推定 算出 お 維持 修 費 Myojo Yuichiro Kanazawa 　　 S A in U Estimating the in Life Cycle Cost

日本 管 理 会 計 学^会誌

管 理 会 計 学20（n年 第13巻 第1・_{2号 （合 併 号 ）}

論 　文

Estimatingthemaintenance 　and 　repair 　cost　inLifeCycleCost 　　calculation ：A case 　of　automobile 　ownership 　inthe　U ．S^．

Vitoon　Puripunyavanich　 ^SatoshiMyojo YuichiroKanazawa

　 　 　 　 Abstract

The　maintenance 　and 　repair　cost　of　dulable　goodS^hastraditionally　been　hidden　from　consumers 　and 　yeI^has been　non −−_negiigiblep^盆rt　ofLife　Cycle　Cosl （LCC ）computation ．　 PrediCting^themaintenance 　and 　repair cost　is　diff三Gult　because　many 　of　these　dulable　goodsdo　not　have　constant 　fanure　Tates ．　For^somedurable producIs^{such 　as　aulo皿obiles ，}it　is　oftenthe　case thatwe have　at藍east　a　rough 　idea　astotheirreliabi置ity．　^In

this　study 　we 　propose^andillustratea　method 　to　convert 　automobile reliabilitydata孟ntheU ．S．！otheir monetary maintenanoe and repaircost．　In^{our　metho4 　we}firsl　estimate　a　staI重stical　modcl 　from　the　widely available 　reliability 　data．　 Thenwe 　predict^{the　reliabi 玉}ityfromthe ^［nodeL 　Finally　we 　convert 重he　predicted

reliability 　10_costfigtlles．　 Tbeproposedstatisticalmodel 　takes_{care 　of}thepossiblebias　introduced　by

partially^missingreliability　data．　Conversion^to　costfigureisdone^on1he　twenty−six　1996−model −year

vehicles 　popularin　Ihe　U ．S．　during　1992−−1999，

　 　 　 　 K画yWords

Life　Cycle　Cost_；Reliability　of 　Aロtomobile_；Nonignorable　Nonresponse_；Multinornial　Logistic　Regression Model

ラ イ ^フサ イ ク^{ル コ ス} ト算 出^にお^ける維 持お よび修理 費用 ^の推 定

　　　　　　　^{ア メ リ カで の} 自動車所有^の 例

　　　　　　　^VitoonPuripunyavanich 明 城 聡 　^{金 澤}雄^{一 郎}

く論 文 趣 旨^〉

これ まで耐 久消費 財^の 維持お よ び 修 理^にか^か る 費 用^に関 し ては， ラ イフサイ クル ^コ ス ト計算^にお

いても無視^{でき ない}費用^であ^るにも^{か かわ} らず消費者は あ ま り知らさ れ て^こな か^っ た．一定の故障 頻度を持^たな^い多くの耐久 消 費 財に^つ いて そ の維持お^{よ び}修 理費用 を 推 定 する^こと は 困 難である．

しか しな が ら例 え ば自^{動 車のよ う な}財^{につ いては}， 少な くと もその信頼性^に関 しては 大 ま か^に で は あるが 情 報 を得^ること がで きる 。そ こで本研究^ではア メ リ カ自動車信頼性デー_{タ か ら維 持} ・_{修 理} 費 用 を 算 出 方 法^{につ い}て提 案 する ．こ の 方 法では まず 広 く利用 可能^な信頼性^デ ー_{タ か}

ら統 計 的^モデ

ル を推定する．_そして モ デ^ルか ら推定 さ れる 自動車^の信頼 性^か ら費用^へ 変換 を行 う，こ こで用^い る

統計的^モ デル で は部 分的^に欠損 し^{て い} る 信 頼 性 デー_{タ か ら起こ り うる偏 りの問 題に}対処す る^こと を可能^{に して い る}．_具体 的^な費用算出 例 と し^て 1996年^モ デルイ ヤー_{におい て人 気の あ}

