place)CCRR == AverageAverage RepairRepair CostCost..

Include all failures (potential and functional failures)Include all failures (potential and functional failures)

Include secondary damageInclude secondary damage

Include the cost of multiple failures in the functional failure portion of the costInclude the cost of multiple failures in the functional failure portion of the cost

Include operational impact if it has been converted to a "cost"Include operational impact if it has been converted to a "cost"



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HardHard--Time:Time:HardHard--Time:Time: Cost CalculationsCost CalculationsCost CalculationsCost Calculations

HardHard--Time TaskTime Task

HTHTOPOP = Hard time task cost per operating time= Hard time task cost per operating time

HTHTOPOP = [C= [CHTHT (S) + C(S) + CRR (1(1--S)] / [(S) IS)] / [(S) IHTHT + (1+ (1--S) K IS) K IHTHT]]

WhereWhere::

CCHTHT == CostCost OfOf OneOne HTHT

== ((MHsMHs toto performperform task)task) xx (cost(cost perper MH)MH) ++ costcost ofofmaterialsmaterialsSS == PercentagePercentage ofof itemsitems thatthat survivesurvive toto thethe hardhard timetime limitlimit

IIHTHT == TaskTask IntervalInterval

KK == Premature Failure FactorPremature Failure Factor

= Average age of premature failures as a percentage of I= Average age of premature failures as a percentage of IHT.HT.((NoteNote: K I: K IHTHT is used to estimate MTTF of premature failures.)is used to estimate MTTF of premature failures.)

CCRR == AverageAverage RepairRepair CostCost ifif HTHT notnot accomplishedaccomplished..

EnsureEnsure secondarysecondary damagedamage isis includedincluded

ForFor hiddenhidden functionsfunctions includeinclude thethe costcost ofof multiplemultiple failuresfailures..

IncludeInclude operationaloperational impactimpact ifif convertedconverted toto aa "cost""cost"



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FailureFinding:FailureFinding:FailureFinding:FailureFinding: Cost CalculationsCost CalculationsCost CalculationsCost Calculations

FailureFailure FindingFindingFFFFOPOP == FailureFailure FindingFinding tasktask costcost perper operatingoperating timetime

FFFFOPOP == CCFFFF // IIFFFF ++ CCRR // MTBFMTBF

WhereWhere::CCFFFF == CostCost OfOf OneOne InspectionInspection

== ((MHsMHstoto performperform task)task) xx (cost(cost perper MH)MH) ++ costcost ofofmaterialsmaterials

IIFFFF == TaskTask IntervalInterval

MTBF =MTBF = Mean time between failures (with task in place)Mean time between failures (with task in place)

CCRR == Average RepairCost.Average RepairCost.

Average cost of repairing the functional failures found by theAverage cost of repairing the functional failures found by the

inspection and those that become evident by multiple failures notinspection and those that become evident by multiple failures not

prevented.prevented.

Include operational impact if it has been converted to "cost".Include operational impact if it has been converted to "cost".



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Overview:Overview:Overview:Overview: Cost CalculationsCost CalculationsCost CalculationsCost Calculations

NoNo PMPM (Run(Run toto Failure)Failure)

NONOOPOP == NoNo PMPM costcost perper operatingoperating timetime

NONOOPOP == CCRR // MTBFMTBF

WhereWhere::

CCRR == AverageAverage RepaiRepairr CostCost

Average cost to repair the functional failure andAverage cost to repair the functional failure andsecondary damage.secondary damage.

ForFor hiddenhidden functions,functions, includeinclude thethe costcost ofof multiplemultiple

failuresfailures.. Include operational impact if it has beenInclude operational impact if it has been

converted to "cost".converted to "cost".

MTBFMTBF == MeanMean timetime betweenbetween failuresfailures (with(with nono tasktask inin

place)place)



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Overview:Overview:Overview:Overview: Cost CalculationsCost CalculationsCost CalculationsCost Calculations

OtherOther ActionAction

OAOAOPOP == OtherOther actionaction costcost perper operatingoperating timetime

OAOAOPOP == CCOAOA // LLRR

WhereWhere::

CCOAOA = Total cost to develop and implement= Total cost to develop and implement

Other ActionOther Action

LLRR == TotalTotal remaining life of system/fleetremaining life of system/fleet



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Overview:Overview:Overview:Overview: Cautions and WarningsCautions and WarningsCautions and WarningsCautions and Warnings

All methods are approximationsAll methods are approximations

Subject to changes in dataSubject to changes in data

Consider sensitivityConsider sensitivity

Schedule followSchedule follow--up validation of assumptions (Ageup validation of assumptions (Age

Exploration)Exploration)

User is responsible for understanding the limits andUser is responsible for understanding the limits and

applicability of each methodapplicability of each method

Not every failure mode requires in depth analytical analysisNot every failure mode requires in depth analytical analysis

(pick your battles)(pick your battles)

Estimates can be used in many casesEstimates can be used in many cases

Note:Note: Equations discussed on the following slides describe theEquations discussed on the following slides describe the

current methods provided in NAcurrent methods provided in NA--0000--2525--403. Users should stay403. Users should stay

abreast of differences between latest NAabreast of differences between latest NA--0000--2525--403403 methodsmethods

and those used in IRCMSand those used in IRCMS



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Overview:Overview: Spreadsheet ExerciseSpreadsheet ExerciseSpreadsheet ExerciseSpreadsheet Exercise

ExerciseExercise



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Overview:Overview:

Analytical MethodsAnalytical MethodsAnalytical MethodsAnalytical Methods

Spreadsheet ExerciseSpreadsheet ExerciseSpreadsheet ExerciseSpreadsheet Exercise

ExerciseExercise


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Review andSummaryReview andSummaryReview andSummaryReview andSummary

Module ObjectiveModule Objective Module ObjectiveModule Objective

Review and SummaryReview and Summary Review and SummaryReview and Summary

IntroductionIntroduction IntroductionIntroduction

Interval CalculationsInterval Calculations Interval CalculationsInterval Calculations

Cautions and WarningsCautions and Warnings Cautions and WarningsCautions and Warnings

Cost CalculationsCost Calculations Cost CalculationsCost Calculations

Spreadsheet ExerciseSpreadsheet Exercise Spreadsheet ExerciseSpreadsheet Exercise



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Unit IV Module 1Packaging

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Unit IV Module 1Packaging

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