Kaizen Costing -Formulation and Practical Use of the Half-Life Model

8/20/2019 Kaizen Costing -Formulation and Practical Use of the Half-Life Model

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Control Measures for Kaizen Costing

-Formulation and Practical Use of the Half-

Life Model

Thomas M. Fischer / Jochen A. Schmitz

Prof. Dr. Thomas M. Fischer Lehrstuhl fur ABWL,

Controlling und Wirtschaftsprufung

Wirtschaftswissenschaftliche Faultat !atholische

"ni#ersitat $ichstatt%&ngolstadt Auf der 'chan( )* +-)*

&ngolstadt Tel. -+)/ 0 *12%/*3 e%mail seretariat%

cwp4u%eichstaett.de www.u%eichstaett.de

mailto:[email protected]:[email protected]://www.ku-eichstaett.de/http://www.ku-eichstaett.de/mailto:[email protected]:[email protected]


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Abstract

!ai(en costing focuses on continuous reductions of costs,

which should 6e reali(ed for e:isting products in a

compan7. For planning and control purposes,

comprehensi#e and efficient tools for measuring

performance are re9uired. For this purpose we suggest the

so%called ;half%life model;. &t is 6ased on the practical

e:perience, that an7 defect le#el decreases at a constant

rate o#er a certain time period. This paper gi#es the

mathematical formulation for this model and illustrates its

practical use with different e:amples.

1 The aradigm of !aizen costing

Kaizen costing focuses on continuous reductions of costs,

which should be realized for existing roducts in a coman!"

.

To shae a coman!#s cost structure according to cometiti$e

re%uirements, a sound anal!sis of a coman!#s cost dri$ers is

needed. From a customer#s ersecti$e, onl! so&called $alue&

adding cost dri$ers are rele$ant, e.g. no. of durabilit! tests,

mean&time&between&failure, etc. As those cost dri$ers ro$ide

the customer&$alue, customers will a! for the resources

consumed. 'owe$er, resource consumtion should be reduced

in order to imro$e a coman!#s roducti$it!. (n the other


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Therefore, non&$alue&adding cost dri$ers ha$e to be adusted

according to best ractice&standards. To a$oid losses, the!

must either be reduced to a cometitor#s minimum le$el or the!

ha$e to be eliminated comletel!. To reach this goal, a

coman!#s cost dri$ers ha$e to be anal!sed s!stematicall!.

Cost driver analysis

0ach 1e! cost comonent of the abo$e mentioned ga

between the le$el of actual costs and the identified best

ractice cost le$el has to be anal!sed in the following stes.

• Determine the activities that drive the key cost components of the cost gap.

For examle, the actual costs could contain enalties, which

ha$e been aid to customers. To a$oid losses in the future,

the! should be eliminated comletel!. Therefore it is necessar!

to identif! the acti$ities that caused enalties b! brea1ing their

root causes down into a finer and finer le$el of detail, such as,


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enalties caused b! artial shiments, late shiments, and/or shiments of wrong roducts.

•Determine the root causes of the activities that drive the key cost components.

A more detailed anal!sis of the shiment&related dri$ers showed three root causes3

"4raw materials not within secification5 4confusing sales

order documentation5 and -4oor wor1manshi in the

manufacturing rocess.

• Determine the financial impact of the root causes of the cost gap.

(nce the root causes of the acti$ities dri$ing the 1e! cost comonents of the cost ga are

1nown, relati$e ercentages of the total financial imact of the cost ga are assigned to the

acti$ities and to the root causes. 6n this wa!, the financial imact of a secific 1e! cost

comonent can be traced bac1 to the secific acti$it! and root cause. Finall!, the identified root

causes can be groued together in turn to determine their financial imact. For examle, the

largest financial imact could rise from the root cause oor raw materials. The riorit! of

imro$ement rograms should be adusted according to the financial imact of the root causes.

For monitoring the cost reductions realized b! the imro$ement of a coman!#s cost dri$ers, an

aroriate management tool is needed.

