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1© BAE Systems 2011 BAE Systems Proprietary Information

BAE Systems Proprietary Information

Project Team Sizing and Cost Forecasting using Norden-Rayleigh Curves

Alan R JonesBSc (Hons) ARCS MBA MMS FACostE CCE/A

Manager - Estimating Capability DevelopmentMilitary Air & InformationBAE Systems

ACostE Conference 2011, Day 2 Learning Event3rd November 2011

2Project Team Sizing and Cost Forecasting using Norden-Rayleigh Curves

© BAE Systems 2011 BAE Systems Proprietary Information


John William Strut, 3rd Lord Rayleigh was an English physicist who discovered the gas Argon (for which he won the Nobel prize in 1904) and also described why the sky appeared blue!

He was a BA and MA from Cambridge, graduating in 1868 and was later Cavendish Professor of physics.

The Rayleigh Distribution is a continuous probability distribution.

… zzz … zzz …zzz …

Norden-Rayleigh Curves: Background

It usually arises when a two-dimensional vector (e.g. wind velocity) has its two orthogonal components normally and independently distributed……….




Enough of that ..this is what it looks like !

Cost Profile at a Point in TimeCost Profile at a Point in Time

Cumulative Cost Over TimeCumulative Cost Over Time

Norden-Rayleigh Curves (or N -R Curves)

0

100

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400

500

600

700

800

0 20 40 60 80 100

Time

Cos

t

0

5,000

10,000

15,000

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25,000

30,000

0 20 40 60 80 100

Time

Cos

t

Based on the Rayleigh Distribution




Readers of the ACostE’s Journal may think that this curve looks familiar …

Norden-Rayleigh Curves (or N -R Curves)

Vol.49 No 4 July 2011 … page 11an article by Greg Gendall, updated by David Garland

Characteristic shape of a Norden-Rayleigh Curve




Norden-Rayleigh Curves: Development Projects

A number of studies (conducted by Norden, Lee and others) using data extracted from Earned Value Management systems on Research & Development projects, have shown that, typically, the cumulative cost build up follow the Rayleigh Distribution quite closely1.

The Rayleigh Distribution models a development programme’s effort ramp-up, peak value and tail-off over time

Rayleigh Cumulative DistributionR(t) = C ( 1- e- 0.5(t/d)2

)

Rayleigh Cumulative DistributionR(t) = C ( 1- e- 0.5(t/d)2

)

C = Cost Scale ParameterFinal Development Cost at Outturn

d = Schedule Scale ParameterEquivalent to the Mode Position

R(t) = Total cost or effort expended to time, t

Equivalent to ACWP in EVM

Source: 1. Lee DA, (2002), Norden-Raleigh Analysis: A Useful Tool for EVM in Development Projects, Logistics Management Institute, The Measurable News, March 2002




The classic S-shape can be shown to describe the cost histories of items as different as software2 and tanks3 and implies that there is an underlying commonality in development programmes.

Source: 2. Putnam, L.H and W. Myers (1992), Measures for Excellence – Reliable Software on Time, within Budget, Prentice–Hall3. Gallagher, M. A. and D. A. Lee (1996), “Final-Cost Estimates for Research & Development Programs Conditioned on Realized

Costs,” Military Operations Research, Vol. 2, No. 2, (1996): pp. 51–65.

Norden-Rayleigh Curves: Development Costs




A study by Lee, Hogue & Hoffmann4 showed that data from many DoD programmes could be collapsed onto a single curve

Source: 4. Lee DA, Hogue MR and Hoffman DC, (1993), Time Histories of Expenditures for Defense Acquisition Programs in the Development Phase. – Norden-Rayleigh and Other Models, [presented at the 1993 Annual Meeting of the ISPA]

Norden-Rayleigh Curves: Development Costs

R(t)C

Normalised Costs

td

Normalised Time Period




Norden theorised that any development programme …….

