Curran Modelling Cost

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Int J Adv Manuf Technol (2006) 31: 407420DOI 10.1007/s00170-005-0205-8

O RIG IN A L A RTICLE

R. Curran . A. K. Kundu . J. M. Wright . S. Crosby .

M. Price . S. Raghunathan . E. Benard

Modelling of aircraft manufacturing cost at the concept stage

Received: 8 October 2004 / Accepted: 6 June 2005 / Published online: 26 January 2006# Springer-Verlag London Limited 2006

Abstract The work presented is concerned with the esti-mation of manufacturing cost at the concept design stage,when little technical information is readily available. The

work focuses on the nose cowl sections of a wide range ofengine nacelles built at Bombardier Aerospace Shorts ofBelfast. A core methodology is presented that: defines manu-facturing cost elements that are prominent; utilises technical

parametersthat are highly influential in generating those costs;establishes the linkage between these two; and builds theassociated cost estimating relations into models. The meth-odology is readily adapted to deal with both the early andmore mature conceptual design phases, which thereby high-lights the generic, flexible and fundamental nature of themethod. The early concept cost model simplifies cost as acumulative element that can be estimated using higher levelcomplexity ratings, while the mature concept cost model

breaks manufacturing cost down into a number of constituentsthat are each driven by their own specific drivers. Bothmethodologies have an average error of less that ten percentwhen correlated with actual findings, thus achieving anacceptable level of accuracy. By way of validity and appli-cation, the research is firmly based on industrial case studiesand practice and addresses the integration of design andmanufacture through cost. The main contribution of the paperis the cost modelling methodology. The elemental modellingof the cost breakdown structure through materials, partfabrication, assembly and their associated drivers is relevant tothe analytical design procedure, as it utilises design definitionand complexity that is understood by engineers.

Keywords Nacelle nose cowl . Cost predictionmodelling . Early concept cost prediction . Mature conceptcost model

Nomenclature

C Manufacturing cost C0Add Additional cost

C0Ass Cost of assembly

C0Fab Cost of fabrication

C0i finish Finished material cost

C0i raw Raw material cost

C0Mat Cost of materials

CEBU Manufacturing cost of engine build unitCFC Manufacturing cost of fan cowl

CN Total manufacturing cost of nacelleCPred Predicted manufacturing costCTC Manufacturing cost of tail coneCTR Manufacturing cost of thrust reverserDfan Fan diameterC Cost differential between trend-line and

baselineCComplexity Cost differential due to cumulative com-

plexity factorCGeom Cost differential due to geometryCManuf Cost differential due to manufacturabilityCSpec Cost differential due to specificationR Regression constant

rGeom Geometric cost ratiorManuf Manufacturing cost ratiorSpec Specification cost ratioui Cost of raw material per unit weightWi Weight of material

1 Introduction

The current emphasis in many aerospace manufacturingcompanies is the reduction of recurring unit costs for bothdeveloping, and mature products [11]. Historically, themain thrust of cost estimating has been associated with the

R. Curran (*) . A. K. Kundu . J. M. Wright . S. Crosby .

M. Price . S. Raghunathan . E. BenardSchool of Mechanical and Aerospace Engineering,Queens University Belfast,Ashby Building Room 5.4, Stranmillis Road,BT9 5AH Belfast, UKe-mail: [email protected].: +44-28-90974190Fax: +44-28-90382701


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high level bidding process or very detailed process timebased models [10]. This is in the context of an aircraftdesign process that has not been oriented towards costissues, relative to the technical challenge, and which hastended towards engineering practices that are governed andunderstood only by individual cost experts [5]. Market

pressures continue to force both companies and customersto demand aerospace products at reduced prices, resulting in

the shift from:

Price CostProfit Contingency ) Profit

Price Total Cost

The effect of this trend has been a greater attention oncost effectiveness, including competitive design configura-tions that return sufficient profit margins [3, 8, 12]. There isan associated requirement to be able to accurately and ex-

peditiously quantify the benefits of such changes. This re-quires sufficient information of an appropriate accuracy and

form [6] being available to verify models for conceptualdesign [13].