Tools for monitoring the cost reductions

For lanning and control of cost reductions, comrehensi$e and efficient tools for measurement

are re%uired. From a manager#s ersecti$e, tools for monitoring the imro$ement of a

coman!#s cost dri$ers are needed. For this urose we suggest the so&called half&life model.


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6t is based on the ractical exerience, that an! defect le$el decreases at a secific rate o$er a

certain time eriod3 A half&life cur$e measures the time it ta1es to achie$e a +7

ercentimro$ement in a secified erformance measure,- for examle, cutting the number of

defecti$e lots recei$ed from a $endor b! half 8see exhibit "9.

"#hibit 1$ :eduction of defecti$e lots with the half&life model

8Source3 Arthur M. Schneidermann, Setting ;ualit! goals3 ++9

6n general, starting oints for cost reductions ma! be found within the roduct features, the

acti$ities erformed in the $alue chain, or the resources consumed in those acti$ities. As non&

$alue&adding cost dri$ers, e.g. customer resonse time, deferred deli$eries, late deli$eries,

and first&ass&!ield, need to be reduced in order to imro$e a coman!#s rofitabilit!, the! ma!

be considered to be defect le$els in a more general sense.

of non&$alue&adding cost dri$ers, therefore, the half&life model ro$ides a useful tool for closing

an existing cost ga in the 1aizen costing rocess.

-=ar$in, "**-, . >*5 Schneiderman, "**?, . ".


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% Formulation of the half-life model %&1 'asic

half-life model

6n this model, =t reresents the defect le$el at an! gi$en time t. The word

defect is used in its most general sense, which includes errors, rewor1, !ield loss,

unnecessar! reorts, c!cle times 8manufacturing, design, administrati$e, etc.9, unscheduled

downtime, in$entor!, emlo!ee turno$er, absenteeism, lateness, unrealized human otential,

accidents, late deli$eries, order lead time, setu time, cost of oor %ualit! and warrant! costs. 6n

fact, =t can be an!

measurable %uantit! that is in need of imro$ement but onl! if the aim is to reduce this

erformance measure. @e will also use the word roblem interchangeabl! with the word

defect. =t can reresent an! measure that

de$iates from its otimal $alue.

The difference of the initial defect le$el =t- and the minimum defect le$el =min

decreases b! +7 ercent within a constant time eriod, which is called 8defect9 half&life t>.

)onsider for examle, an initial defect le$el of ",777 units and a

defect half&life of six months. Then, after the first six months, the defect le$el would be down to

+77 units, after the next six months down to +7 units, and so on.


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To determine the half&life function of a business rocess, the following fi$e stes ha$e to be

carried out within a coman!3

"4selection of the business rocess and half&life arameter to be anal!sed 8e.g.

c!cle time of customer order rocessing95 4determination of an

aroriate half&life measure 8e.g. da!s95 -4determination of the initial defect

le$el 8=to95

4e$aluation of the defect le$el 8=t95 +4

calculation of the half&life time 8t>9.

Blotting the defect le$el =t against time t on a semi&log scale re$eals a negati$e

linear relationshi between the two $ariables 8see exhibit "9. The shorter 8longer9 the half&life of

the anal!sed rocess, the steeer 8lower9 the line runs.

After one half&life 8t>9 has assed, the remaining defect le$el 8=t9 at time t can be described as

follows3

8"9 =t C ?=#

Deendent on the number i 8i e @ 9 of erformed half&life c!cles the defect le$el 8 =t 9 can

generall! be calculated as3

89 EtC;&9#!

6nserting i C % t E time, t- C initial time into the e%uation !ields the following

exression3

f t & to

8-9 =t Et> 7 =t


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To calculate the half&life t > we ha$e to ta1e the natural logarithm of e%uation -. An examle

shall illustrate the ractical use of the modified half&life model. 6n

Januar! 8 t- E/ a coman! had to deal with =t- E/,--- customer comlaints. 6n

Jul! 8t C 29 the le$el of customer comlaints has come down to =2 E /3. 'ow long is the half&

life t> 4

89 t> E%%%%%%%%%%%%%%%%%%%E%%%%%%%%%%%%%%%%%%%%E 3.- months.> ln=t % ln=t ln/3 % ln/,---

'ow man! half&life c!cles ha$e been realized between Januar! and Jul!4


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*

8+9 i E %LA>

2%/ G lnl3%&nl.HHH G 1 c7?.

