overhaul diesel

every failure had a significant operational impact.Results indicate an increasing failure rate as theengine ages to the 24,000 hour overhaul time. Theevidence indicates a constant failure useful liferegion, but the increasing failure rate from theWeibull models suggests that the periodic over-hauls do not prevent wearout failures. As a result,the Coast Guard should consider refining dieselengine overhaul policy in order to prevent increas-ing age-related failures.

IntroductionIncreasing pressure on organizational main-tenance functions has spurred various main-tenance management initiatives in the pastthirty years. Faced with an aging cutter fleet,challenging operations tempo, and a multi-tude of missions, the United States CoastGuard (USCG) is currently investigating newFleet maintenance policies. Reliability cen-tered maintenance (RCM) strategies helpdetermine what maintenance tasks to per-form and when. RCM decision algorithmsattempt to maximize system contribution toorganizational goals by reducing downtime,

expense, environmental, and safety hazardswhile providing insight into the true capabili-ties of a given asset.

One work-intensive maintenance action isthe routine overhaul of main propulsiondiesel engines (MDEs). Under the traditionalguidelines, for the three white-hull (Reliance,Secretary, and Famous) classes, the CoastGuard will overhaul a main diesel engine sixtimes a year at an approximate cost of$250,000 in parts and 3000 labor hours peroverhaul. This overhaul typically consists ofremoving and inspecting all pistons and lin-ers and major ancillaries and making selectedcomponent replacements. IncorporatingRCM to defer or eliminate these costly over-hauls would bring substantial savings.

The intention of the engine overhaul is torestore the life and reliability of the propul-sion diesel engine. Figure 1 shows the classicview of the relationship between failure rateand operating time. A new system may expe-rience more than normal failures during the“burn-in” phase, followed by a period of

ABSTRACTThe United States Coast Guard has recently investigated new strategies to maintain cutter propulsiondiesel engines. Reliability centered maintenance with statistical methods may allow the time betweencostly scheduled overhauls to be increased. One indicator of engine aging is the number of failures expe-rienced with increasing operating hours. The purpose of this paper is to investigate the failure-time rela-tionship of the ALCO 251 marine diesel propulsion engine operated on Reliance class cutters. Thisanalysis used exponential, Weibull, and three-part composite Weibull failure density functions to modelengine casualty data dating back to 1978. The data does not indicate the source of the engine failure, but

T E C H N I C A L P A P E R

NAVAL ENGINEERS JOURNAL SPRING 2004 3 1

Statistical Methods for PlanningDiesel Engine Overhauls in theU. S. Coast Guard■ C. M. Milkie and Dr. A. N. Perakis

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steady or normal amount of failures, andlastly, again more than normal failures ascomponents wearout. These relationshipsand the corresponding Weibull shape para-meter β (which will be explored later in thisreport) are listed in Table 1. Ideally, a sched-uled overhaul is performed at a time nearthe end of what is called the “useful life” inFigure 1 and restores the reliability to apoint near the beginning of this useful liferegion. Under the RCM philosophy, a time-based overhaul will have little effect onengine failure modes which are not relatedto operating time, or related the time select-ed for the overhaul interval.

Yet time-based overhauls have many advan-tages. First, consistent budget planning forsupport functions can ease financing vari-ability. Second, performing all major enginemaintenance at the same time may have the

lowest average impact on asset availability.Third, institutional structure and knowledgesupport scheduled overhauls (and vice-versa). Finally, correctly timed overhauls pre-vent the increase in engine failure rate forthose wearout failures which would other-wise occur for an engine operating in the“wearout” region.

Executing scheduled overhauls risks severaloperational impacts. First, very often theoverhaul poses the hazard of misalignment orimproper installation of new components.Likewise, many operators will attest to anincrease in engine casualties during a periodafter an overhaul. Lastly, the scheduled dieselengine overhauls disrupt a cutter’s inportroutine with an immense resource drain.

Time-based overhauls to refurbish or replacemajor engine components may not be appro-priate if engine failures are not time related.Usually, the engine manufacturer recom-mends an overhaul interval. The suggestedinterval may be too short because either themanufacturer has a vested interest to sellreplacement parts, considers life-cycle main-tenance secondary to other design goals,does not know what environment the enginewill be operated in, or needs to reducepotential liability. Another reason to rejectthe idea of time-based scheduled restoration

Statistical Methods for Planning Diesel Engine Overhauls in the U. S. Coast Guard

3 2 SPRING 2004 NAVAL ENGINEERS JOURNAL

FIGURE 1: Bathtub Curve (Smith,D. 1997)

Table 1Bathtub Curve Aging Regions

Interval Failure Rate β Typical Failure ModesInfant Mortality Decreasing <1 manufacture, QA, impurities,

incorrect adjustment, alignment,installation

Random Failures Constant =1 stress-related, environmentalWearout Failures Increasing >1 corrosion, oxidation,

friction wear, fatigue


is that under RCM methodologies, equip-ment fails from a variety of failure modes.Preventive maintenance can manage mostfailure modes, with properly timed scheduledrestoration only appropriate for failuremodes of gradual deterioration.

