cost drivers learning event, 2 nd november 2005 1 cost improvement curves: modeling reuse, learning,...

Cost Drivers Learning Event, 2nd November 2005

1

Cost Improvement Curves:Modeling Reuse, Learning,

Amortization and Yield Improvement


Raymond P. Covert

MCR, LLC2000 Corporate Ridge, Suite 400

McLean, Virginia 22102

(703) 506-4600

www.mcr.com

E-mail: [email protected]

© 2005 MCR, LLC

http://www.acoste.org.uk/


16 September 2005 2

Agenda

Introduction Cost Improvement Factors The Plant Model Nonrecurring and recurring costs Nonrecurring cost improvement Recurring cost improvement Example hardware cost improvement model Summary Acronym List References



16 September 2005 3

Introduction

This presentation is intended for an audience with an intermediate understanding of cost analysis methods

We will discuss the phenomenon of “cost improvement”, which is loosely defined as the observed reduction of cost of successive units or projects

0

50

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0 10 20 30Unit Number

Rec

urr

ing

Co

st,

$



16 September 2005 4

Cost Improvement Factors and Learning Cost Improvement is the observed reduction of costs between

successive units or projects Factors affecting cost improvement:

Nonrecurring and recurring accounting standards affect measurement Reuse of existing designs, materials, equipment, effort, or products Learning or gained experience in value added effort Skill Mix changes Process shortcuts that eliminate effort or expenses Yield improvements that reduce cost Production Rate increases allowing for amortization of pooled costs

and greater efficiency Technological advances allowing greater yield and efficiency Inflation which measures the time variable cost of a “basket of goods”

*True “learning” is a subset of cost improvement, so cost improvement is more than learning



16 September 2005 5

The Plant Model

Can use a plant economic model to show the effects of different factors on cost improvements [Ref. 1, p. 183]

Skills Labor Rates

Engineering 1 2 3 4 5

Manufacturing

Quality and ReliabilityLabor Hours $

Tooling Fee

Testing Labor Overhead G&ALabor

Other + OverheadTravel and Other Direct Costs $ $ Price

Material Prices Total Cost

Material Measures A B C D E Material + Overhead

Pounds G&A

Yards FeeMaterial quantities $

Gallons

Linear Feet Material Overhead



16 September 2005 6

The Plant Model

The plant economic model contains the three classic Elements of Cost: Labor, Materials and Expenses

These costs can be Project related or Pooled (period costs) Direct or Allocable (overhead and fringe) Nonrecurring or Recurring costs

Materials (M) Labor (L) Expenses (E) Total = M+L+E

Direct 105,000.00 2,500,000.00 80,000.00 2,685,000.00 Burden 26,250.00 3,000,000.00 64,000.00 3,090,250.00 Total 131,250.00 5,500,000.00 144,000.00 5,775,250.00 Administration 10,000.00 125,000.00 6,250.00 141,250.00 Distribution 5,000.00 25,000.00 1,250.00 31,250.00 Corporate Transfer 125.00 250,000.00 12,500.00 262,625.00 Marketing 30,000.00 200,000.00 10,000.00 240,000.00 Research 50,000.00 275,000.00 13,750.00 338,750.00 Development 20,000.00 125,000.00 6,250.00 151,250.00 Finance 20,000.00 195,000.00 9,750.00 224,750.00 Total 135,125.00 1,195,000.00 59,750.00 1,389,875.00 Total 266,375.00 6,695,000.00 203,750.00 7,165,125.00

Pooled Costs (Period)

Project Costs

TOTAL COSTS



16 September 2005 7

Areas of Cost Improvement Cost improvement can be obtained in two areas:

Between subsequent programs Within programs between subsequent production units

Between Programs Nonrecurring cost improvements between successive programs Recurring cost improvements continuing to the subsequent

programs Within programs

Recurring cost improvements

The next step is to define these terms precisely and show how to model them



16 September 2005 8

Nonrecurring and Recurring Costs Nonrecurring (NR) and recurring (REC) cost definitions

Nonrecurring costs - unique costs of effort, material and expenses tied to a production run rather than a particular unit

Recurring costs – costs of repeated effort, material and expenses repeated for each subsequent unit

Hard to segregate NR and REC in small or single unit production What was recurring work if we only build one unit? What was the theoretical first unit cost (T1)? What if we build a prototype unit and make it the first production

unit? What was the fist prototype unit cost (P1) and T1 cost? What will the theoretical second unit cost (T2) be?