3ln%3t


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/-

'ow man! customer comlaints ha$e to be exected in o$ember 8tC""94


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8?9 =t%t

/ l l

3

I =to G ? J /,--- K 1/ customer

complaints.

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The underl!ing assumtion of the half&life model shows high similarit! to the deca!

henomenon 1nown from h!sics. There a deca! constant l exresses the robabilit! that a

radium nucleus will deca! within the next moment. Thus, the number of radium atoms at actual

time t can be exressed as follows3

nt G e

nf. no. of atoms at time t, nto$ no. of

atoms at initial time

l3 deca! constant.

6f the number of atoms decreases b! +7 ercent at a certain time eriod 8i.e. half&life t'9, the

deca! constant is determined b! l C 8ln / t'9. 0ntering this in the abo$e formula we get3

Setting to C 7 and Emin C 7, this e%uation is identical with the half&life model which we used for

measuring continuous imro$ement.

A closer loo1 at the mathematical deri$ation of the half&life function shows that the half&life time

of a business rocess is determined b! a single measure of the defect le$el at time t 8 =t9. The

half&life model describes the efforts of a coman!

to reduce non&$alue adding cost dri$ers. To close an existing cost ga between

)

e.g. =erthsen/Gogel, "**-, . ?*.


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target costs and drifting costs as soon as ossible, an aroriate selection of measures for the

coman!#s most critical defect le$els is necessar!3

H no. of defect roducts5

H no. of customer comlaints5

H no. of late deli$eries5

H no. of incomlete deli$eries5

H no. of roduct rewor1s5

H order c!cle times5

H deartment c!cle times 8:ID, Manufacturing, Sales, Ser$ice95

H function c!cle times 8Set&u, Maintenance, Transort9.

The half&life model enables managers to lan ex ante the rogress of continuous imro$ement

rograms+. 6t is imortant to reach a high relati(e imro(ement rate 8i.e. realized degree of

imro$ement within a certain time eriod, e.g. da!, month, !ear93 the shorter the half&life of a

business rocess, the higher is the imro$ement rate of the organization. Thus, the half&life time

becomes an indicator of a coman!#s caabilit! to erform organizational learning.

%&% Modif)ing the basic half-life model

The assumtion for the basic half&life model is that an! defect le$el decreases at a secific

rate?. The roosed model focuses on the determination of necessar! reductions in $arious

measures of cororate oerations 8e.g. order c!cle times, deferred deli$eries9, which are

defined as the difference between some initial $alue of the arameter 8 = 9 and its desirable

minimum $alue

8=mm 92. This aroach ma! raise the %uestion of wh!, in the context of continuous imro$ement

of rocesses, the targeted minimum le$el 8=mm9 should be held constant, e$en though new

+ Stata, "*>*, . ?*.

? Schneiderman, "*>>, . +-.


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/)otimal minimum $alues might occur o$er time. To ma1e redictions about future $alues of the

examined arameters 8=t9, forecasts would ha$e to be based on the initial $alue 8 = 9 instead of the

ex ante determined imro$ement $alue = &=mm9. This would a$oid forecast errors resulting

from a mista1enl! estimated desired $alue 8=mm9. 6n doing this,

the original mathematical foundation of the concet gi$en b! Schneiderman needs to be altered.

This is done in the following wa!.

=mm reresents the minimum achie$able le$el of =t. @hen tal1ing about

defects or errors, =mm is otentiall! zero. 'owe$er, when considering for

examle c!cle times or !ields, a $alue of zero might $iolate the laws of h!sics. The term =t

%=min can be thought of as a mathematical generalization of

waste or muda as it is called b! the Jaanese. This exression is not targeted at manufacturing

defects onl!5 it is alicable to an!thing in need of imro$ement.

