job aids for con 370 - dau€¦ · job aids for con 370 . evm, statistics, regression, & cost...

Version 2.1

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Job Aids for CON 370

EVM, Statistics, Regression,

& Cost Improvement Curves

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1

Excel Spreadsheet Functions

Functions can be entered by using the equal sign such as: = average(A1:A10)

or can be accessed by selecting fx which brings up a list of functions and function categories as seen in

the examples below.

Math and Trigonometry Functions

Function Description

EXP Returns e raised to the power of a given number (i.e. the antilog of the natural logarithm)

LN Returns the natural logarithm of a number

LOG Returns the logarithm of a number to a specified base

RAND Returns a random number between 0 and 1

SQRT Returns a positive square root

SUM Adds its arguments

Statistical Functions

Function Description

AVERAGE Returns the average of its arguments

MEDIAN Returns the median of the given numbers

MODE Returns the most common value in a data set

3

Adding the Analysis Toolpak (Office 2013)

4

Data Analysis

Running Descriptive Statistics

Descriptive Statistics Dialog Box

7

Cost

Mean 9.642857143Standard Error 2.242326294Median 8.1Mode #N/AStandard Deviation 5.932637733Sample Variance 35.19619048Kurtosis -1.41642864Skewness 0.53941421Range 15Minimum 3.8Maximum 18.8Sum 67.5Count 7Confidence Level(80.0%) 3.22840217

Descriptive Statistics

Mean: mathematical average.

Median: middle value of ordered data.

Mode: value which occurred most frequently.

Range: distance between the high and low value.

Variance (s2): measure of squared variability around the mean.

Standard Deviation (s): measure of variability around the mean;

can be interpreted as the “average” estimating error.

Coefficient of Variation (CV): standard deviation expressed as a

percentage of the mean. It can be interpreted as the average

“percent” error. CV (not shown on output)

Standard Error: short for “standard error of the mean”; √

. If we were to sample repeatedly from the

same population, there would be variability in the sample means. The sample means form a distribution,

and this term represents the variability in that distribution of sample means. It is used in confidence

interval and hypothesis test calculations.

Confidence Level: this entry on the output provides the value: t √ . In this case an 80% confidence

level was selected for the mean in the descriptive statistics dialog box. The 80% confidence interval for

the true population mean would be 9.64 3.2284

Skewness: Skewness characterizes the degree of asymmetry of a distribution around its mean. Positive

skewness indicates a distribution with an asymmetric tail extending toward more positive values.

Negative skewness indicates a distribution

with an asymmetric tail extending toward

more negative values.

Kurtosis: Kurtosis characterizes the relative peakedness or flatness of a distribution compared with the

normal distribution. Positive kurtosis indicates a relatively peaked distribution.

Negative kurtosis indicates a relatively flat distribution.

Descriptive Statistics Output

8

Graphical Analysis – Developing a Histogram

Determine the number of bins desired.

One rule of thumb is n or in this case

28 5 .

Divide the range by the number of bins to

determine bin width 407 5 = 81.4 Add bin width to the minimum value and

cumulatively until you have 5 bins.

Select the Data Analysis feature as before

and then select Histogram.

Select the input range for the data and the

bins.

Select “Labels” if your input range includes

titles in the first row.

9

Note that the bin labels are displayed to the left of the tick marks (i.e. the first tick mark represents

1781.4, the second tick mark is 1862.8, etc.).

Bins Frequency1781.4 11862.8 21944.2 32025.6 4

2107 18More 0

Histogram

0

5

10

15

20

1781.4 1862.8 1944.2 2025.6 2107 More

Bins

Freq

uenc

y

Hours

Mean 2012.821429Standard Error 20.12146013Median 2052.5Mode 1904Standard Deviation 106.472759Sample Variance 11336.44841Kurtosis 1.455674766Skewness -1.374624171Range 407Minimum 1700Maximum 2107Sum 56359Count 28

Based on the histogram above, the mode of 1904 would fall in the third interval.