These models must provide a causal linkage betweendesign and manufacture in order to provide better accuracyand provide relevant information to the engineers in order tosupport decision-making [1, 2, 7, 17]. A methodology is

presented that: defines the manufacturing cost elements tobe considered; identifies the technical parameters that arehighly influential in generating those costs; establishes themodelling between these two; and builds the cost estimatingrelations into a cost framework [16]. This paper focuses onthe detailed analysis of engine nacelles in order to formulatea methodology with generic relevance.

2 Manufacturing cost breakdown

The total manufacturing cost [14] ofa nacelle CN is given bythe sum of the individual costs of five generic components,

CN X5

iCi CNC CFC CTR CTC CEBU (1)

where CNC is the cost of the nose cowl; CFC isthe cost of thefan cowl; CTR is the cost of the thrust reverser; CTC is the

cost of the tail cone assembly; and CEBU is the cost of enginebuild unit (EBU), e.g. anti-icing, pipes, electrics, etc.Typically, the cost of each of the nacelle componentsidentified in Eq. 1 is individually estimated as follows:

CNose Cowl X5

iC5i

C0Mat C0

Fab C0

Ass C0Sup C

0Amr C

0Misc

(2)

where C0Mat is the cost of material, C0

Fab the cost of fab-rication, C0Ass the cost of assembly, C

0Sup the cost of support,

C0Amr the cost of amortisation and C0

Misc is miscellaneouscost. A fundamental allocation of costs can therefore beattributed to certain categories of cost.

2.1 Material cost

Material is classified into two categories: (1) raw material(sheet metal, bar stock, forging, etc.); and (2) finishedmaterial (e.g. lip-skin, engine ring, some welded/cast parts,etc., and sub-contracted items). The weight fractions of the

two nacelles are given in Table 1, which shows that NacelleB is actually heavier despite having less finished materialweight than Nacelle A. Table 2 details raw material weightfractions while Table 3 gives various materials cost perunit weight; both tables being normalized, the former withrespect to total material weight and the latter to aluminiumsheet metal cost. From Table 2 it is apparent that the higherweight of Nacelle B is attributable to the fact that (a) thereis a greater weight of aluminium alloy sheet used, as thenacelle is larger in geometry; and (b) more titanium alloy isused due to stricter certification requirements with fireresistance/protection, etc. These two factors increase theweight of Nacelle B even though its manufacture does not

require aluminium forging. It is also worth noting, asshown in Table 3, that the highest cost per unit weight

belongs to the mechanical fasteners. The overall cost perunit weight of Nacelle B is smaller than that of Nacelle A, a

possible reason being the previously mentioned neglect ofaluminium forging in Nacelle B production.

The AGS (aircraft general supply) consists of varioustypes of fasteners, e.g. blind rivets (more expensive), solidrivets and other types of fasteners. They are classified asraw material as it is impractical to cost each type separately.

Table 1 Material weight fractions

Material type Nacelle A Nacelle B

(WA/WAT) (WB/WAT) (WB/WBT)

All 1.000 1.135 1.000

Raw 0.714 0.874 0.770

Finished 0.286 0.261 0.230

Table 2 Raw material weight fractions

Material Nacelle A Nacelle B

(WA/WAT) (WB/WAT) (WB/WBT)

Aluminum alloy sheet 0.2523 0.5098 0.4489

Aluminum alloy forging 0.1355 0.0000 0.0000

Al. alloy honeycomb 0.2928 0.2814 0.2478

Titanium alloy 0.2736 0.3308 0.2913

Composite 0.0125 0.0000 0.0000

Mech. fasteners (nuts, etc) 0.0261 0.0036 0.0032

Solid rivets 0.0072 0.0099 0.0087

Total weight fraction 1.0000 1.1356 1.0000

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2.2 Fabricated parts cost

Fabrication is fundamental to manufacturing cost build-upand incorporates cost drivers such as geometry, technicalspecifications, manufacturing philosophy, functionality andman-hour rates [15]. Table 4 gives the cost of parts

manufactured in non-dimensional form, attained from theman-hours involved at each of the six assembly stagesoutlined. All values are dimensioned to the appropriate totalcost of Nacelle A. It is apparent from the table that the costof fabrication has been substantially reduced for Nacelle B.The actual man-hours taken to manufacture parts for each ofthe six stages of Nacelle A assemblies can be obtained fromshop floor engineering process plans. Factored indices for