According to Schneiderman>, the modified half&life model is mathematicall! formulated as

follows3

After one half&life 8t>9 has assed, the remaining imro$ement ga =t & =mm9 can be described

as follows3

829 = & = . C/ = & = .

Deendent on the number i of erformed half&life c!cles 8i e@9, the imro$ement ga 8 =t &

=m.n 9 can generall! be exressed as3

Schneiderman, "*>>, . +-./)


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8>9

= % =: t : min


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The number of half&life c!cles i which occurred within a certain business rocess, is deendent

on the se%uence of half&li$es t>, which could ha$e been

realized in the eriod between initial time t- and time t. 6nserting this relation

into e%uation 8>9 !ields the following exression3

8*9 =t min ? 3J \ t- min J ■with=t C defect le$el at time t,

C defect le$el at initial time t7

= .mm

C minimum defect le$el,

t C time t,

C initial time,

t> C half&life time.

To calculate the half&life t> of a secific business rocess we ha$e to ta1e the natural logarithm

of e%uation 8*9.

Again, an examle can illustrate the ractical use of the modified basic half&life model.

At the end of Januar! 8t- /9 in the new fiscal !ear, the sales manager at EL )or. had to deal

with = /,--- customer comlaints. As a minimum achie$able defect le$el the coman! wants

to ha$e =min G/- customer comlaints. 6n Jul! 8t C 29 the le$el of customer comlaints has come

down to

=2 /1).

'ow long is the half&life t> 4

t &/-%ln%2 &/%ln3

8"79 t> %%%%%%%%%%%%%%%%%%%r2 ------7 —------------r2&&&&&&&&&&& 3.- months .ln=

t& =

min&ln=

t- & ln/1)&/- &ln/,---&/-

'ow man! half&life c!cles ha$e been realized between Januar! and Jul!4 t&/-

2&/ ln/1)&/-%ln/,---&/- o l ir8""9 i C&&&&&&&&&/ C A&&&&&&i C i&&&&&&&&&&&&&&&1 G/8%%%%%%%%%%L » 1 half%life c7cles.t 3 / /

3

Schneiderman, "*>>, . +-./


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'ow man! customer comlaints could the sales manager exect to deal with in o$ember 8t C

""94

8"9

=// E 8T9t>

.7t- % =min =min E 23

./,--- %/- /- E )/ customer complaints.

6n which month t will the coman! ha$e reached the number of =t E3/ customer comlaints4

8"-9 t C t>Nln=t & =min&ln=t- & =min//-

ln%3

For =t- E /,---, =min E /-, t- E / 8Januar!9 and t> E 3 months the results are3

8"9 3Nln 3/ %/-% ln/,--- %/-O

t E %%%%%%%%%%%%%%/%%%%%%%%%%%%%/ /K /) months i. e end of Fe6ruar7 ne:t 7ear .

3

@hen will the coman! robabl! reach the achie$ed minimum defect le$el

=min C /- 4

min

6f we would li1e to answer this %uestion, we ha$e to thin1 of the 8theoretical9 ossibilit! that =t C

=min 8note3 6n the abo$e described basic half&life model, the

same %uestion would arise for Y t C -9. Thus, the e%uations for determining the

half&life will contain the following exressions3

8"+9 ln=t & =min C ln- N O 8basic half&life model3 ln=t C ln- N O 9.

This means, t will ta1e an infinite $alue. 6n other words, the achie$ed minimum defect le$el =min

could be realized onl! in infinite time.

This roblem could be handled b! the definition of a tolerance zone

e C l=t & =mi8 where


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H e = " for discrete =t 8e.g. no. of customer comlaints, late deli$eries etc.95 and

H 7 P e < " for continuous =t 8!ield, c!cle times etc.9.

The smaller the $alue of e, the higher the corresonding $alues of t would become.

@ith the data of the abo$e described examle, for different $alues of e the corresonding $alues

of t> would be3

H e C -./ &Qt C 2.++ months5

H e C -.-/ &Qt C -."* months5 and

H e C -.--/ &Qt C 2.> months.