っ た26車種 を

取 ^り上げ た，

〈 キ ー_ワー _ド〉

ライ ^フ サ イ ク^ルコ ス ト， 自^{動 車 信}頼 性， 無視^{で き ない}非 応 答， 多項^{ロ ジス}テ ィ ッ ク回帰^{モ デ ル} 2003年3月26日　 受付

2004年3月30日　 受理 筑 波 大 学

Submitted26，^{March 　2003}． Accepted　30，^March2004． Universityof　Tsukuba

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Wmpftat7 ig13ts^ag1･2t (al#g)

1Introduction

The L`cost"

of a product forconsurners has traditionallybeen equated with itsprice ^at the time of

purchase,For some products, however,thisdefinition^{of cost can} bd quitemisleading. For example,

inthe case of many durable_goods,significant cost will be incurredinthe use and maintenance of the product ^{over a} period ^of years. LifeCycleCost (LCC),^{which includesall the costs associated with}

acquisition, use, maintenance, and disposal,ismore reasonable alternativetoevaluate such products.

Consumersthemselves havebecome increasinglyaware of not only the cost of acquiring butthe cost associated with use, maintenance and disposalof the durableproducts.^{This awareness} hasbeen_partially translated^intotheU,S,regulations. Forexample, the U.S.government,^{through the} Energy Policyand

ConservationAct (EPCA)^{of 1975,hasbeen asking home} appliance manufacturers todiscloseenergy

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consumption on theirproducts(McNeill^{et al.1979,Hutton et ai. 1980).}

^{The EPCA also included a "New Auto FuelEconomy} Program,"inwhich Departmentof Ttansporta- tion(DOT) ^{was directedtoset} C`corporate average fueleconomy" _standard fornew car starting inmodel

year1978,and fbrnew lighttrucks starting in1979.Eachautornaker was required tomeet the standard, subject to1arge finesfornon-compliance. The _{program put} Environmental ProtectionAgency (EPA)

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incharge of measuring fueleconomy foreach model, of setting up NationalVehieleand FUelEmissions '

LaboratorytQdeterminecar manufacturers' compliance with federalemissions and fuel economy stan-

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daTds.The prograrri^asked Department of Energy (DOE)^topublish^the IltielEconomy Guide^{as an} aid toconsumgrs considering the purchase^{ofa new car,} The Guide Iistsestimates of iniles pergallon(mpg)

foreach vehicle aMailable forthe new model year. These estimates have beenprovided by the EPA.

Of ^all durab!e_products consurners purchase, ^automobile iswithout doubt themost expensive, Fbr

exarnple, according tothe U,S.Consumer ExpenditureSurveyin1998,expenditure on vehic]e purchases,

gasoline^{and motor oil and other vehicle expenses amounted to} $6,358or 17.06% of average household

expenditure of $37,260,

Consumers tend tohave a pretty good ideaon acquisition cost of automobile beforethe time of

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purchase from_the sticker price^and pricequetation^services frem such organizations as ConsumerUnion.

By lookingat the window-stickers and using the FUelEconomy Guide,consumers can and are expected

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toroughly estimate the average yeaily fuel cost fot any vehicre,

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It^isdiMcult,however,topredict^{repair cest} for^{a specific} automobile becauseitvaries fromone modei

toanother and the average maintenance and repair cost, for^{example, inthe U.S.Consumer}Expenditure

Survey,^{doesnot apply to the} particular^{automobile of consumer;s choice.} Untilnow there hasbeen no regulation requiring Federal and State_government oMce toestimate the repair cost of automobile.