The mean of 2012.82 falls in the fourth interval.

The median of 2052.5 falls in the fifth or last interval. Since most of the data is located in this interval, the median is most representative of the “typical” value that occurred in this sample.

10

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

0 0.5 1 1.5 2 2.5 3

Cost

Cost

Graphical Analysis – Looking at Trends in the Data

Generating a Scatterplot

Resulting graph

11

Customizing the Graph

12

Adding a Trendline

13

Linear Regression

Accessing the Regression Function

Regression Dialog Box

14

Regression Equation

X 0 1Y b b X Cost = .6661 + 6.5456 (Weight)

Where: XY is the estimated or predicted value of Y for any given X

b0 is the Y intercept

b1 is the slope (for a one unit change in Weight, Cost changes by 6.5456)

X is the value of the independent variable

T‐Statistic

The comparison of a calculated T value with a table value tests the significance of a regression equation. It permits analysts to identify situations where, because of sampling error, a regression relationship may have a rather high coefficient of determination when there is no real relationship between the independent and dependent variables (i.e., there is no statistical significance). The “t‐Stat” for Weight indicates that the sample slope for Weight is 11.0278 standard deviations from

zero. The likelihood that the population slope is equal to zero is expressed as the “P‐value” which is

.0001 or .01%. In other words, there is only a .01% chance that the actual population slope is zero. Since

we are confident that the slope is not equal to zero, then we are confident that there is a statistical

relationship between Cost and Weight, and we should consider using Weight as an explanatory variable.

The P‐value is the level of significance. Some applications instead report the level of confidence or the

“1 – P” value. This is shown in COSTAT as the “Prob Not Zero” and in EZ Quant as “Inclusion Assurance”.

Different sources vary in their recommendation as to what constitutes an “acceptable” probability,

either stating that the level of confidence should be above .80, .90, or .95; or that the level of

significance should be below .20, .10, or .05.

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.980055948R Square 0.960509662Adjusted R Square 0.952611594Standard Error 1.291468687Observations 7

ANOVAdf SS MS F Significance F

Regression 1 202.837686 202.837686 121.6132475 0.000106741Residual 5 8.33945685 1.66789137Total 6 211.1771429

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 0.666083283 0.949148453 0.70176934 0.514134864 -1.773780489 3.105947055Weight 6.545564273 0.593549097 11.02783966 0.000106741 5.019797746 8.0713308

Linear Regression

15

R‐squared (R2 )

The R2 (Coefficient of Determination) is a measure of the amount of variation around the mean that has

been explained by the regression equation. The R2 in our example of .96 or 96% can be expressed as,

“96% of the variation in the Cost can be explained by the variation in Weight”.

The R2 value can range from .00 to 1.00, with .00 indicating that none of the variation has been

explained and with 1.00 indicating that all of the variation has been explained (in which case all of the

data points would fall on the regression line). Like many statistics, sources will vary on what is a “good”

R2 value, but usually a value above 80% or a value above 90% is considered “good”.

Multiple R

The R (Coefficient of Correlation) is a measure of the linear correlation between X and Y. The R value can

range from – 1.00 to + 1.00, with the sign of R indicating the direction of the correlation. The R value can

be directly computed using a formula which furnishes the correct sign, or calculated as the square root

of R2 with the sign attached according to whether the slope of the regression line is positive or negative.

The Multiple R (Coefficient of Multiple Correlation) is the positive square root of R2. This statistic is used

to measure the combined association between the dependent variable and multiple independent

variables.

Adjusted R‐squared (R2a )

Since the R2 can only improve as additional independent variables are included in the model, the R2a is

considered a more representative measure, particularly when comparing models, because it adjusts the

R2 for the number of independent variables in the model.





16

Standard Error (SE) or Standard Error of the Estimate (SEE)

The standard error of 1.29 is a measure of the variability around the regression line. If Cost is in

thousands, then a reasonable interpretation of the SE would be, “If we were to use this equation we

would typically expect to be off by give or take $1.29K” or “The average estimating error would be

$1.29K”. While not a precise definition, it does communicate that the SE is a measure of the accuracy of

the equation. The lower the standard error is, the more accurate the equation.