6n our examle, for a tolerance zone e C =t & =mm C // &/ C /, time t for reaching the achie$ed

minimum defect le$el =mm C /- can be calculated as follows3

3Nln// &/-% ln/,--- &/-O8"?9 t C&&&&&&&&&&&&&&&&&&&&&R&&&&&&&&&&&&&&&&&a / 3/ months i. e 'eptem6er ne:t 7ear.

ln%

3

0xhibit summarizes the different $alues of actual defect le$els =t for an!

secific erformance measure. 6t becomes ob$ious, that roections for necessar!

imro$ements of a secific erformance measure can differ, deending on which half&life model

is chosen.

"7 &

"77

>7

?7

7

7

" - + ? 2 > * "7""""-""+"?"2">"*7"-+?2>

months


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"#hibit %$ )omarison of the different concets of the half&life model * +alidit) of the

half-life model

The $alidit! of the half&life model deends uon the reliabilit! and stabilit! of a once comuted

half&life o$er time. 0xhibit - summarises the results of fitting ? indeendent imro$ement

roects to the model.

,mro(ement roect half-life time tH no& of imro(ement coefficient of .months/ c)cles i determination 0%

Gendor defect le$el transistors *.? -.2 7.**2

Uate deli$eries to customers 87.& wee1s9 -7. 7.> 7.**

Defect le$els customers# incoming ;) "7." 2." 7.*>*

Failure rate di soldering rocess -.2 >.? 7.*>7

@6B ?.- "." 7.*2*

Defecti$e lots recei$ed from $endors ".? ".2 7.*2?

)ustomer returns because of roduct ". .* 7.*2

Defects caused b! its iston rings +.+ -.+ 7.*?>

Absenteeism caused b! accidents ".> .7 7.*+?

First !ear warrant! costs 2.> .? 7.*+7

Defects er unit 2.? .? 7.*>

Missing roduct features ".+ .* 7.*2

)(B; goggles manufacturer .2 ".* 7.*

)ustomer returns caused b! administrati$e ?.- -.> 7.*"

0%uiment downtime "-." ." 7.*7

Manufacturing c!cle time "?.* .+ 7.*-2Scra and reair costs +.7 ".? 7.*">

Failure costs 8internal claims9 -2.* ".* 7.*7*

Accident rate ".+ .> 7.*72

Gendor defect le$el 6) linears 2. .* 7.*7?

Failure rate line assembl! 2.+ -. 7.>>?

Defects in $acuum molding +.? .? 7.>>

0rror rate eretual in$entor! "." -.7 7.>?

Field failure rate 7.- ".- 7.>+2

Defects on arri$al "?.* .7 7.>>

Defecti$e stoc1ings .2 . 7.>-

Eield loss B)< hoto imaging .* .- 7.>-

Gendor defect le$el transformers 2. +.7 7.>Bost&release redesign "*.7 .+ 7.>

Uate orders to customers -.7 .2 7.>->

Gendor defect le$el microrocessors ">.+ ".* 7.>->

(erations sheet errors 7.? . 7.>-

Gendor defect le$el caacitors +.2 ?.- 7.>"

Scra costs "-.> ".2 7.>7+

:ewor1 rate >.7 ". 7.>7"

Da!s late in deli$er! 7.> 2.? 7.22

@arrant! failure rates -?. .+ 7.2?*

Scra costs die coat insection . .7 7.2+

T!ing errors in ban1 telegram deartment .* .7 7.2+

B)< hoto imaging resist fla1e ".* -.- 7.2>

Scra and reair costs +.7 7.> 7.2?Manufacturing c!cle time 2.? .2 7.2"

6nsertion defect rate -.- -. 7.2->

Eield loss die coat insection . .- 7.2--

Broduct de$eloment c!cle time ++.- "." 7.2--

Aluminum smears from 6) test ads . +." 7.2"2

Accounting miscodes ?. .+ 7.27*

Setu time *.+ 7.? 7.?*7

onconformances "?.* 7.2 7.???