Nacelle B can be established through DFM studies at theconceptual stages of design. At each stage of the partsmanufacture, the man-hours are given as a fraction of thetotal man-hours of all the parts. It will be seen in Sect. 4 thatthe fabrication time can be modelled and correlated to the

weight fractions of each material required for the manu-facture of each corresponding nacelle, with associatedvalues summarised in Table 5.

2.3 Assembly cost

Again, as for fabrication, the cost drivers are taken toinclude geometry, technical specifications, manufacturing

philosophy, functionality and man-hour rates. Table 4 alsoincludes the Nacelle A and B nose cowl assembly costs forthe six stages. Again, as for fabrication the cost of assemblyis less for Nacelle B. It appears to be advantageous to build

more assembly into the early stages of production. The costof the airframe structure is separated from all other non-structural components, e.g. anti-icing ducting, linkages,cables, accessories, etc. These can be categorised as theEBU fitment for the nacelle, in preparation for fitting theturbofan engine and not included in the cost. Section 4 willoutline how it is possible to model the assembly cost to thenumber of parts and the AGS count for each nacelle.Table 6 outlines the key data required for the current casestudy given in non-dimensional form.

2.4 Cost of support

A certain amount of additional cost is incurred when theproduct is assessed in quality inspection. Rework anddesign concessions are necessary, or parts are otherwisescraped. These costs are termed support cost and in generalare small and hard to determine. A flat-rated cost of 5% ofthe total cost (material + parts manufacture + assembly) isused herein.

2.5 Cost of amortisation

Amortisation includes the non-recurring costs of design,

methods and tooling. Amortisation is here applied over 200aircraft, i.e. distributed over 400 nacelle units, but shouldreflect the business projections for the aircraft sales.

Table 3 Raw material cost per unit weight of each nacelle

Material Cost per unit weight

Nacelle A Nacelle B

Aluminum alloy sheet 1.00 1.00

Aluminium alloy forging 4.19 4.19

Al. alloy honeycomb 2.25 2.25

Titanium alloy 3.50 3.50

Composite 3.62 0.00

Mech. fasteners (nuts, etc) 18.44 18.44

Solid rivets 0.63 0.63

Finished material 1.00 0.92

Table 4 Actual fabricationand assembly costs

Stage Fabrication cost Assembly cost

Actual Actual

Nacelle A 1 Forward bulkhead assembly 0.0557 0.1007

2 Primary assembly 0.1114 0.0564

3 Aft bulkhead assembly 0.0382 0.1157

4 First sub-assembly 0.6234 0.26885 Second sub-assembly 0.0732 0.2110

6 Third sub-assembly (final) 0.0981 0.2474

Total 1.0000 1.0000

Nacelle B 1 Forward bulkhead assembly 0.0623 0.0222



4 First sub-assembly 0.1912 0.1656

5 Second sub-assembly 0.1554 0.1836


Total 0.5337 0.6867

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2.6 Miscellaneous cost

Miscellaneous cost incorporates additional unavoidablecosts such as insurance, packaging, etc., but also includethe unforeseen cost of contingencies that are allocated as amanufacturing cost [4]. Normally these are small and, inthis paper, are taken as 5% of the total cost (material + partsmanufacture + assembly).

3 Early concept modelling

Many commercially available cost estimating packages useweight as the baseline cost driver and then generate measuresof secondary cost drivers to refine the cost estimate. Weightis a cost driver that is synonymous with parametric costing[13] and is at the core of most commercial cost estimating

packages. However, it is difficult to get an accurate weightestimate early in the concept stage. Notwithstanding, thesuitability of several high-level cost drivers is presented inFig. 1, including fan diameter, air-wash area and thrust, aswell as weight. It can be seen that weight seems to be the best

pointer to manufacturing cost with R2=0.955, where 0.955denotes that 95.5% of the scatter in the points is characterised

by the linear fit. The data was normalized in order to helpascertain which parameters tend to impact most on manu-facturing cost. For the range of parameters covered, it can beseen that the slope of the cost verses fan diameter char-

acteristic was greatest at 2.34, followed by air-wash area at1.02, weight at 0.69, and thrust at 0.35. Consequently in thisstudy, fan diameter was taken as the most readily available

baseline parameter that is known early in the concept stageand which displays the highest degree of correlation to cost.