Casualty rate as an engine ages provides onemeasure of the degree of degradation.Casualty rate information can be determinedfrom failure data aggregated for an entirecutter class. The Weibull shape parameter βcan be thought of to be an indicator of rateof change of the failure or casualty rate asshown in Table 1. Ideally, engine failure dataidentifies the culprit component and failuremode. The data in this analysis is only iden-tified as an operationally significant propul-sion diesel engine casualty. This limitation isacceptable because the analysis determinesthe overall failure rate correlation to engineaging. In the context of RCM, this agingrelationship helps judge the appropriatenessof a scheduled engine restoration.

Current Coast Guard Diesel Engine Overhaul PlanningMoore and Perakis (1999) detail severaltrend monitoring techniques used to predictthe need for diesel engine restoration (over-haul). The Navy Oil Analysis Program(NOAP), Full Power Trial (FPT), and DieselEngine Maintenance Program (DEMP) aresupposed to be used in conjunction withengine operating hours to schedule overhaul.Early in this project, the authors analyzedFleet data from FPTs and DEMPs in anattempt to ascertain engine “health” as cor-related with age. The analysis showed nomentionable correlation between the severalparameters (hourly lube oil consumed, aver-age exhaust temperature, firing pressures)and engine operating hours. As practiced,these measurements are of little value toplanning overhaul intervals on a Fleet-widescale. Until recently, the USCG has reliedalmost exclusively on time-based, scheduledrestoration of the diesel engine.

The Coast Guard Naval EngineeringManual outlines procedures for lube oilspectrographic analysis. Cutters rely onNOAP quarterly analyses to indicate thecondition of the engine. Spectrographicanalysis detects an increase in wear metalsabove an established threshold. According toMoubray (1998), AE spectroscopy candetect most wear metals, corrosion, andextraneous contaminants up to severalmonths before an operational failure.Consistent sampling is critical to predictingany incipient failure with the NOAP.

Other condition monitoring techniques aidoverhaul planning. One method, enginevibro-acoustic analysis, shows promise fordetermining overall engine “health.” At thetime this report was written, Coast Guardpolicy was to extend the 24,000 hour over-haul upon operator’s request up to 28,000hours. At 28,000 hours the cutter mayextend the overhaul to 32,000 hours after anextensive vibro-acoustic analysis. This andother condition-based methods are continu-ally being investigated, improved, and imple-mented. The new USCGC Healy (WAGB 20)fully incorporates vibration monitoring aspart of the regular preventive maintenance(Burt, et al. undated draft). The AtlanticFleet maintenance command has contractedout condition-monitoring “snapshots” forolder engines. An analysis on the USCGCSeneca (WMEC 906) concluded that thescheduled top-end engine overhaul may bedeferred (MPR 1998).

Data and MethodologyComprehensive failure data should be avail-able for a reliability analysis. Sources of datainclude cooperative organizations such as theGovernment-Industry Data ExchangeProgram (GIDEP), warranty claims for man-ufacturers, or field data from the operatoritself. Data in this report is field data collect-ed at a central location. All Coast Guardunits report significant engine casualties(CASREPS) to a central location. The data


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analyzed is an extract from the CASREPdatabase from 1978-1998. For each reportedCASREP, seven data fields are recorded:

– Hull Number

– Initial Date

– Initial Time

– Completion Data

– Completion Time

– Equipment Indicator Code (EIC)

– Allowance Parts Listing (APL)

The data extract should contain almost alldiesel engine corrective maintenance actions.There are several reasons why the data setmay underreport the casualties.

To understand reporting inconsistencies, theauthors consider how and why a cutterreports casualties. First, the CASREP com-municates to operational commands that thecutter’s ability is degraded. A casualty mayoccur and be repaired by an attentive crewbefore a CASREP needs to be sent. The briefloss in operational ability is without conse-quence. However, the casualty is importantfrom a systems reliability standpoint becausethe failure mode may be age related. A sec-ond reason for underreporting may behuman error by not including the database asan addressee on the CASREP message. Thefailure would then never be included in anyanalysis relying on that data. Other draw-backs of the dataset arise from the quality ofinformation contained in each field.