7


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3-Defects at turn on ".* ".- 7.?

:eects caused b! bends and dents ".- ".2 7.+*7

Downtime of facilities .+ ".- 7.+?

6n&rocess defect rate +.- "." 7.++7

Brocess sheet errors ". ." 7.+-+

0rrors in urchase orders .- ".+ 7.+-"

(ff&sec reects >.> +." 7.+-"

Manufacturing scra 2.7 -.* 7.+-7Uate sare arts to customers +.- "." 7.2"

)omuter rogram execution errors *.* 7. 7.-?

A(erage 1&% %&2 &3*4

"#hibit *$ Galidit! of the half&life model 8Source3 A. M. Schneiderman, Setting

;ualit! =oals3 +9

A large $alue for the number of imro$ement c!cles indicates a mature roect, while a small

$alue is indicati$e of a start&u effort. The final column contains the coefficient of determination

8@ 39 of the regression and is a measure of how well emirical data fit with the theoretical half&life

model. A $alue of @ 3 close to one indicates that the model exlains the data at a high statistical

confidence le$el. A $alue close to zero imlies that little of the obser$ed data is exlained b! the

model. The secific interretation of $alues between but not e%ual to either zero or one is so far

an unresol$ed issue3

The %uestion is often as1ed as to how high @ 3 should be before the results are $alid. The

answer to this %uestion, unfortunatel!, is it deends. For some alications, an @ 3 of 7.*+ is not

good enough, while for others, 7.+ would be considered ade%uate. 6n medicine, for examle,

regression e%uations are often not acceted unless @ 3 V 7.**, while in beha$ioral or mar1eting

studies where human beha$ior is in$ol$ed, @ 3 $alues of about 7."+ or 7. are considered

satisfactor!.*.

The data in exhibit - show an a$erage $alue of @ 3 C 7.22. The statistical significance of the

results should be udged against the %ualitati$e criteria gi$en abo$e. The a$erage number of

imro$ement c!cles was i C .?. That corresonds to a reduction 8b! a factor9 of 33.


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classification is suggested along the dimensions of san of control or organizational

comlexit!"7. For examle, a number of roects aear to be within a single organizational

function as measured b! the team#s abilit! to autonomousl! sol$e, aro$e, and imlement.

These could be called uni-functional roblems&

A second grou of roblems is cross functional in nature, in$ol$ing, for examle, mar1eting,

design, urchasing, manufacturing, %ualit! assurance, and sales. From a traditional ersecti$e

there might be functional winners and losers in the solution of the roblem. Wnder ;6B, these

internal trade&offs are weighed against the entire organization#s commitment to imro$ed $alue

for its customers. (ften the rocess is facilitated b! the one erson in the organization who has

managerial control o$er different functions. Schneiderman, "*>>, . +2.

7


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The half&life model describes imro$ements of mainl! non&financial erformance measures

according to the amount of time needed for a reduction of +7 ercent. These imro$ements ma!

be interreted as dri$ers of future financial erformance of a business or a coman!.

For a rough estimation of achie$able imro$ements in financial erformance, the following stes

needs to be followed3

H select erformance dri$er, e.g. total c!cle time5

H measure imact of a +7 ercent reduction of the selected erformance dri$er on different

cost categories5 and

H calculate total exected sa$ings from a +7 ercent reduction of the selected erformance

dri$er.

The future sa$ings from a +7 ercent reduction of total c!cle time might be easil! deri$ed from a

rofit I loss account as illustrated in exhibit *.

*Thomas, "**", . "-&&"+.