Coefficient of Variation (CV) (not reported in Excel)

The CV is a means of expressing the standard error (SE) as a relative value. While not displayed on the

Excel output, the CV can easily be calculated by dividing the SE by the mean. In our example the SE is

1.29 and the mean (from the Descriptive Statistics output) was 9.64.

The .13 can be expressed as 13% and stated, “The average estimating

error is 13%” or “We would typically expect to be off by give or take 13%”.

ANOVA (Analysis of Variance)

As the name suggests, this is a breakdown of the variance in the regression model. The first entry in the sum of squares (SS) column is the sum of squares regression (SSR) which is the amount of the variation around the mean (202.8377) that has been explained by the equation. The sum of squares residual or error (SSE) is the amount of the variation around the mean (8.3395) that the equation has not explained. The sum of squares total (SST) is the total squared variation (211.1771) around the mean. The MS is the mean square column. The mean square residual or error (MSE) of 1.6679 is the variance of the equation. The F is the F statistic. In a single independent variable equation the F test is performing the identical function as the T test, i.e. testing the significance of the independent variable. As such, the Significance F will be identical to the P‐value. In an equation with multiple independent variables, the F test considers the combined significance of all of the independent variables.





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•Com

plex

ity•S

ched

ule

•Ter

ms

and

cond

ition

s•C

ontra

ct ty

pe•M

arke

t con

ditio

ns•B

usin

ess

base

3. O

rgan

ize

the

Dat

aM

agni

tude

, Cla

ss, C

ateg

ory

2s

=

s

His

togr

am

Bins

Frequency

4.Vi

sual

Insp

ectio

n of

the

Dat

a (c

ont.)

Wha

t doe

s th

e D

ata

look

like

:

( )

Ku

rtosi

s

( +

)

( )

Skew

ness

( + )

Tren

dsU

nusu

al V

alue

s

Tool

s•E

xcel

Ana

lysi

s To

olpa

k; G

raph

s•C

ON

270

Stat

s/R

egre

ssio

n Te

mpl

ates

5.D

eter

min

ing

the

“Typ

ical

” Va

lue

Cen

tral t

ende

ncy

can

be re

pres

ente

d:

Mea

n

YΣY norX

ΣX X

ΣY

is th

e su

mm

atio

n of

the

Y v

alue

sΣ

X is

the

sum

mat

ion

of th

e X

val

ues

“n” i

s th

e sa

mpl

e si

ze

Med

ian

(redu

ces

impa

ct o

f out

liers

)•O

rder

the

data

(e.g

. hig

h to

low

)•O

dd n

umbe

r of d

ata

poin

ts:

sele

ct th

e m

iddl

e va

lue

•Eve

n nu

mbe

r of d

ata

poin

ts:

(two

mid

dle

valu

es)/2

Mod

e•T

he v

alue

that

occ

urre

d m

ost o

ften

7.C

onfid

ence

Inte

rval

s

Prob

abilit

y st

atem

ent a

bout

the

rang

e of

val

ues

in w

hich

we

expe

ct to

loca

te

the

valu

e of

the

popu

latio

n m

ean

(μ).

“t” is

a v

alue

refe

renc

ed fr

om th

e “t-

tabl

e” b

ased

on

sam

ple

size

and

le

vel o

f con

fiden

ce. W

e us

e “n

-1”

degr

ees

of fr

eedo

m.

Y

Con

fiden

ce

2

2

Sig

nific

ance

(1)

Y

Con

fiden

ce

2

2

Sig

nific

ance

(1)

P(

) =

.80

CVs Y

Y

ts n

19

10.D

ecis

ion

Theo

ry

Whi

ch o

ptio

n ha

s th

e sm

alle

st o

r gr

eate

st e

xpec

ted

valu

e:

9. H

ypot

hesi

s Te

sts

An a

ssum

ptio

n ab

out t

he p

opul

atio

n th

at w

ill be

test

ed u

sing

sam

ple

data

.