The date and time fields serve as the timereference. Computing mean time betweenfailure (MTBF) and mean time to repair(MTTR) under an exponential assumptionmay be accomplished by using an averageyearly-use multiplier. Maintenance managersschedule MDE overhauls based on the num-ber of operating hours a particular enginehas. On average, overhaul planning anddetermining operating hours at each failureis possible, but ideally the actual enginehours since overhaul would be recorded.

The EIC designates the source of failure. Thecode may be as specific as “fuel injector” or

more general such as propulsion-related. Useof EIC introduces a fundamental questionfor quantitative reliability analysis: Whatlevel of detail is appropriate to collect usefuldata? Coast Guard CASREPS currentlyreport EIC to identify equipment only, suchas “propulsion diesel engine”.

Initially, the authors believed the APL wouldidentify the affected component; however, noneof the APLs on the data extract could be suc-cessfully matched to those from a master list.

The Role of Quantitative AnalysisOrganizations may undertake a RCM pro-gram without statistical analysis of their fail-ure histories. However, because many orga-nizations, including the USCG, maintain adatabase of failure histories, a quantitativeanalysis of failures can identify a time-depen-dent failure pattern (Moubray 1997). Theage at which an asset demonstrates a signifi-cant increase in conditional probability offailure, or hazard rate (h[t]), establishes thefrequency for scheduled restoration tasks.

A Weibull reliability function (Equation 1) isoften used for reliability analysis because ofthe flexibility to model exponential patternsand non-constant failure rates. Combiningdifferent Weibull functions can produce pat-terns to match any or all regions of the bath-tub curve from Figure 1.

(1)

where:

R(t) = S(t) equals the Survivor Function, rep-resenting the number of a populationremaining in an unfailed state as a functionof time (t).

α is the Weibull scale parameter

β is the Weibull shape parameter

τ is the time at which the interval to be modeled begins




A complication arises with the Weibull dis-tribution when modeling a traditional bath-tub curve. One or two breakpoints may beselected to compose the curve with Weibulldata models. A hand plot (Figure 2) of thefailure data gives rough idea of transitions todifferent failure rate regions by noticing theslope changes on the three line segmentsroughly fit to the data.

The Weibull plot of the fifty-four dieselengine failures in Figure 2 appears to indicatethree regions of differing failure patterns.However, there are several drawbacks to rely-ing solely on interpretation of this graph.Different analysts may select different break-points. Depending on the time scale, a slightdifference could mean thousands of hoursvariation for scheduled overhaul interval.


FIGURE 2: Hand Plot of CasualtyData on Weibull Paper


Another drawback is inability to plot cen-sored data. A more sophisticated numericalanalysis incorporates the fact that some itemsare replaced before actually failing. Lastly,modern spreadsheet programs provide a con-venient avenue to analyze the data rigorouslyto select breakpoints more consistently. Byanswering if the failure rate is increasing andto what degree, the analyst can calculate opti-mal preventive maintenance.

The first step to understanding the aging-fail-ure rate relationship in this analysis is to plotthe moving average of the Weibull shapeparameter (β) on the ordinate with time(operating hours) on the abscissa. It is veryeasy to see that β begins above one, drops tobelow one (random failures or operating in a“sweet-spot”), followed by a rise to greater

than one (wearout). β plotted in Figure 3 is merely the slope of a seven-point best-fit line on aWeibull plot. Moving a best fit line is more accurate than relying strictly on the analyst toselect break points and “fit” a straight line in each region.

Analysis TechniquesSelecting the ModelThe exponential model was assumed to evaluate Coast Guard casualty performance relativeto a 1979 GIDEP summary report on the same model of diesel engine. The CASREP data iseasily manipulated to calculate MTBF and MTTR:

(2)

The relative performance comparison may only be made in this case with respect to an expo-nential model due only having summary results in the GIDEP report. An organization maydesire failure pattern comparisons instead, which may be accomplished two or more sets ofraw failure data.

Weibull PlottingThe following equation converts data following a Weibull distribution to a linear relationship:

(3)

The slope of the resulting line measures the shape parameter. Once the data is plotted it iseasy to distinguish among the three regions.