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//

/3


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)ost )ategor!6mro$ement er cost

categor! from a +7 X

reduction of total c!cle time

T!ical )ost 8ercent of

Sales9

T!ical Sa$ings

8ercent of Sales9

Dereciation 7 X " X . X

+ X "?.>X

"#hibit 5$ Sa$ings from a +7 ercent reduction of total c!cle time 8Source3 Bh. :. Thomas,=etting )ometiti$e3 "+9

6n addition to the roosed methodolog!, the model of the exerience cur$e might be used to

determine the financial imact of continuous imro$ements. The exerience cur$e"7 tries to lin1

imro$ements of mainl! financial arameters 8i.e. $alue added costs er unit9 to the cumulated

outut $olume. 6n order to reach a secific cost le$el, the cost dri$ers ha$e to be shaed. The

following aragrahs describe a methodolog! to lin1 together both concets for the control of

oerations.

The two models are based on different basic assumtions3 the exerience cur$e describes cost

reductions which are deendent on the accumulated roduction $olume and therefore is

indeendent of the time which is needed. 6n contrast, the half&life model shows %ualit!

imro$ements deendent on the time needed and indeendent of the accumulated roduction

$olume. @hile the use of the exerience cur$e is limited to real $alue&added costs er unit, the

half&life concet could be used to describe the de$eloment of an! non&financial erformance

measure.


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which is suorted b! the half&life concet, leads to cost reductions which can be deri$ed from

the exerience cur$e. 'ence, the half&life model could be used to exlain the reasons for

d!namic cost reduction which inturn, could be anal!sed b! the concet of the exerience cur$e.

0xhibit + shows as an examle of the lin1age between the half&life concet and the exerience

cur$e based on emirical data from Airbus 6ndustries"". 6n Januar! "*2? the first Airbus aircraft

was manufactured. 7 and between "*>7 and "*>* the

manufacturing time of a single aircraft as a non&financial cost dri$er has been reduced from

-7,777 o$er ?+,777 down to 7,777 hours. (n the basic assumtion that one manufacturing

hour costs -7 DM, we could easil! deri$e the financial sa$ings of real manufacturing costs.

8ote3 for our calculations we assume, that the data ublished b! Airbus 6ndustries ha$e been

measured in Januar! of the !ears "*2?, "*>7 and "*>* resecti$el!9.

"" Simon, "**, . >.


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?

Half-Life Model

)earsmanufact& time

"#erience Cur(e

accum& outut

.units/

manufact& costs


27/34

2

half&life time t' C

".?2? !ears 8C7."

months9 no. of hl&

c!cles

i C .->2

Jan. 1976

Set. "*22

Ma! "*2*

Jan. 1980

-7,777 h

"27,777 h

>+,777 h

?+,777 h

"7,77,777.&& DM

",*+7,777.&& DM

exerience rate3 U

C 7.2>" no. of

doublings of the

accum. outut3 i C

?.27

half&life time t' C

".>* !ears no. of

hl&c!cles i C 7.27

exerience rate3 U C

7.>+- no. of

doublings of the

accum. outut3 i C

-.7>


28/34

>

Jan. 1989 7,777 h

7imro(ement of cost dri(er7

",77,777.&& DM 8

7financial ima


29/34

*

causes3

continuous reductions of manufacturing Q time 8C

d!namic organizational learning9 effects3

real manufacturing costs decrease with

e$er! doubling of the accumulated outut

otentiall! b! 8"&U9 X


30/34

-7

"#hibit 6$ Uin1 between 0xerience )ur$e and 'alf&Uife Model at Airbus 6ndustries 8assumtion3 " manufacturing hour costs DM -7.779


31/34

-"

6n Januar! "*2? the first airbus model was built with a total manufacturing time of -7,777

hours. @ithin four !ears the manufacturing time has been reduced to ?+,777 hours. According

to the basic half&life model we can calculate the half&life time t ' between the !ears "*2? and

"*>7 to3

t &t-%ln% &/%ln?

8"29 t> C%%%%%%%%%%%%%%3 C%%%%%%%%%%%%%%%3G /. ln=t &ln=t ln7, and "*>* was

measured in Januar! of each !ear. 7 b! the cost rate of -7 DM er hour, we get the total manufacturing costs er !ear. @ith this

data we could easil! calculate the learning rate U for the time eriod between the four !ears

"*2? to "*>73

879 ! /*+- C ! /*2


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-

The a$erage learning rate of U C 2>." X led to a reduction of the manufacturing time since the

roduction has started. The real manufacturing costs of Airbus 6ndustries show with e$er!

doubling of the accumulated roduction $olume a reduction of 8" & 7.2>"9 C ".* X.