− It starts with a core group of people that begins to outline problems

− As they solve the initial set of problems, more problems are encountered

− The team expands when the problems can be assigned efficiently to new members

− New problems are assigned until all major problems have been identified

− At this point the number of obstacles diminish as no new problems are created

− And the team begins to diminish in size, and dwindles to a level of occasional support

Theoretical Rationale for the Norden-Rayleigh Effect

If this does not characterise the nature of Develop ment Projectsin your area, this may not be an appropriate model for you!




There is an implied relationship between team size and total effort exp endedwhich relies on the following assumptions:

Theoretical Rationale for the Norden-Rayleigh Effect

This is why is not usually possible to compress

the development timescale simply by adding more people

• The problems to be solved in any development project are finite but not known at the outset.

• The number of people employed in solving problems is proportional to the number and complexity of the problems yet to be solved and these problems must be first identified, investigated and defined before additional personnel can solve them.

• The majority of costs must relate directly to the time spent by the development team solving problems i.e. hardware purchases, overheads and other costs must be a small proportion of the total cost

• The contract must fund a single, integrated development project in its entirety

Otherwise the problem identification and

resolution rates will not follow the theoretical principles described




Norden-Rayleigh Curves: Cautionary Notes

The Norden-Rayleigh Curve is unlikely to be suitable f or:

Modern Software projects with the following characteristics pose problems…• Where software is released in a rolling pattern of upgrades• No single product is being developed from concept to prototype• Focus is on enhancing current software and correcting defects• Team is never disbanded

Incremental Development or Volatile DevelopmentsUmbrella ContractsMajor Dependencies on Third Party Resource (Bottlen ecks)

• Government Funded Testing• Parallel Partners not under a single direct control such as a Joint

VentureHardware Intensive Projects

• Consuming a high proportion of Commercial Off-the-Shelf Hardware not requiring significant integration

• Procurement costs not phased throughout the development




0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Norden-Rayleigh Curves: F18 Reality Check

Source: 5. Stem D, (2005) F/A-22 and F/A-18 E/F Development Risks: An Evaluation of the Acquisition Strategy and Cost and Schedule Reports, RAND Corporation, DoD Cost Analysis Symposium




0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Norden-Rayleigh Curves: F22 Reality Check

Source: 6. Stem D, (2005) F/A-22 and F/A-18 E/F Development Risks: An Evaluation of the Acquisition Strategy and Cost and Schedule Reports, RAND Corporation, DoD Cost Analysis Symposium




Norden-Rayleigh Curves: Does it work in BAE Systems?

First of Class Marine Platform (Design and Develop)

0%

10%

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30%

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60%

70%

80%

90%

100%

0 2 4 6 8 10 12 14 16 18 20

Year from Start

% o

f Fin

al C

ost

FoC Cost to Date Norden-Rayleigh



Practical Considerations – From Rayleigh to Weibull then Beta

Norden-Rayleigh Curve:Use in Spreading Development Costs

Microsoft Excel

Worksheet Function




Where k = 2

Rayleigh: Special Case of Weibull Distribution

A Norden-Rayleigh Distribution is a special case of the more general WeibullDistribution , which used in reliability analysis to predict failure rates

Microsoft Excel

Worksheet Function

… and this helps because?

Norden-Rayleigh Weibull

Cumulative Distribution Function

-0.5(t/d)2

1 - e-( t/λ)k

1 - e

k t k-1 eλ λ

-( t/λ)k

λ k – 1 1/k

kMode occurs @ d => λ=> λ=> λ=> λ

2

MS Excel is Weibull friendly!