Table 6 Part and AGS count Stage No. of parts AGS






Total 1.0000 1.0000







Total 0.6055 0.8399

Table 5 Weight and cost fractions

Stage Al sheet Al forging Al honeycomb Ti alloy

W/WT C/CT W/WT C/CT W/WT C/CT W/WT C/CT

Nacelle A 1 Forward bulkhead assembly 0.0369 0.0125 0.0000 0.0000 0.0000 0.0000 0.1096 0.1293

2 Primary assembly 0.0640 0.0216 0.0270 0.0381 0.0000 0.0000 0.0126 0.0150

3 Aft bulkhead assembly 0.0847 0.0284 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

4 First sub-assembly 0.0405 0.0137 0.0216 0.0305 0.2928 0.2219 0.1514 0.1785

5 Second sub-assembly 0.0252 0.0085 0.0486 0.0685 0.0000 0.0000 0.0000 0.0000

6 Third sub-assembly (final) 0.0009 0.0004 0.0383 0.0540 0.0000 0.0000 0.0000 0.0000

Total 0.2523 0.0852 0.1355 0.1912 0.2928 0.2219 0.2736 0.3228

Nacelle B 1 Forward bulkhead assembly 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1665 0.1961

2 Primary assembly 0.0761 0.0256 0.0000 0.0000 0.0032 0.0025 0.0680 0.0080

3 Aft bulkhead assembly 0.0987 0.0332 0.0000 0.0000 0.0000 0.0000 0.0733 0.0865

4 First sub-assembly 0.0284 0.0095 0.0000 0.0000 0.2782 0.2109 0.0000 0.0000

5 Second sub-assembly 0.2635 0.1997 0.0000 0.0000 0.0000 0.0000 0.0230 0.0271

6 Third sub-assembly (final) 0.0431 0.0326 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Total 0.5098 0.3006 0.0000 0.0000 0.2814 0.2134 0.3308 0.3177

N.B. All quantities are proportioned to the appropriate nacelle A total (subscript T)

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3.1 Cost drivers

In addition to identifying the statistical design cost driversand relations shown, design, manufacture and procurementengineers were consulted to establish categories that could

be used to fully characterize the cost variance evident on anyone nacelle. Simply, these are represented by a geometriccomplexity factor fGeom, manufacturing complexity factor

fManuf, and specification complexity factor fSpec. The keydesign and manufacturing attributes that were used to defineeach of the factors are listed in Table 7.

Equation 3 reiterates that recurring manufacturing cost isnow assumed to be a function of four parameters, includingsize and the three specific design attributes or character-istics. For the current case study, the component size istaken to be the engine fan diameter Dfan; although someother parameter may provide a better linkage to cost.

C fn Dfan;fGeom;fManuf;fSpec

(3)

Having determined the key cost drivers, the next step wasto gather data that would quantify these. The wider research

program is tackling this issue on a number of levels, forexample, ranging from a knowledge-based rating to an

analytical definition. Table 8 details complexity ratings thathave been quantitatively rated by industrial experts througha tacit knowledge approach. A rating of1 was taken as the

baseline level and a rating of 4 was equated to the mostextreme value for any particular complexity measure.However, it should be noted that the ratings are beingverified and supported by a more analytical methodologythat is being developed but which requires more input dataand, therefore, relates more readily to the preliminary ordetailed design stage.

The clear diamond symbols in Fig. 2 show the recurringmanufacturing costs of the nose cowls, as defined by Eq. 2,

plotted against component size or engine fan diameter. Therewas available data for 11 different nose cowls, denoted later

in the paper as Nose Cowl A through Nose Cowl K. It can beseen from the trend line that the characteristic is linear andthat statistically there was a regularity of R2=0.897. Thismethod implies that ideally there is a linear characteristic andthat the aforementioned complexities give rise to the dif-ferentials from that baseline characteristic.