There ^{are state} government regulations such as the Lemon Laws stipulating the manufacturers to

take some responsibility to the defectof the product^they manufactured. CaliforniaLemon Law - CA

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Civil^{Code Section1793,22} (Tanner^{Consumer ProtectionAct)isone such example. Althoughthe Lemon}

Laws likethisone are protecting^consumers intheirfirstyear^{of car ownership} throughoutthecountry, typlcalconsumers still haveat leastseven more yearstothink about the repair cost, because^"the median

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Estimating the malntenance and repair cost inLifeCycle Cost calculation :

-A _{case efautomobile ownership intheU.S.-}

age of cars on the road in 1999ismore than 8 _years, compared with 6} _years in 1990" (April¹⁹⁹⁹

Consumer Reports_page 97),Publiccan consult publications ^{such as} Consumer Reportsor can access to theirwebsite ferthefrequency^{of repair} of the specific make and model. Inthispaper ^{we will} propose

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and illustratea methed to convert that knowledgeofthe frequencyof repair to ^`:monetary repair cost."

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^Incurrent practice,rnaintenanee and repair cost of ageneralproduct isestimated thtough the usage

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of databases and professional^opinions (Taylor^{!981). The reason forthisisthe factthat the repair cost}

depends on maintainability and reliability parameters,^{While most electronic components are considered} tohaveconstant failurerates (exponentialdistributions)-_which coincidentally simplifies themathernatics

forcalculating the often used mean time befbrefailure(MTBF)^{and mean time to repair} (MTTR),

reliabilitylmaintainability of non-electronic components havenon-constant failurerates and can leadto the unwary tointractablemathematics (Fricker^{1979,De Neumann 1983),} Automobiles,as computerized

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as they may be,havesignificant ^mechanical components. This makes itvery diMcult to ebtain theoretical model ofthe reliability and maintainability of autprnobiles, leavingus an ^{only choice of} statistical method

fortracingthem.

Our ^method isas follows:We firstestimate ^astatistical ^model regressing thereliability summariesi in five_point ordinal scale published inthe Consumer Reportson several designcharacteristics of automobile and several attributive dummy ^variables, We ^choose theseexplanatory variables becausetheyare easily aNailable tobuyersthinking of purchasing^{anew car.} Then we predictthereliability score from thernodel,

Finallywe convert our predicted reliability score to cost figureusing the datafrotnseveral sources.

As an example, ^we estimate the vehicle-specific maintenance and repair costs inU,S.^dollarsfor

twenty-six popular 1996-model-yearvehicles intheirfirsteight years^{of ownership.} They are selected

fromthethirtybest-sellingpassenger^{cars and the twenty} best-sellingminivans, SUVs,and pickup^trucks inthe United Statesduring 1992-1999 and were consistently on the best-sellinglistthroughout the period.Sincethesepopularfifty^{vehicles and theirsiblings covered 73.1% of all the vehicles sold in1996}

and covered al]market segments-passenger car, minivan, SUV, and pickuptruck-important toaverage consumers, ^we believe^{the choice} isrepresentative,

^This paper ^{isorganized as} foIlows.The methods usecl inestimating the statistical model and con- verting the ^model into cost figureare describedinsection 2,Insection 3,the result ispresented, ^and in

section 4 we discussthe result. Appendix A exp]ains how we estimated the statistical model. Appendix

B descrlbesindetai1how ^{we calculated the} vehicle-specific ratio formaintenaiice and repair cost.

2Methods

Maintenance and repair cost bymodel and year^were ingeneral^{not available.} What we haveinsteadare;

1,^Yearly clataon average cost forautomobile maintenance and repair over alt consumers from the Consu7nerEupenditureSurveyi

2.Estimatesof ^`CtypicaV' itemizedmaintenance and repair cost by^{model fbreight major mechanical}

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^systems for1996-model-yearvehicles compiled fromthtchell^MechanicalPartsevLaborEstimating

Guide2002 _part of which islistedinthble 1;

'Table

1:Subsystemand totalrepair costs fOreight major mechanical systems includinglaborand their reliabilities for1996-model-yearvehicles in1999.