8.Pr

edic

tion

Inte

rval

s

Prob

abilit

y st

atem

ent a

bout

the

rang

e of

val

ues

in w

hich

we

expe

ct th

e ne

xt

obse

rvat

ion

(yio

r xi)

to o

ccur

.

iP

(

y

)

= .8

0

Step

1 –

Stat

e H

ypot

hesi

s

00

a0

H:

H:

Tw

o Ta

iled

Test

0

0

a0

H:

H:

or

0

0

a0

H:

H:

O

ne T

aile

d Te

st

Conf

Lev

el=

1-

Fail

to R

ejec

t Ho

Sig

Leve

l =

Reje

ct H

o

Tp

Sig

Leve

l =

/2

Rej

ect H

o

Conf

Lev

el=

1-

Fail

to R

ejec

t Ho

Sig

Leve

l =

Reje

ct H

o

Tp

Sig

Leve

l =

/2

Rej

ect H

oCo

nf L

evel

= 1-

Fail

to R

ejec

t H0

Sig

Leve

l=

Rej

ect H

0

Tp

Conf

Lev

el=

1-

Fail

to R

ejec

t H0

Sig

Leve

l=

Rej

ect H

0

Tp

Step

2 –

Defin

e yo

ur re

ject

ion

regi

on

Two

Taile

dO

ne T

aile

d

or

Step

3 –

Cal

cula

te t c

Pr

obab

ilitie

s

.60

.25

.15

1.00

St

ates

of

Natu

re

O

ptio

n 1

A

B

C

Exp

ecte

d V

alue

Opt

ion

2 A

B

C

E

xpec

ted

Val

ue

O

ptio

n 3

A

B

C

Exp

ecte

d V

alue

0is

the

valu

e of

the

hypo

thes

ized

mea

n

Yts

11n

Step

4 –

Mak

e a

deci

sion

Doe

s fa

ll in

the

reje

ctio

n re

gion

or t

he fa

il to

reje

ct re

gion

?

If th

e sa

mpl

e m

ean

() i

s “s

igni

fican

tly” d

iffer

ent f

rom

wha

t we

coul

d ex

pect

if H

0w

ere

true,

th

en w

e ca

n re

ject

the

Nul

l hyp

othe

sis

at o

ur “s

igni

fican

ce le

vel”.

If no

t “si

gnifi

cant

ly” d

iffer

ent,

then

we

fail

to re

ject

the

null

hypo

thes

is.

Y

t

20

vers

ion

2.1

5.G

raph

ical

Ana

lysi

s

You

wan

t to

note

tren

ds, p

atte

rns,

and

un

usua

l val

ues

in th

e da

ta.

Are

the

rela

tions

hips

wha

t we

expe

cted

to s

ee.

1.Id

entif

icat

ion

of C

ost D

river

s(e

Xpla

nato

ryva

riabl

es)

Mea

ning

ful c

ost d

river

s th

at c

aptu

re

phys

ical

, tec

hnic

al, p

erfo

rman

ce, a

nd

othe

r cha

ract

eris

tics

are

iden

tifie

d th

ru d

iscu

ssio

ns w

ith e

xper

ts, r

evie

w

of te

chni

cal l

itera

ture

, ind

ustry

re

ports

, pre

viou

s an

alys

es, a

nd

pers

onal

exp

erie

nce.

Qua

litie

s of

a g

ood

cost

driv

er:

•Cau

sal (

dire

ct re

latio

nshi

p)•M

ajor

(im

porta

nt c

hara

cter

istic

)•S

igni

fican

t (ex

plai

ns v

aria

tion)

•Qua

ntifi

able

(eas

ily m

easu

red)

•Col

lect

able

(dat

a av

aila

bilit

y)•P

redi

ctab

le (k

now

n in

adv

ance

with

so

me

degr

ee o

f con

fiden

ce)

3.D

ata

Col

lect

ion

Gat

herin

g da

ta o

n th

e co

st a

nd c

ost

driv

ers

for t

he s

ame

or s

imila

r ite

ms

or s

ervi

ces.