7. (n the assumtion

that those cost sa$ings could be reached b! continuous rocess imro$ement, then we could

deri$e, b! the use of the half&life model, target $alues for the manufacturing time of "27,777

hours in Setember "*22 and >+,777 hours in Ma! "*2*.

6n the same manner, we can show that a half&life time of t' C ".>* !ears should be realised

between Januar! "*>7 and Januar! "*>*. A closer loo1 at the emirical data shows that the

learning seed of the realised imro$ements decreases. From this, a further reduction of the

manufacturing time from ?+,777 hours down to 7,777 hours can be deri$ed. Multilied b! the

cost rate of -7 DM er manufacturing hour, Airbus 6ndustries could reduce its manufacturing

costs from ".*+ million DM down to ". million DM. @ithin the !ears "*>7 to "*>*, the real

manufacturing costs of Airbus 6ndustries ha$e been reduced with e$er! doubling of the

accumulated roduction $olume at an a$erage rate of 8" &7.>+-9 C ".2 X.

6t becomes ob$ious, that sa$ings in manufacturing costs can be effected b! corresonding

reductions in manufacturing time. 6n other words3 Future imro$ements of financial results are

directl! lin1ed with imro$ements of the corresonding non&financial erformance dri$er.

which is necessar! to reach a certain cost le$el. Thus, e$en in stagnating or declining industries

we could control targeted cost reductions, neglecting the low le$els or the absence of doublings


33/34

--

of the accumulated roduction $olume. A comarison of lanned le$els and realised le$els of a

secific cost dri$er shows recisel! whether or not a certain intensit! of %ualit! imro$ement is

sufficient to reach the targeted cost le$el or if further adustments in the resources a$ailable are

necessar!.

2 Conclusion

The half&life model ro$ides a useful tool to shae the non&financial cost dri$ers of a coman!

towards a cometiti$e le$el. 6n combination with the exerience cur$e, the financial imact of

continuous imro$ement roects can be e$aluated.

'owe$er, the e$idence gi$en b! the results of both the half&life model and the exerience cur$e

deends on the stabilit! of the organizational structures in a coman!. 6n the case that rele$ant

changes in the oerational structure are carried out 8e.g. b! rocess reengineering or b! a

change in the management9 the cost, time, and %ualit! arameters used as inut $ariables b!

both models will change. Thus, the half&life times and the learning rates would ha$e to be re&

determined. Therefore, the alicabilit! is limited to rocesses with fixed structures. A further

roblem with the alication of the half&life model is the focus on ust one single arameter of

erformance. 6n some cases, existing interdeendencies between different erformance

measures need to be accuratel! determined, e.g. 8among others9 cost, time and %ualit!

arameters might change due to continuous imro$ement roects. Therefore a too narrow&

sighted focus might result.

0eferences

At1inson, J. '. / 'ohner, =. / Mundt,


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-

=erthsen, ). / Gogel, '., "**-. Bh!si1 & 0in Uehrbuch zum =ebrauch neben Gorlesungen, "2.

$erb. und erw. Aufl., >. Setting ;ualit! =oals, in3 ;ualit! Brogress, /"*>>,. +" & +2.

Schneiderman, A. M., "**?. Metrics for the (rder Fulfillment Brocess 8Bart 9, in3 Journal of

)ost Management, Fall "**?, . ? & "2.

Simon, '., "**. Breismanagement, nd ed., @iesbaden, =abler, "**.

Stata, :., "*>*. (rganizational Uearning & The Ke! to Management 6nno$ation, in3 Sloan

Management :e$iew, Gol. -7, Sring "*>*, . ?- & 2.

Thomas, Bh. :., "**". =etting )ometiti$e, ew Eor1, Mc=raw&'ill, "**".

Kaizen Costing -Formulation and Practical Use of the Half-Life Model

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