Table 7 Attributes used to characterise cost drivers

Specification Manufacturability Geometry

Functionality Part count Cylindricity

Certification Process capability Circularity

Aerodynamic smoothness Assembly philosophy Concentricity

Structural efficiency Manufacturing tolerances Curvature

Table 8 Complexity ratings for 11 nacelle nose cowls

Nacelle Specification Manufacturing Geometry

A 1 3 2B 3 4 3

C 1 2 1

D 2 1.5 1

E 3 1 2

F 3 1 3

G 2 2 2

H 1 4 3

I 1 1 3

J 2 4 3

K 2 1 3

y = 2.3352x - 0.2162

R2

= 0.8971

y = 0.3438x + 0.1007

R2

= 0.8716

y = 0.6805x + 0.0928

R2

= 0.955

y = 1.0185x + 0.0824

R2

= 0.8625

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

0 2 4 6 8 10

Normalised cost driver

NormalisedManufa

cturingCost

Fan Diameter

Weight

Airwash Area

Thrust

Fig. 1 Recurring manufacturingcosts of nose cowls

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3.2 Cost prediction model

The approach taken was to identify nacelles with two of thecomplexity ratings (fGeom, fManuf, orfSpec) being equal and thethird being different in order to calibrate the cost differential.In a principle similar to the solution of simultaneous equa-tions, the difference in the dependant variable, i.e. the costdifferential between the nacelles, is equal to the rating dif-ferential for that complexity factor. However, this should becalculated as a ratio of fan diameterDfan in order to allow forthe baseline influence of component size. For example,

Nacelles E and F in Table 8 can be used to establish the costimpact of the geometric complexity factorfGeom relative to fandiameterDfan. This procedure yields three costing ratios of theform described in Eqs. 4 through 6.

rGeom

C2Dfan2

C1

Dfan1

fGeom2 fGeom1 ; (4)

rManuf

C2Dfan2

C1

Dfan1

fManuf2 fManuf1 ; (5)

rSpec

C2Dfan2

C1

Dfan1

fSpec2 fSpec1 (6)

Consequently, the total cost impact of each of thecomplexity ratings can now be calculated relative to a

baseline cost that is a function of size. For example, Eqs. 7,8 and 9, show the calculation of the cost differentialassociated with each of the complexity factors.

CGeom rGeomDfan fGoem 1 (7)

CManuf rManufDfan fManuf 1

(8)

CSpec rSpecDfan fSpec 1

(9)

To establish the linear baseline equation as a function ofsize, the trend identified for the original data points isshifted vertically downwards by the cost differential C

between it and the baseline nacelle chosen. This gives anequation of the form described in Eq. 10, where zequates tothe vertical shift from the original data.

C mdataDfan zdata C0 (10)

Subsequently, the predicted cost CPred of any newnacelle with a given engine fan diameter Dfan and com-

plexity factors of fGeom, fManuf and fSpec, is calculated asshown in Eqs. 11 and 12.

CPred mdataDfan zdata C0 CComplexity (11)

Ccomplexity CGeom CManuf CSpec (12)

R2 = 0.8971

R

2

= 0.9372

0

1

2

3

4

5

0 1 2 3

Normalised Fan Diameter

NormalisedManufacturingCost

Original data

Baseline prediction

Linear (Original data)

Linear (Baseline prediction)

Fig. 2 Original cost versusbaseline cost

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4 Results

The clear diamond symbols in Fig. 2 denote the originalcost of each nacelle while the solid circles represent theactual cost minus the predicted cost differential arisingfrom the complexity, as described by Eq. 13. This shouldrepresent the idealistic baseline cost that is a function ofsize only.

C Ccomplexity C CGeom CManuf CSpec

(13)

The characteristics should imply whether the methodol-ogy is improving the regularity and predictability of the

cost, and it can be seen in Fig. 2 that the linearity is furtherrefined to R2=0.937. Also, the concept of a cost floor ishighlighted in the figure through the slope of the two trendlines, where the differential is subsequently increased as thefan diameter increases. This is also a testament to thecorrect choice of cost drivers.