=> 2 t eλ2

-( t/λ)2

NB: The Outturn Scale parameter has been

removed for simplicity

So … use Weibull for Rayleigh

Probability Density Function

-0.5(t/d)2

t ed2

λ = d 2




Rayleigh: Special Case of Weibull Distribution

Weibull Distribution in MS Excel:

Cumulative Distribution Function = Weibull( t , k , λ , TRUE)Probability Density Function = Weibull( t , k , λ , FALSE)

Using Norden-Rayleigh in MS Excel:

Cumulative Distribution Function = C x Weibull( t , 2 , Mode 2 , TRUE)

Probability Density Function = C x Weibull( t , 2 , Mode 2 , FALSE)where C = the Outturn Scale Parameter

Weibull Distribution Probability Density

FunctionMode

t Start End (infinite)




Norden-Rayleigh Distribution Properties

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 1 2 3 4 5

Schedule (relative to Modal Position)

Cos

t

The distribution continues to infinity, but to 3 dp’s it can be assumed that:

Schedule Cost

1 39.347%

1.5 67.535%

2 86.466%

2.5 95.606%

3 98.889%

3.5 99.781%

3.75 99.912%

4.5 99.996%

So, how precisely inaccurate do you want to be?

Mode >

Pragmatic end-point is 3.5

times the Modal Position

If you know the mode, then you can predict the effective end-point – in

terms of cost and schedule




Beta Distribution in MS Excel:

Cumulative Distribution Function = Beta( t , α , β , Start, End)

Using Beta Distribution as an approximation to Norden-Rayleigh in MS Excel:

Cumulative Distribution Function = C x Beta( t , α , β , Start, End)

where C = the Outturn Scale Parameter (Cost Outturn)

α = 2.125

β = 3.875

Mimmicking the N -R Curve with a ProjectBeta Distribution

Beta Distribution Probability Density Function

cf Rayleigh Distribution

Start

End(finite)

Modet (infinite)

Sum = 6




How good is the approximation?

Norden-Rayleigh v ProjectBeta: Comparison

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60

80

100

120

0 1 2 3 4 5

Time Since Start Relative to the Modal Position

Cos

t %

Cumulative Cost Over Time

Mode of Rayleigh Distribution

Rayleigh Distribution ~ Weibull Distribution

ProjectBeta Distribution

Mode of ProjectBetaDistribution

Spot the Difference!Spot the Difference!




Norden-Rayleigh Curves: Composite Curves

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0.5

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at a

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nt in

Tim

e

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Time since Start

Cum

ulat

ive

Cos

t

Combining 2 Rayleigh ModelsA composite of 2 Rayleigh curves can be used to describe projects where major additional requirements or variants are added part way through the development.

If the additional requirements are identified before the peak, then it may still be possible to model the overall expenditure with a single Rayleigh Curve

Original RequirementsAdditional RequirementsCombined Requirements




Norden-Rayleigh Curves: Composite Curves

0

0.5

1

1.5

2

2.5

3

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Time since Start

Exp

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at a

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nt in

Tim

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Time since Start

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Combining 3 Rayleigh ModelsA composite of 3 Rayleigh curves may be used to describe a project which has three distinct phases such as Conceptual Design, Detailed Design, followed by Prototype and Test

Conceptual DesignDetailed DesignPrototype and TestCombined Development




Incremental Development in BAE SystemsDemonstrator Phase 1

0 12 24 36

Months

Cos

t

Demonstrator Phase 2 / 2+

0 12 24 36

Months

Cos

t

Demonstrator Phase 3

0 12 24 36

Months

Cos

t

Demonstrator Phase 4

0 12 24 36

Months

Cos

t

Is this evidence that the relationship is somewhat ‘loose’

or …




Incremental Development in BAE Systems

Demonstrator Phases 1-4

0 12 24 36

Months

Cos

t

Phase 4

Phase 3

Phase 2+

Phase 2

Phase 1

Total

Actual

… just that booking discipline on incremental overlapping

development is a little challenging?