FIGURE 3: Average VaryingWeibull ShapeParameter (Beta -β)


Censored Data TechniquesThe data analyzed for this project experiencecensoring from two sources. First, eachengine is overhauled at 24,000 hours. Forthe purposes of this study, the overhaulresets the clock on each propulsion system.The overhaul is right-censoring, or replace-ment before failure. If not corrected for,right-censoring skews reliability parameterestimates conservatively. The second censor-ing occurs because the casualty data extractis only from 1978-1998. All systems underobservation are right-censored at the end ofthe observation period. Six censored eventsarise from overhauls and five from observa-tion termination for a total of eleven right-censored events.

Inozu and Perakis (1991) use the MaximumLikelihood Estimate under right censoring.The Maximum Likelihood Estimate was notused for the analysis in this report but is asfollows:

(4)

(5)

Equations (4) and (5) can be solved simultane-ously to find α and β from the casualty data.

Another method, which was used for theanalysis in this report, is the product-limit(Kaplan-Meier) survivor function (S(t)) esti-mate (Crowder et al. 1991), which is a con-venient way to obtain reliability estimatesfrom the data:

(6)

where dj is the number of failures at time ajand nj is the number of items at risk at aj(i.e. unfailed and uncensored just prior totime aj).

Π (t) indicates the product over all j such thataj < t

The interval survivor function is derived fromthe above equation. Next, Equation (3) veri-fies a Weibull assumption by checking a lin-ear relationship on a Log [Log] v. Log plot.

ResultsExponential ModelUnder the exponential assumption fromEquation (2), the following estimates fromthe casualty data are obtained:

Clearly, the CASREP and GIDEP analysesare from different types of data. The GIDEPdata is for a short observation period. TheALCO-251 in this case is an emergencydiesel generator. The data likely includes allfailures, including those easily repaired bythe operator. Conversely, the CASREP dataaggregates only those failures of significantoperational consequence. Both analyses yieldcomparable availability values, but the main-tenance planning parameters MTBF andMTTR demonstrate the importance of selec-tive data recording schemes and application.

Weibull ModelEquation (3) is used to convert the failuredata to a linear relationship plotted in Figure4. The slope of the best-fit line for this datarepresents b for a Weibull failure distribu-tion. From Equation (3), α = 20393.


Table 2Results from Exponential Model

MTBF MTTR AvailabilityCASREP 6350 hours 257 hours 91%GIDEP 329 hours 8 hours 98%


Censored Data ModelEquations (6) and (3) are used to re-plot therelationship and refine our β and α estimate tocorrect for right censoring. Table 3 comparescensored and non-censored techniques withMTBF, (in this case equal to the expectedvalue E(t) of a Weibull distribution) computedusing Equation (7) (Billington et al. 1991):

(7)

The results show that ignoring censoredtechniques over-estimates the failure rate. Ifscheduled maintenance actions referenceMTBF computed without censored-datatechniques, equipment would be over-main-tained because MTBF is underestimated.Inozu and Perakis (1991) arrived at similarconclusions.

Failure PatternIn order to determine which failure patternor patterns the engine system follows, itmust be known whether β is greater than,less than, or nearly equal to one. Figure 3shows three regions: first, above one, thenless than one, then much greater than one.Table 4 summarizes the regions. Theseresults suggest that there is in fact an operat-ing useful life region, and that failures doincrease as the engine ages to the restorationperiod.

Fitting the Bathtub CurveSubjectively, it appears that the casualty datasupports a failure pattern slightly increasing,then steady useful-life, and finally an increas-ing rate in a wearout region. Dividing theWeibull plot into these three regions gives usthree shape parameters. A numerically accu-



FIGURE 4:Weibull Plot ofCasualty Data WithoutCensoring

Table 3Weibull Model Parameter Censoring Comparison

NO CENSORING CENSORINGβ 1.56 1.38α 20392 25618

MTBF 18324 hours 23604 hours

Table 4Shape Parameter for Aging Regions

OPERATING HOURS ESTIMATED AVERAGE SHAPE PARAMETER (β)0 – 7500 1.25

7500 – 12500 .8512500 – 24000 1.82


rate failure rate curve can aid inplanning maintenance intervalssuch as scheduling restorationbefore the end of the useful life.McCormick (1981) suggests twoways to integrate these parametersinto one hazard rate model. Thesynthesis method weighs the influ-ence of each of the regional failurepatterns using Equation (8) below.If each individual failure patterncan be linked to a specific failuremode than synthesizing the pat-terns with weights relative to fail-ure mode frequency will yield atotal system failure pattern. Thecomposite method uses Equation(9) below and follows the individ-ual regional failure rate pattern forthe appropriate time interval with-out the influence of weighting other failure rate patterns. The composite method is the mostappropriate for our analysis, but Figure 6 shows that it does not produce the traditional “Bathtub Curve.”