Finally, Fig. 3 plots the original data against thepredicted values where the solid circular symbols repre-sent the predicted cost. It can be observed that there isagain a reasonable degree of linearity (R2=0.967). Anydeviation of the predicted trend line from the original

appears to be slight, but it increases with increased fandiameter. In terms of the model accuracy, the proposedcomplexity method delivered an average percentage error

0

4

8

12

16

Al Alloy

Sheet

Al Alloy

Forging

Al Alloy

Honeycomb

Ti Alloy Composite Mech

Fasteners

Solid Rivets

Cost/TotalWeigh

tofNacelleA

Nacelle A

Nacelle B

* *

* - Material not present inNacelle B

Fig. 4 Material cost-to-weightratios

R2 = 0.9671

R2

= 0.8971

0

1

2

3

4

5

0 1 2 3

Normalised Fan Diameter

NormalisedManufac

turingCost

Prediction

Original data

Linear (Prediction)

Linear (Original data)

Fig. 3 Original cost versuspredicted cost

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of 10% between its predicted costs and the original cost,whereas the trend line for the original regression analysisof the data, shown in Fig. 1, had an average absolute errorof 14% in predicting the cost of each nose cowl. It is thusapparent that the model yields a sufficient level ofaccuracy as an early concept prediction tool.

5 Mature concept cost modelling

The input required for the mature concept model requiresmore detail than that required for the early concept predic-tion but remains relatively high level. In developing themodel [9], the data and factors pertaining to the designinformation and manufacturing data from two nacelle nosecowls were utilised and are given in Tables 1, 2, 3, 4, 5 and6, including:

Materials utilised Breakdown of weights, costs Breakdown of parts and AGS count Fabrication and assembly costs for each six assembly

stages

Each of the cost elements were individually investigated inorder to identify suitable analytical relations based on thehistorical data. This included identifying primary andsecondary cost drivers that could be employed to refine theaccuracy of the model, in a similar fashion to the earlyconcept model, whereas size, expressed through fandiameter, was utilized previously. The mature conceptmodel benefits from using more detailed analysis, forexample, using the weight and cost breakdown of theutilised materials along with the part and AGS count.

5.1 Cost model

5.1.1 Material cost

The nose cowl material cost C0

Mat is expressed as:

C0Mat Xn

iC0i raw

Xni

C0i finish; where C0i raw

Wi ui Pi

(14)

where Wi is the weight of the material, ui is the standardcost of raw material per unit weight, and Pi is the

procurement factor. Typically, there were seven types ofmaterials that were categorised: aluminium alloy sheet,aluminium alloy forgings, aluminium alloy honeycomb,titanium alloy, composite, mechanical fasteners and rivets.The latter highlights that material costs are not modelled as

pure raw materials but include some processing cost. Thedistinction relates to raw material arriving at the shopfloor and is a simplification used in industry.

5.1.2 Fabrication cost

The man-hours required to fabricate each part is acombination of processes such as machining, forming,

0.40

0.060.00

0.14

1.39

0.11

0.000

0.4

0.8

1.2

1.6

Aluminum

Alloy Sheet

Aluminum

Alloy Forging

Al. Alloy

Honeycomb

Titanium

Alloy

Composite Mech.

Fasteners

Solid Rivets

Percentage

Error

Fig. 5 Percentage errors be-tween each individual actualand model material costs forNacelle A

Table 9 Actual and predicted material costs with correspondingpercentage errors

Material Cost Nacelle A Nacelle B

Actual 47.5045045 35.8083452

Model 47.7685622 33.6525012

% Error 0.55585815 6.0205074

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etc. As the weight of each material used is one of the maincost drivers, it is possible to model the fabrication cost