Wha

t dat

a so

urce

s ar

e av

aila

ble;

w

hat d

ata

has

been

use

d in

the

past

.

Exp

erts

sho

uld

be c

onsu

lted

whe

n se

lect

ing

sim

ilari

tem

s an

d se

rvic

es.

“Sim

ilar”

sele

ctio

n cr

iteria

:•S

ame

form

, fit,

func

tion

as w

hat i

s be

ing

estim

ated

•Sam

e dr

iver

s as

wha

t is

bein

g es

timat

ed•S

ame

rela

tions

hips

bet

wee

n th

e va

riabl

es a

s w

hat i

s be

ing

estim

ated

4.N

orm

aliz

atio

n

Are

the

prev

ious

pric

es, c

osts

, ho

urs,

mat

eria

ls, e

tc. a

val

id b

asis

fo

r com

paris

on.

You

need

to a

ccou

nt fo

r:•D

isco

unts

due

to q

uant

ity•L

earn

ing

curv

es•I

nfla

tion

or e

scal

atio

n•D

iffer

ence

s in

con

tent

(i.e

. wha

t is

or is

not

incl

uded

in th

e da

ta)

•Mat

eria

l diff

eren

ces

•Diff

eren

ces

in c

ompl

exity

•Per

form

ance

diff

eren

ces

•Var

ying

sel

ler p

ricin

g st

rate

gies

•Acq

uisi

tion

envi

ronm

ent

•Con

tract

type

•Mar

ket c

ondi

tions

•C

hang

es in

tech

nolo

gy•A

re y

ou lo

okin

g at

wha

t it c

ost,

or,

wha

t we

paid

2.Sp

ecifi

catio

n (w

hat y

ou e

xpec

t)

Bas

ed o

n yo

ur u

nder

stan

ding

of t

he

cost

driv

ers,

wha

t do

you

expe

ct th

e re

latio

nshi

p to

look

like

bet

wee

n “c

ost”

and

the

cost

driv

ers.

6.Se

lect

ing

a Fi

tting

App

roac

h an

d Fi

tting

the

Dat

a

A) L

inea

rLi

near

with

Inte

rcep

t

Line

ar w

ithou

t Int

erce

pt

(F

acto

rs)

B) N

on-L

inea

rLi

near

(

)

with

an

X

trans

form

atio

n su

ch a

s: X

2or

Tran

sfor

m X

and

Y

Hig

her o

rder

mod

els

Is th

e eq

uatio

n co

nsis

tent

with

my

spec

ifica

tion

(exp

ecta

tion)

?

X b

b

Y

10

X

X b

Y1

X X1

10

X

b(X

)

b

Y

22

10

XX

b

X b

b

Y

Dev

elop

ing

Line

ar C

ost

Est

imat

ing

Rel

atio

nshi

ps

6. A

)Lin

ear M

odel

with

Inte

rcep

t

Pre

dict

ed a

vera

ge v

alue

of Y

for

a gi

ven

valu

e of

X

b 0Y

inte

rcep

t

b 1sl

ope;

cha

nge

in Y

giv

en a

one

-un

it ch

ange

in X

X

val

ue o

f the

inde

pend

ent v

aria

ble

for w

hat y

ou a

re p

redi

ctin

g

b 0b 1

XY

xY

b

X1

X b

b

Y

10

X

X b

b

Y

10

X

CX

01

ˆy

= m

x +

b

Y =

A +

BX

y

= b

+ b

x

0

5000

1000

0

1500

0

2000

0

2500

0

020

040

060

080

010

00

SqFt

Price

“Cos

t” is

use

d in

the

gene

ral s

ense

to

refe

r to

reso

urce

s su

ch a

s do

llars

, ho

urs,

qua

ntiti

es o

f mat

eria

ls, e

tc.