(8)

(9)

where λ1, λ2, and λ3 are the respective interval hazard function, and T1 and T2 are the intervalbreakpoints.


FIGURE 5:Weibull Plot ofCasualty Data WithCensoring

Conclusions and RecommendationsThe results of the failure data analysis on theReliance class propulsion system casualtiessupport a lifecycle with an increasing failurerate. The original hypothesis that the evi-dence would indicate either a constant ordecreasing failure rate as operating hoursincrease appears false. The evidence showsthat overhauls do not prevent an increasingwearout failure rate.

The exponential model is not capable ofindicating an increasing or decreasing failure

rate. The Weibull model shows an increasingrate. The 3-part Weibull model most accu-rately represents the failure data. The threeintervals show an increasing, then roughlyconstant, then finally increasing failure rates.

Recently, the Coast Guard has pursued con-dition monitoring and RCM analysis todevelop a preventive maintenance program(MPR Associates, Inc. 1998). Engine failuredata analysis complements condition moni-toring by evaluating current policies. If over-haul intervals are extended as a result, the


CHRISTOPHER MILKIE is industrial manager, USCG Integrated Support Command, Alameda,California. From 2000-2003, he was the high-endurance cutter type desk manager at the USCGMaintenance and Logistics Command, Pacific (MILCPAC). He graduated in 2000 from the University ofMichigan with masters degrees in naval architecture and marine engineering (M.S.E.) and in publicadministration (M.P.A.). He was assigned to the USCGC Jarvis (WHEC 725) from 1996-1998as engineer-

Coast Guard can re-program any deferred orsaved resources. This statistical analysisbrings up many questions that should beaddressed in order to optimize a mainte-nance strategy. Specifically, integrating statis-tical analysis and data collection schemeswith RCM and condition monitoring poli-cies is an opportunity for continuedresearch.

REFERENCES

Anderson and Neri. Reliability-CenteredMaintenance. Elsevier Applied Science, London,1990.

Billington, R. and Allan, R. Reliability Evaluationof Engineering Systems. Plenum Press, New York,1992.

Burt, Mazurana, Steinle, Reick. “USCGC HEALY(WAGB 20) – A Case Study for ImplementingReliability-Centered Maintenance.” [Draft]

Crowder, Kimber, Smith, and Sweeting.Statistical Analysis of Reliability Data. Chapman& Hall, 1991.

GIDEP. Operations Manual. Government-Industry Data Exchange Program, 1994.

Inozu and Perakis. “Statistical Analysis of FailureTime Distributions for Great Lakes MarineDiesels Using Censored Data.” Journal of ShipResearch, Vol. 35, March 1991, 73-82.

McCormick, Norman. Reliability and RiskAnalysis. Academic Press, New York, 1981.

Moore and Perakis. “Development of a DieselEngine Reliability Database (DEREL) for the U.S.Coast Guard.” Marine Technology, December1999.

MPR Associates, Inc. MPR Report 1965, “Resultsof Engine Analysis Demonstration on USCGCSENECA (WMEC 906).” November 1998.

Moubray, John. Reliability-CenteredMaintenance Second Edition. ButterworthHeinemann, 1997.

Smith, Anthony. Reliability-CenteredMaintenance. McGraw-Hill, New York, 1993.

Smith, David. Reliability Maintainability andRisk. Butterworth Heinenmann, 1997.



FIGURE 6:Hazard Rate (lamda)λ(t) from 3-PartComposite WeibullModel


in-training. He graduated from the U.S. Coast Guard Academy in 1996 with a B.S.E in naval architec-ture and marine engineering. He is a member of ASNE and SNAME.

DR. ANASTASSIOS PERAKIS is a tenured associate professor of naval architecture and marineengineering at the University of Michigan. He holds a Ph.D. (1982) and a masters (1980) in ocean engi-neering (ocean systems operations research) from M.I.T. as well as an M.B.A. from the Sloan School ofManagement , M.I.T. (1982). Relevant work includes “Reliability Analysis of Marine Diesel PropulsionSystems: Towards Rational Maintenance, Repair, and Replacement Decisions,” Michigan Sea GrantCollege Program (NOAA) from 1986-1989. He is a member of INFORMS, SNAME, Technical Chamber ofGreece, International Association of Marine Economist, Chairperson NA&OE Committee onDepartment of Defense Graduate Fellowship Awards.


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