16 September 2005 9

NR/T1 Factors for Space Programs

NR/T1 is the ratio of NR costs to T1 costs Analysis of NR/T1 Ratios of 100 programs from the

NAFCOM database* provide the following results:

TYPERocket Engine

Earth Orbiting

Launch Vehicle Manned Planetary

NUMBER 4 61 10 8 17MIN 27.65 0.00 2.61 1.29 2.38MAX 202.24 7.59 39.78 11.56 18.35MEDIAN 128.83 2.02 16.00 3.48 6.18MEAN 121.89 2.35 16.93 4.44 6.52

min ML mean (average) max

ML = most likely = 3 * mean - (min + max)

* NASA / Air Force Cost Model (NAFCOM) Includes subsystem hardware, systems engineering, program management, integration, assembly and test, ground test equipment, launch and orbital operations support



16 September 2005 10

New Design and Reuse*

The amount of new design on a program and reuse from previous programs is a key factor in determining NR/T1 Reuse = 1 – New Design Assumes all have some prototype development Almost never have 0% redesign or 100% redesign Use table to estimate NR/T1 cost ratio from % new design

% New Design Description NR/T1

0.0 Off the Shelf 0.10.1 0.20.2 0.30.3 0.50.4 0.80.5 1.30.6 1.70.7 2.10.8 2.50.9 2.81.0 3.0New Design

Tech Maturity

Min Mods

Moderate Mods

Major Mods

NR/T1 vs. % New Design

0.00.51.01.52.02.53.03.5

0.0 0.2 0.4 0.6 0.8 1.0

% New Design

NR

/T1

* For earth orbiting spacecraft




Modeling NR Costs Using Reuse

Use our plant economic model to build-up the T1 costs

Use T1 costs and reuse (or percent new design) to determine NR costs

Look at effect of reuse on NR cost How does this affect total cost improvement?

Total acquisition costs = NR+ REC costs

Not really interesting until we look at other cost improvement factors like learning and amortization




The Learning Curve

(Wright) Cumulative Average Learning Curve Based on accumulated experience and ability to do the

same task with less labor (time)

Cumulative Average Unit Cost =

Cost of ith Unit = Where:

T1 = Theoretical 1st unit cost N = number of units i = unit number LCS = learning curve slope ln = natural log

)2ln(

)ln(

1_ *$LCS

AveCum NT

)2ln(

)ln(1

)2ln(

)ln(1

1_ )1()(*$LCSLCS

iUnit iiT

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 2 4 6 8 10 12

Units

Co

st,

$

Cumulative average

Unit




Observations on Learning Can be measured in hours and dollars (Euros and Pounds are

OK as well!) This implies that it covers the same work content

Accounting standards need to include NR and REC cost definitions True learning should be independent of other factors such as:

Reuse of existing designs, materials, equipment, effort, or products Skill Mix changes Process shortcuts that eliminate effort or expenses Yield improvements that reduce cost Production Rate increases allowing for amortization of pooled

costs and greater efficiency Technological advances allowing greater yield and efficiency Inflation which measures the time variable cost of a “basket of

goods”




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0.2

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0.8

1.0

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Units

Co

st,

$

Unit Cost

The Production Rate Curve Production Rate Curve

Division of labor and overheads with number (N) of units produced over a period of time

Strongly influenced by amortization of period and fixed costs Unit cost =

“Bath tub” shape due to added capital equipment and labor when production capacity is exceeded

Niablefixed

Unitvar$$

$

Max capacity

Increase fixed costs




Yield

"Yield" is the fraction of units that meet specifications Unit cost =

Process Screening

Fail = Does Not Meet Specifications

Pass = MeetsSpecifications

N Units Started

yieldNiablefixed

unit *

$$$ var

MeetsSpecifications

Does Not Meet Specifications

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1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0

Yield

Un

it C

os

t, $

Unit Cost




Sensitivity Analysis What affects cost improvement the most?

Reuse? Amortization (production rate)? Yield?