21

7.C

onfid

ence

or S

igni

fican

ce

How

con

fiden

t am

I th

at th

ere

is a

st

atis

tical

rela

tions

hip

betw

een

the

X

varia

ble

and

the

Y v

aria

ble?

Sho

uld

I con

side

r usi

ng th

is e

quat

ion

or n

ot?

YS

lope

= 0

No

Rel

atio

nshi

p

X

Y

Slo

pe ≠

0R

elat

ions

hip

exis

ts

X

7.C

onfid

ence

(con

t.)

The

T st

atis

tic m

easu

res

how

far t

he

slop

e is

from

in

sta

ndar

d de

viat

ions

. The

furth

er fr

om

, the

m

ore

conf

iden

t we

are

that

ther

e is

a

rela

tions

hip

betw

een

the

depe

nden

t an

d in

depe

nden

t var

iabl

e.

Reg

ress

ion

outp

uts

typi

cally

pro

vide

th

e co

nfid

ence

leve

l (or

sig

nific

ance

le

vel)

asso

ciat

ed w

ith th

e T-

stat

istic

.O

r (n

–k

–1)

“k” i

s th

e nu

mbe

r of i

ndep

ende

nt

varia

bles

in th

e eq

uatio

n an

d th

e “1

” re

pres

ents

the

inte

rcep

t

AN

OVA

(Ana

lysi

s of

Var

ianc

e)

SS

T –

Sum

of S

quar

es T

otal

(th

e to

tal s

quar

ed v

aria

tion

of th

e ob

serv

atio

ns a

roun

d th

e m

ean)

SS

R –

Sum

of S

quar

es R

egre

ssio

n(th

e am

ount

of t

he v

aria

tion

arou

nd

the

mea

n ex

plai

ned

by th

e eq

uatio

n)

SS

E –

Sum

of S

quar

es E

rror

(the

amou

nt o

f the

var

iatio

n ar

ound

th

e m

ean

note

xpla

ined

by

equa

tion,

i.e

. the

une

xpla

ined

var

iatio

n)

DF

–D

egre

es o

f Fre

edom

(n –

p)

“p” i

s th

e nu

mbe

r of e

stim

ated

pa

ram

eter

s in

the

equa

tion

SST

ΣY

Y

SSR

ΣYY

SSE

ΣY

Y

e.g.b

,b,b

8.A

ccur

acy

How

acc

urat

e is

the

equa

tion?

Var

ianc

e (M

SE

) =

MS

E: M

ean

(ave

rage

) Squ

ared

Erro

r

Stan

dard

Err

or (S

E) =

Variance

“Ave

rage

” or “

typi

cal”

estim

atin

g er

ror

Coe

ffici

ent o

f Var

iatio

n (C

V) =

CV

x 1

00 c

an b

e in

terp

rete

d as

the

“ave

rage

” per

cent

est

imat

ing

erro

r

9.Va

riatio

n

How

muc

h of

the

varia

tion

in th

e de

pend

ent v

aria

ble

can

be e

xpla

ined

by

the

varia

tion

in th

e in

depe

nden

t va

riabl

e?

Coe

ffici

ent o

f Det

erm

inat

ion

( R2

)

RSSR SSTor1

SSE SST

Som

etim

es c

onsi

dere

d a

mea

sure

of

the

stre

ngth

of th

e re

latio

nshi

p be

twee

n th

e va

riabl

es.

R2

is a

mea

sure

of c

orre

latio

n, n

ot

caus

atio

n, s

o do

n’t j

ust a

ssum

e th

at

an a

ssoc

iatio

n im

plie

s ca

usat

ion.