C0Fab

relative to the amount of each material used at each

corresponding assembly stage. However, only the first fourmaterials were considered in this analysis as their weightamounts to approximately 95% of the total, i.e. it could beassumed that with respect to driving the cost they are themost significant of the materials (aluminium alloy sheet,aluminium alloy forgings, aluminium alloy honeycomband titanium alloy). Figure 4 illustrates the cost-to-weightratios for each of the materials, where each cost wasnormalised according to the total weight of Nacelle A.Mechanical fasteners appear to have quite a large value;

however, this is due to the fact that they are quite expensivebut they accumulate to only a very small portion of the totalweight of each nacelle. Since only the weight fractions are

being modelled, it is not necessary to include the fastenersin the analysis. A multiple regression analysis (MRA) wasthus preformed for each nacelle, using previously attainedinformation on the fabrication times and the materialweight fractions at each of the assembly stages, as outlined

by Tables 4 and 5. The regression models prediction of thefabrication cost was evaluated as given by Eq. 15,

C0Fab 0:078 0:205WAlSheet 0:539WAlForging

0:346WAlHoneycomb 113:122WTiAlloy

(15)

7.12

0.01 0.00 0.00

3.78

0

2

4

6

8

Aluminum

Alloy Sheet

Aluminum

Alloy

Forging

Al. Alloy

Honeycomb

Titanium

Alloy

Composite Mech.

Fasteners

Solid Rivets

Percentag

eError

* *

* - Material not present in Nacelle B

.

Fig. 6 Percentage errors be-tween each individual actual andmodel material costs forNacelle B

-0.2

0

0.2

0.4

0.6

0.8

1 2 3 4 5 6

Assembly Stage

FabricationCost/Tota

lFabricationCostof

NacelleA

Actual Cost

Model Cost

Fig. 7 Comparison of the actualand model fabrication cost forNacelle A

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5.1.3 Assembly cost

The assembly operation time and cost was modelled in asimilar way to that of the fabrication time. The assembly

cost C0Ass

was modelled as a function of the number of

parts NParts and the AGS countNAGS. These two parameterswere recognised to have the biggest influence on theassembly time and, consequently, the assembly cost.Table 6 gives the appropriate data of the part and AGScount at each corresponding assembly stage. After themultiple regression analysis was preformed it yielded thefollowing relationship given by Eq. 16.

C0Ass 0:017 0:389NParts 0:465NAGS (16)

5.1.4 Additional costs

There remain several additional costs C0Add

that are cal-

culated in a very similar manner but which, nonetheless,

should be incorporated. The support cost C0Sup, amor-tisation cost C0Amr

and miscellaneous costs C0Misc

can

be taken as a percentage of material cost, fabrication costand assembly cost. In this paper they are accumulated andflat-rated as follows:

C0Add C0Sup C

0Amr C

0Misc (17)

C0Add 0:1 material cost fabricationcost

assemblycost(18)

-0.1

0

0.1

0.2

0.3

1 2 3 4 5 6

Assembly Stage

FabricationCost/Total

FabricationCostof

Nacelle

A

Actual Cost

Model Cost

Fig. 8 Comparison of the actualand model fabrication cost forNacelle B

Table 10 Model fabrication andassembly costs

Stage Fabrication cost Assembly cost

Model Model






Total 0.9082 0.9573







Total 0.6255 0.7294

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Consequently, all elements of cost can be estimated

using the above relations, and no further modelling of theadditional costs need be carried out as they depend onlyupon the three previously modelled costs.

5.2 Model results

5.2.1 Nose cowl material cost

The cost of material C0

Mat

is predicted by evaluating the

sum of the total raw material costPn

i C0i raw

and the cost

obtained from the subcontracted items Pn

i C0i finish, as

outlined by Eq. 14. Now, C0i raw is evaluated in full using

Eq. 19:

C0i raw Wal ual Pal sheet Wal ual Pal forge

Wal ual Pal honeycomb Wti uti Pti

Wcomp ucomp Pcomp

WAGS uAGS PAGS fastener

WAGS uAGS PAGS rivet

(19)

Finished material consists of a variety of items that aresupplied to the assembly line without in-house work beinginvolved. Their acquiring policies vary at each negotiation.A similar relation for the cost of finished material may also

be evaluated, although this is highly influenced by externalfactors and cost of supply.