Norden-Rayleigh Curves Hands on …Using Weibull and ProjectBeta Distributions in Excel




Creating a Basic N -R Curve in Excel

Exercise Instructions (Part 1):

• Open the Excel Workbook RayleighCurveExercise.xls using the shortcut on the laptop’s Desktop

• Select the Tab “Basic Curves” if not already selected• The following cell colours are used:

HeadersConstants

Input VariablesCalculated ValuesExcel Generated < not used in the first two exercises




Creating a Basic N -R Curve in Excel

Exercise Instructions (continued):

• Create a N-R Curve using Excel’s Weibull function• Approximate a N-R Curve using Excel’s Beta function• The graphs will be plotted automatically

• Using either curve, vary the Endpoint or the Outturn cost or both (yellow cells only)

• You should observe that the shape of the curve remains the same –only the scales change. The Mode is displayed as a point of reference, but the same is true for any other point on the curve

Colours:Headers

ConstantsInput Variables

Calculated ValuesExcel Generated




Using Excel’s Weibull Function

Creating a Basic N -R Curve in ExcelFor these models, we will assume a fixed start point of Zero,

and a variable end point with an initial value of 35 months

The key curve parameter for a N-R curve is always 3.5 –that being the ratio of the end point in relation to the Mode

Mode = C4+(C5-C4)/C6

C14 = C$8*WEIBULL(B14,2,C$7*SQRT(2),TRUE)

Mode = Start + (End - Start)Parameter

Value = Outturn * WEIBULL(Month,2,Mode * SQRT(2),TRUE)




Using Excel’sBeta Function

Creating a Basic N -R Curve in ExcelFor these models, we will assume a fixed start point of Zero,

and a variable end point with an initial value of 35 months

The key curve parameter for The ProjectBeta curve is approx 2.125 in order to simulate a true N-R curve

C14 = D$8*BETADIST($B14,$D$6,6-$D$6,D$4,D$5)

Value = Outturn * BETADIST(Month, αααα, 6 - αααα, Start, End)

Mode = D4+(D6-1)*(D5-D4)/4

Mode = Start + (alpha - 1)*(End – Start )4




Exploiting the Basic Property of a N -R Curve

Exercise Instructions (Part 2):

Based on the baseline cost estimate of £ 5.543m for your project over 18 months, Project Management have now performed a schedule risk analysis (SRA) and have reported that potentially there could be:

− A two month delay in project start-up

− A potential 6 month slip on the end date

− And a risk of a delay in resource ramp-up of approximately 3 months

Using either the Rayleigh (Weibull) or ProjectBeta method (or both), determine the impact on the cost estimate based on this view of potential slippage

− Assume that the current maximum resource requirement is required but not exceeded





All calculations have been input with the exception of the SRA Outturn Cost

Select a method

Input the SRA revised start and end points given





All calculations have been input with the exception of the SRA Outturn Cost

Select a method

Input the SRA revised start and end points given

Using the basic shape property of N-R curves, input a calculation for the SRA Outturn so that the peak headcount matches the budget

Hint: The Outturn is proportional to the slippage

… the graphs will plot automatically



Norden-Rayleigh Curves Forecasting Development Costs & ScheduleUsing Earned Value Management Data




Using Norden-Rayleigh Curves with EVMAccording to Christensen and Rees7, after a program is 20% complete, earned value data should be sufficient to fit a Rayleigh distribution to the data

− The 20% point is not demonstrated empirically, but the authors believe that EACs are sufficiently stable at this point to use in forecasting EACs

To use EVM data in this manner requires an appreciation of the likely change in the schedule completion (e.g. programme slip) as well as cost performance:

− ACWP in relation to BCWP− BCWP in relation to BCWS

0

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Months from Start

Cum

ulat

ive

Cos

t

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200

300

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500

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800

0 10 20 30 40 50 60 70 80 90 100

Months from Start

Cos

t per

Mon

th

BCWSBCWPACWP

Source: 7. Christensen DS, & Rees DA (2002), “Is the CPI-Based EAC a Lower Bound to the Final Cost of Post A-12 Contracts?” , The Journal of Cost Analysis and Management, Winter 2002.