Major System Subsystem Ford^{Taurus Honda Accord Tbyota} Camry ･･,

A!C Blower + Heater Core Cemp:e$sor

[[btal ReHabi]ity

$461

$559$1,020

4

$973

$594$1,567

4

$551

$SS6$1,437

･･･

5

Cooiing Water Pump

RadiatDr + Hose Tetal Reliability

$260$671$e31

2

$408$383$T91

5

$324$55S$8S2

･･･

5 Electrical Windew Motor

Wiper Moter

Total Reliabllity

$150$148$298

2

$182$265$447

4

$316$240$556

･･･

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Subsysterns cerresponding to Augst 2000issueef Consumer Reports were listed.

3.Desigricharacteristicsof 1996-model-yearvehicles and theirsales data from WbTzi'sAutomotive

M7arbooksin1996and 1997;

4.The totalnumber of up-to-eight-year-old vehicles ofon theroad in1999from WardlsMotor Vbhicle thctsand Figures in2000inFigure^2;

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5.Thelikelihoodsof problems ineach of theeight major systems for1996-model-yearvehicle between 1996-2eOlfrom April1997-2002 Consumer Reports_part of which isalsolistedinTable 1;

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6.Annual(1996-2001)Classifications^of 1996-model-year yehicles intofive(three^{inApril2000issue}

^and thereafter)reliability categories fromApril1997-2002 ConsumerReportsl

^7,Annual(1992-2001)^{estimates of the number of} problems ^of 1992-2001-model-yearvehicles by reliability categories inApril1993-2002 Consumer Reports. Table 2 isthe estimates for1996- ^{model-year vehicle.}

We ^{will use} thesedatatoconstruct estimates of lifetimemaintenance and repair cost. The Consumer E!v-

penditure Surveyisbasedon a carefu11y designedsample, theestimates of "typical"

itemizedmaintenance and repair cost and designcharacteristics ef 1996-model-yearvehicles are engineering data,and the total number of up-to-eight-year-old vehicles of on theroad isbased on sales data,These may be _presumed

statistically reliable. However the samples on which reliability calculations are basedare selfselected:

they are solicited by ConsumerReports.It^seems _possiblethat owners of unreliabre automobiles are

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Estimating the maintenance and repair cost inLifeCycleCostealculation :

"A _{case of automobile ownership inthe U.S.-}

[lable2:The annual estimates of the number of problems^of 1996-model-year vehicle when itsreliability

falIsintoone of the five(three^{in1999 and} thereaeter)categories, ReliabilitySurnmary

^{Year 1(1) 2(1) 3(2) 4(3) 5{3)}

1996 O.490 O.402 O.283 O.258 O.190 1997 O.775 O,640 D.503 O.3B2 O.2S6 1998 O,9Sl O.859 O,661 O.519 e.297

1999 1.124 O.747 O.450 2000 1.225 O,889 O.503

2001 1.352 O.950 O.530

2002 l.451 1.099 O.679

2003 1.558 1.223 O.705

overrepresented inthe^sample, leadingto asarnple selection bias.Thisisaggravated by the factthat if thereare too fewresponses fbr^a _givenmodellmodel-year insome year, ConsumerReports^{reports a miss-}

ingvalue. We next turn to a careful descriptionof the reliability data,and the statistical methodelogy applied toreduee selection biases.

Predicted ReliabilityScore vs ReliabilitySummaries

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There havebeen two automobile reliability scores publishedⁱⁿ Consumer Reports,"predicted

reliability score" and "reliability summaries." The reliability summaries are the weighted sum of the problem^rates

of al1_problem spots year byyear,^car bycar, Consumer Reportsdescribedthat ^`tthe reliability summaries show how each model compares with theoveral) average forthat model year"^{and "the scores in}reliability summaries are on relative scale, compared with the ayerage foral1models of the same yeat,from much worse than average tomuch betterthan average" on a five-pointscale (April^{1998 Consumer Reports).}

The predictedreliability scores, on the other hand, are thejudgment^{based on the three most recent}

years^of reliability summaries. With theirauto engineers' knowledgeof the current year's^{models and} the

reliability dataforthepast ^models, ConsumerReportsclaim that^they havebeenable togivereliability prediction formest current models.