Depends on the scenario (looked at 5 scenarios) Small quantity satellite production Medium quantity satellite production Large quantity satellite production Electronic box production Integrated circuit production

Use plant model with uniform distributions of quantity, reuse, amortization and yield to show sensitivity




The Plant Model Equations Start with parameters we wish to vary:

Total number of projects over which non-pooled costs will be amortized Learning curve slope (LCS) Yield parameters (start quantity, yield, final quantity) Percent reuse for nonrecurring costs Pooled rate factor (factor for adjusting pooled / period costs)

Determine Direct costs T1 costs are constants

T1(labor) = 100, T1(material) = 20, T1(expenses) = 12 NR costs = f(T1, Reuse) from reuse table Recurring Costs from learning curve Total direct costs = NR + Rec costs

Add indirect costs to direct costs using these factors Materials (5%), Labor (150%), Expenses (70%)

Add period costs (constants adjusted by pooled rate factor)

MIN MAX BASE1 2 Total Projects 1

0.999 1 LCS 1800 1200 FinalQuantity 1000

Start Quantity 20000.2 0.7 Yield 0.50.2 0.8 Reuse 0.8

1 3 Pooled Rate Factor 2




Small Quantity Satellite Production

Most sensitive to new designMIN MAX BASE

1 2 Total Projects 10.9 1 LCS 1

1 3 FinalQuantity 2Start Quantity 2

0.99 1 Yield 10.2 0.7 Reuse 0.5





Medium Quantity Satellite Production

Most sensitive to: New Design Learning curve slope



Start Quantity 50.99 1 Yield 1

0.2 0.7 Reuse 0.5250 400 Pooled Rate Factor 300




Large Quantity Satellite Production

Most sensitive to: Learning curve slope



Start Quantity 300.99 1 Yield 1

0.2 0.7 Reuse 0.5250 400 Pooled Rate Factor 300




Electronic Box Production

Most sensitive to: Period costs (amortization)



Start Quantity 630.5 0.8 Yield 0.80.2 0.8 Reuse 0.810 30 Pooled Rate Factor 20




Integrated Circuit Production Most sensitive to yield MIN MAX BASE

1 2 Total Projects 10.999 1 LCS 1

800 1200 FinalQuantity 1000Start Quantity 2000

0.2 0.7 Yield 0.50.2 0.8 Reuse 0.8





Results of Scenarios Model results tell us what we probably already know

In small quantity production, reuse is the most important cost improvement factor

In large quantity, labor intensive production, learning is the most important factor

In large quantity electronic box production, production rate is the most important factor

In very large quantity, automated processes, yield is the most important factor

Scenario Quantities Primary Cost Improvement Factor:Small quantity satellite production 1-3 Reuse (New design)Medium quantity satellite production 4-10 Reuse & Learing curve slopeLarge quantity satellite production 20-40 Learning curve slopeElectronic box production 20-80 Amortization (production rate)Integrated circuit production 800-1200 Yield




Summary

Many factors affect cost improvement Cost improvement can be obtained between

subsequent programs or subsequent production units Use plant model to show sensitivities of these factors We chose reuse, learning, amortization (production

rate) and yield Effects are scenario dependent

Depends on quantity of production and production volumes Also depends on amount of process automation and

external factors such as plant amortization




Acronym List NR = Nonrecurring cost T1 = Theoretical first unit recurring cost T2 = Theoretical second unit [recurring] cost P1 = Theoretical first prototype unit cost REC = Recurring cost LCS = Learning curve slope ML = Most likely NR/T1 = Ratio of NR to T1 costs N = number of units i = unit number ln = natural log




References1. Stewart, R. and Wyskida, R., “Cost Estimator’s Reference Manual”, 1997, John Wiley and

Sons, New York.

2. “Pricing Handbook: Cost Accounting Standards”, Federal Aviation Administration, http://fast.faa.gov/archive/v1198/pguide/98-30C14.htm


cost drivers learning event, 2 nd november 2005 1 cost improvement curves: modeling reuse, learning,...

Documents

learning cost improvement

cost improvement factors

subset of cost improvement

cost improvement curves

phenomenon of cost improvement

unit cost t1

yield improvement cost

unit cost t2