To define the Schedule Scale

Parameter i.e. Mode

To define the Cost Scale Parameter i.e. Expected Outturn




Using Norden-Rayleigh Curves with EVMAccording to Christensen and Rees7, after a program is 20% complete, earned value data should be sufficient to fit a Rayleigh distribution to the data

− The 20% point is not demonstrated empirically, but the authors believe that EACs are sufficiently stable at this point to use in forecasting EACs

To use EVM data in this manner requires an appreciation of the likely change in the schedule completion (e.g. programme slip) as well as cost performance:

− ACWP in relation to BCWP− BCWP in relation to BCWS

0

5,000

10,000

15,000

20,000

25,000

30,000

0 10 20 30 40 50 60 70 80 90 100

Months from Start

Cum

ulat

ive

Cos

t

0

100

200

300

400

500

600

700

800

0 10 20 30 40 50 60 70 80 90 100

Months from Start

Cos

t per

Mon

th

BCWSBCWPACWP

Source: 7. Christensen DS, & Rees DA (2002), “Is the CPI-Based EAC a Lower Bound to the Final Cost of Post A-12 Contracts?” , The Journal of Cost Analysis and Management, Winter 2002.

This requires an understanding of the achievement – often

difficult to measure or assess on development projects




Finding an EAC for a N -R Curve without a BCWP measure

What if you don’t have EVM, or any meaningful measur es of achievement?

• Assuming that you are comfortable that the Project is likely to follow a Norden-Rayleigh profile (or ProjectBeta profile), there are three fundamental options for creating an EAC from actual data alone

• You can try to find an EAC by:

1. … Fitting a Norden-Rayleigh Curve to the actual data by trial and error2. … Finding the Least Squares Error3. … Least Squares Linear Regression of the ETC

… we’re going to do all three!




Finding an EAC for a N -R Curve without a BCWP measureCurve Fitting Techniques

How do you fit the data with two unknowns (Cost Outturn and Schedule Endpoint)?

• Guess and iterate?• Non-linear Regression?

There are two feasible options for the latter:

Excel Solver (Multi-parameter Goal Seek)

… normalise the data in order to exploit the basic shape properties of the distribution

Linear Transformation

… transform the distribution into a linear format to allow a linear regression analysis to be performed

0

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Months from Start

Cum

ulat

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Cos

t

0

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500

600

700

800

0 10 20 30 40 50 60 70 80 90 100

Months from Start

Cos

t per

Mon

th

BCWSACWP




Using Norden-Rayleigh Curves without BCWP: Rationale

• All three of the following methods exploit the elasticity and constancy of the Norden-Rayleigh Curve

• The Norden-Rayleigh Curve will maintain its basic shape if it is stretched or compressed horizontally, vertically or both

• This allows the same relative positions on two curves to be compared and aligned

• The methods require the generation of a Norden-Rayleigh distribution curve using an initial “guess” for the Start and End points (and, by implication, the Modal position) and the Outturn Value (i.e. EAC)

• All 3 methods minimise the error between two such curves or partial curves to identify the Norden-Rayleigh cost and schedule parameters

0.00

0.20

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0.60

0.80

1.00

1.20

0 10 20 30 40 50 60 70 80 90 100

Months from Start

Cum

ulat

ive

Cos

t

0

1,000

2,000

3,000

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10,000

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Months from Start

Cum

ulat

ive

Cos

t

Ratio = BCWSY / BCWSX

Ratio = ACWPY / ACWPX



Norden-Rayleigh Curves Hands on …Curve Fitting Norden-Rayleigh Curves in Excel




Method 1: Finding an EAC by Trial and Error

• Open the Excel Workbook RayleighCurveExercise.xls• Select the Tab “EAC by Trial and Error ”• All ACWP Actual data to date has been input for you• All model calculations have been completed for you already• Select a method from the drop-down box in Cell(G2) (i.e. Rayleigh or ProjectBeta)• Using the yellow cells only in Columns D or E

for the chosen method, vary the Start and End month, and the Outturn Cost so that the EAC Curve and ACWP Actual data are superimposed with the minimum amount of error