Table 11 Errors of predictedmodels

Stage Percentage difference of total cost

Fabrication Assembly







Average 3.9861 3.0508







Average 9.5065 3.6628

0

0.05

0.1

0.15

0.2

0.25

0.3

1 2 3 4 5 6

Assembly Stage

AssemblyCost/Tota

lAssemblyCostof

Nacel

leA

Actual Cost

Model Cost

Fig. 9 Comparison of the actualand model assembly cost forNacelle A

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Tables 1, 2 and 3 outlined the weight fractions (Wi) andcorresponding costs per unit weight (ui) associated witheach of the raw and finished materials. The raw andfinished material costs for each nacelle were thus evaluatedhence giving the predicted material cost appropriate to theabove model. Table 9 details these costs, however they aredimensioned to the corresponding total nacelle weight for

proprietary reasons. The table also outlines the percentageerror resulting from the model which still prove to be quitesmall. The average error experienced was approximately3.3%. Finally, Figs. 5 and 6 outline the resulting percentage

errors for each individual material, proportioned to the totalerror for both corresponding nacelles.

5.2.2 Nose cowl part fabrication cost C0

Fab

The model described in Section 5.1.2 was carried out foreach of the six assembly stages and the four main materialsfor each of the nacelles. The findings are representedgraphically in Figs. 7 and 8 for Nacelles A and B,respectively. Tabular results can also be found in Table 10for each of the fabrication costs displayed being propor-tioned to the Nacelle A total. It can be observed that themodel is very comparable to the actual costs (with aresulting R-squared value of 0.877), which corresponds to

an acceptable level of correlation. The accuracy of themodel is further investigated in Table 11 which outlines the

0

0.05

0.1

0.15

0.2

0.25

1 2 4 63 5

Assembly Stage

AssemblyCost/TotalAssemblyCostof

Nacelle

A

Actual Cost

Model Cost

Fig. 10 Comparison of theactual and model assembly costfor Nacelle B

4.27

9.18

0.56

0

2

4

6

8

10

Material Cost Fabrication Cost Assembly Cost

Percentage

Error

.

Fig. 11 Percentage errorsbetween the actual and modelcosts for Nacelle A

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difference (given as a percentage of the total cost) betweenthe actual and model costs for each of the six stages. Thetable also details the average errors for each nacelle, these

being approximately 4% and 9.5% for Nacelles A and B,respectively.

5.2.3 Nose cowl assembly cost C0Ass A further model was then tested on the assembly cost andagain the results are given in graphical and tabular form inFigs. 9 and10 and Table 10. The regression analysis detailsan R-squared value of 0.820. This establishes that the ac-curacy of the performed model is in accordance with actualmeasurements. Table 11 again summarises the associatederrors between the actual and modelled costs. It states thatthe average error of Nacelle A is approximately 3% and 4%for Nacelle B.

It has already been illustrated in Figs. 7, 8, 9 and 10 howwell the regression models for the fabrication and assemblycosts correlate with actual measurements although there are

few data points relative to only two nacelles. It is beneficialto note that the total costs for each corresponding nacellecan be compared directly; Figs. 11 and 12 outline theresulting percentage errors experienced. The maximum

percentage error observed was 17.2%, and the three modelshave an average accuracy of


14/14

dustrial usage with parameters as considered in this paper.The cost implications involved in learning to manufacture,support/procurement policy, miscellaneous cost, etc., canmake or break an otherwise good design.

A good data bank would lead to a more credible param-etric relationship to extract the necessary indices/factors.But it is not easy to obtain a large number in the product linein aerospace where about ten different products could be

decades of work, by that time the technology change wouldforce the data to obsolescence. The difficulty in accuratecost estimation should not be underestimated.

Acknowledgements This multidisciplinary research was fundedthrough the Innovative Manufacturing Initiative (IMI) program of theEngineering and Physical Sciences Research Council (EPSRC) of theUK, under the DEMAROC grant (GR/M59716: 19992002).Furthermore, the industrial collaboration from Bombardier Aero-space Shorts has been invaluable and is central to the validity andoriginal value of the research.

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