Pastexperiences, however,showed that_predicted reliability scores might not be as accurate as the

name implied. Fbr example, out of 103,163 and 150 of 1996-model-yearyehicles surveyed inApri]

1997-1999issuesrespectively, 46.6%,^45.4%,^and 44.0% ^ef them registered reliability summaries that

were differentfrom the reliability scores predictedinApril1996issue.inthisstudy we chosereliability summaries as the measurement of reliability fortwo reasons: firstitreflected the aetual response, not prediction, from the readers in Annual Questionnaire;^{second the way itwas} computed-relative to

the average foral1models of the same year, ^{which can} be easily determined-enabled us to calculate

vehicle-speeific reliability summaries,

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Nonignorable ^Missing Value Problem

There aare two potentialproblems in Consumer RepoTts'reliability summaries: the number of ^responses

fromowners of automebiles with fewsales might betoolimitedtoreliably evaluate thesecars, making

"insuMcient data"entries toappear intheirreliability summaries; comparatively more owners might hewe

responded totheir^surveys iftheyhad beendissatisfied^{with the} reliability of their^own vehicles, elther out of obligation to make the informationewailable to pub]ic,^{or simply toconvey their}frustration.

Especiallythe`[non-ignorable" non-response problern<sup>of the</sup> latter-in<sup>sample survey</sup> terminology, a variable Y with unit nonresponse iscategorized as `lrion-ignorably missing" ifsome of the Y are missing

because ofthe underlying values ittakes-could rnake the responses fromowners of unreliable automebiles overrepresented inthe sample and seriously distortthe analysis, Seeappendix A forhow theseproblems

were addressed,

Data for Estimating ^the StatisticalModels

Reliabilitysummaries were the response variable forthe mu]tinemial cumulative probabilitylogistic

regression model inequation (1)^{inappendix A. We used} reliability summaries for1996model years published inApril1997-2002Consumer Reports.We assigned scores 5^{to1to entries of much} betterthan

average tomuch worse than aNerage in1997to1999issues,In^April2000issueand thereafter,reliability summaries were recorded on a 3 point-scale-better^{than average, average, worse than} average-and

called the "reliability

verdict."2 We assigned scores 3to 1tothem. There were 84(47,7%),³⁵ (19.9%),

47 (26.7%),⁴⁸ (27.3%),⁵³ (30,1%)^{and 63} (35.8%)^missing reliability summaries ^out ef 176models in 1996, 1997,1998, 1999,2000 and 2001respeetively. We ^coded thern as "NA"

and includedthem. The

observed data^{indicatorwas the responGe varjable for}the binomiallogisticregression model inequation

(3)^{inappendix A,The models in}(1)^{and (3)were} sirnultaneously estimated,

^{Due to the qualityof the parts,the nature of the design,or the production technique, sorne medels}

suffer preblems ^{at a rate} farloweror higherthan^what one might expect from^{sheer aging.} Explanatory

variables formodel (1)^{were: cars' design}characteristics-maximum horsepower,displacementinliters,

weight in_pounds and lengthininches;two dummy variables-one indicatingmariufacturers' country of

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origin beingJapan and the other being Europe3-choosing U.S. as baselineieight t`segment;'

category

dummy ^{variables indicatingwhether} a ^vehicLe was small, large,^luxury,sportfsporty, coupe, pickup truck,

SUV and minivan selecting medium passenger ^{cars as} baseline;one dummy variable indicatingwhether

the ^model was completely redesigned or newly introduced in 1996 by the Big Three (redesigned^for

short),4 These data were taken from Ward's Automotive^}fliarbookin1996. The designcharacteristics were those of the mid-prieed models. We assume sales volume and reliabi]ity summary of each model could affect missing entries of itsreliability summary, and used the sales figurearid reliability score as

explanatory variables inmodel {3).

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