• When you are happy that you have a good enough fit, select the other method and repeat the process

Colours:Headers






Method 2: Finding an EAC by the Least Squares Error

• Open the Excel Workbook RayleighCurveExercise.xls• Select the Tab “EAC Least Squares Err Rayleigh ” or “… Beta ”

• All ACWP Actual data to date has been input for you

• All model calculations have been completed for you already except two• Using the lavender cells only in Column D input an initial guess for the Start

month – any low positive value!• Input an initial

guess for the Endmonth – any value greater than the current month

• Input an initial guess for the EAC Outturn Cost – any value greater than the current actual

Colours:Headers







• Using the lavender cell only in Column K input a calculationfor the Sum of Squares of the Errors

• In the green cell below input a calculation

for the Sum of the Errors

SUMSQ(E10:E18)

Error – the difference between the ACWP actual data and the EAC Model Curve

based on the Initial Guess Values

Colours:Headers



Calculate the Sum of Errors

SUM(J10:J18)





• Select Excel Solver from the Tools menu

If it is not there, select Tools/Add-ins…then select the Solver Add-in option

which opens the Solver dialogue box

Set the Target Cell to minimise the Sum of Squares of the Errors

Identify the Solver Variables separated by commas

Colours:Headers







Identify the Solver Constraints: 1. EAC Outturn > ACWP2. End Month > Last Actual Month3. Potential Range Limit on Start Month4. Sum of Errors = 0 When all parameters and constraints

have been input, click Solve

Constraint: Sum of Errors should be zero so that the estimate is unbiased

Colours:Headers






Method 3: Finding an EAC by the Least Squares Error• Norden-Rayleigh Cumulative Distribution

Function takes the form:

Rt = C ( 1- e-0.5(t/d)2)

• Re-arranging:(C - Rt) = C e-0.5(t/d)2

• Letting y = (C - Rt) and x = t2

equation becomes:

y = C e-0.5 x/d2

or, taking the natural Log becomes:

ln(y) = ln(C) – (0.5/d2) xwhich is a linear transformation of an exponential function where

Intercept = Ln(C) (C = Estimate At Completion)

Slope = -0.5/d2 (Slope will always be negative)

=> Mode, d = 1

√√√√-2*Slope

0

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10,000

15,000

20,000

25,000

30,000

0 10 20 30 40 50 60 70 80 90 100

Months from Start

Cum

ulat

ive

Cos

t

C

?

y

Rt

ln(y)

x




Method 3: Finding an EAC by the Least Squares Error• Norden-Rayleigh Cumulative Distribution

Function takes the form:

Rt = C ( 1- e-0.5(t/d)2)

• Re-arranging:(C - Rt) = C e-0.5(t/d)2

• Letting y = (C - Rt) and x = t2

equation becomes:

y = C e-0.5 x/d2

or, taking the natural Log becomes:

ln(y) = ln(C) – (0.5/d2) xwhich is a linear transformation of an exponential function where

Intercept = Ln(C) (C = Estimate At Completion)

Slope = -0.5/d2 (Slope will always be negative)

=> Mode, d = 1

√√√√-2*Slope

0

5,000

10,000

15,000

20,000

25,000

30,000

0 10 20 30 40 50 60 70 80 90 100

Months from Start

Cum

ulat

ive

Cos

t

C

?

y

Rt

ln(y)

x

The problem seems to be that you need to know the outturn value in order to perform the

transformation … in other words, you need to know the answer, to get the answer!

However, all is not lost …Excel Solver is there to help





• Open the Excel Workbook RayleighCurveExercise.xls• Select the Tab “ETC Regression ”• All ACWP Actual data to date has been input for you

• All model calculations have been completed for you already except two

• Using the lavender cells only in Column D input an initial guess for the Startmonth – any low positive value!

• Input an initial guess for the End month (any value greater than the current month)

• Input an initial guess for the EAC Outturn Cost (any value greater than the current actual)

Colours:Headers






Method 3: Finding an EAC by the Least Squares Error• For reference, calculations are based as follows

Square the value of t

ETC: Deduct the ACWP from the Outturn “Guess”

Take the Natural Log of the ETC (Outturn-ACWP)

Calculate Revised t by taking the Month minus the Start Point

… but leave the value as t=0 wherever ACWP is zero

WEIBULL( t, 2, Mode 2 , True)

e.g. F11 = A11 - $D$4

e.g. E11 = $D$8 - B11

e.g. G11 = F11^2

e.g. H11 = LN(E11)

Colours:Headers






Method 3: Finding an EAC by the Least Squares Error• For reference, calculations are based as follows

Calculate the Slope and Intercept of a Basic Linear Regression between t2 and Log(ETC) Calculate the Modal Position

J2 = INTERCEPT(y-range, x-range)J3 = SLOPE(y-range, x-range)

J5 = 1/SQRT(-2 * J3) + D4

Colours:Headers






Method 3: Finding an EAC by the Least Squares Error• For reference, calculations are based as follows Colours:

HeadersConstants

Input VariablesCalculated ValuesExcel Generated

Calculate the Ln(ETC) Regression based on the calculated Slope and Intercept

e.g. $J$2 + $J$3 * G10

Error – the difference between the value for LN(ETC) based on the initial Outturn Guess

and that calculated by the regression





• Using the lavender cells only in Column K input a calculation

for the Sum of Squares of the Errors• In the green cell below input a calculation

for the Sum of the Errors

SUMSQ(E10:E18)

Colours:Headers



Calculate the Sum of Errors

SUM(J10:J18)





• Select Excel Solver from the Tools menu

If it is not there, select Tools/Add-ins…then select the Solver Add-in optionwhich opens the Solver dialogue box

Set the Target Cell to minimise the Sum of Squares of the Errors

Identify the Solver Variables separated by commas

Colours:Headers






Method 3: Finding an EAC by the Least Squares Error• Finally …

When all parameters and constraints have been input, click Solve

Identify the Solver Constraints: 1. EAC Outturn > ACWP2. End Month > Last Actual Month3. Potential Range Limit on Start Month4. Sum of Errors = 05. Mode calculated from the initial parameters

= mode calculated by regression

Constraint: Sum of Errors to be zero so that the estimate is unbiased

Colours:Headers






Norden-Rayleigh Curves: Conclusions ?

What have you observed about the three Methods?

• Method 1 is easier than Method 2 which is easier than Method 3• Method 1 (Trial and Error) could be called “Hit and Miss”

• Methods 2 and 3 are not precise … it can be sensitive to the “seed” parameters used (initial guesses) due to the nature of the Solver algorithm used by Excel

• Methods 2 and 3 are repeatable, because Solver is algorithmic

• No method of this nature can be considered to be accurate BUT using multiple methods will give a range estimate – more practical than a single point deterministic estimate for design and development work

• The ProjectBeta curve appears to be a good substitute for a Norden-RayleighCurve … well within the accuracy/uncertainty range that would be considered acceptable at this stage of the life cycle

• Method 2 can easily be adapted for any curve shape that suits your environment• More sophisticated models could be build using multiple composite N-R Curves




The demos and exercises were done in Excel 2003

• In 2007, 2010 Solver can be found on the Data / Analysis ribbon

• If the Add-ins are not loaded, click on the Office button, then select Excel Options,

followed by Add-ins … Manage Add-ins

and select Solver Add-in / OK

Where do you find Solver in Excel 2007 or 2010?



Thank you for listening and joining inAny further questions?

Please power down the laptops

Documents

Project Team Sizing and Cost Forecasting using Norden ... 2011/BAE Systems_Norden... · Project Team Sizing and Cost Forecasting using Norden-Rayleigh Curves ... ACostE’s Journal