SSE

SSR

(SS

T)

22

10. O

utlie

rs w

ith re

spec

t to

X an

d Y

2

LeverageLV

∑

X

2

Y

11. O

utlie

rs w

ith re

spec

t to

the

pred

icte

d va

lue

() (

pred

ictio

n pr

oble

ms)

StandardizedResidual

Y

YSE

StudentizedResidual

Y

YSE

1Leverage

13. R

esid

uals

Did

we

prop

erly

fit t

he d

ata

(i.e.

are

th

e re

sidu

als

rand

omly

dis

tribu

ted

abou

t zer

o w

ith a

con

stan

t var

ianc

e ac

ross

the

rang

e of

X v

alue

s)?

0X

Prob

lem

: Som

e no

n-ra

ndom

pat

tern

s in

the

resi

dual

s ca

n be

indi

catio

ns o

f no

nlin

ear d

ata.

0X

0X

Prob

lem

: Som

e no

n-co

nsta

nt p

atte

rns

can

be in

dica

tions

of p

robl

ems

with

the

form

of t

he e

quat

ion.

0X

0X

Residuale

YY

Is it

par

t of t

he p

opul

atio

n; a

re th

ere

clas

ses

with

in th

e da

ta; c

ould

it b

e a

mea

sure

men

t er

ror;

norm

aliz

atio

n er

ror;

data

ent

ry e

rror

; or

an

unus

ual e

vent

?

Que

stio

ns:

Par

t of t

he p

opul

atio

n;

clas

ses

with

in th

e da

ta;

mea

sure

men

t err

or;

norm

aliz

atio

n er

ror;

data

ent

ry e

rror

; or

unus

ual e

vent

?M

issi

ng a

cos

t driv

er?

Wro

ng m

odel

form

?

2

2

12. I

nflu

entia

l Obs

erva

tions

Is th

ere

a pa

rticu

lar d

ata

poin

t hav

ing

sign

ifica

ntly

mor

e in

fluen

ce o

n th

e sl

ope

and

inte

rcep

t of t

he e

quat

ion

than

the

othe

r dat

a po

ints

?

Que

stio

ns:

Par

t of t

he p

opul

atio

n; c

lass

es w

ithin

th

e da

ta; m

easu

rem

ent,

norm

aliz

atio

n,

or d

ata

entry

err

or; o

r unu

sual

eve

nt?

Mis

sing

cos

t driv

er?

Wro

ng m

odel

?

rand

om p

atte

rn; c

onst

ant v

aria

nce

Leve

rage

Residual

stddevsfrom

∅

isanoutlier

stddevsfrom

∅

isanoutlier

stderrorsfrom

∅

isanoutlier

stderrorsfrom

∅

isanoutlier

23

7.R

elia

bilit

y of

the

Fact

orIf

an a

vera

ge o

f rat

ios

was

use

d, h

ow

muc

h va

riabi

lity

is th

ere

in th

e ra

tios?

$/P

age

of

Pro

gram

Scr

apT

ech

Dat

aA

4.5%

$45

B4.

3%$7

0C

3.8%

$35

D

4.0%

$50

E

3.9%

$65

F4.

2%$4

0Va

riabi

lity?

Low

Hig

h(N

oV

aria

bilit

y: C

osts

acc

umul

ated

us

ing

a fa

ctor

; sel

f-fu

lfilli

ng p

roph

ecy,

or

pot

entia

l CA

S 4

01 p

robl

em?)

Hig

h V

aria

bilit

y: in

vest

igat

e ex

pens

e an

d ba

se c

onte

nt, n

orm

aliz

atio

n, d

ata

entr

y, m

easu

rem

ent,

diffe

rent

cla

sses

, et

c. In

vest

igat

e tr

ue c

ost r

elat

ions

hip

for

fixed

cos

t (re

gres

s w

ith in

terc

ept)

.O

ther

cos

t driv

ers

impr

ove

CE

R?

1.Id

entif

icat

ion

•Wha

t is

bein

g es

timat

ed b

y th

e fa

ctor

? A

re th

e sa

me/

sim

ilar

cost

s es

timat

ed/p

ropo

sed

else

whe

re?

(CA

S 4

02, F

AR

31.

202/

3 co

mpl

iant

?)•W

hat i

s an

app

ropr

iate

bas

e fo

r th

e fa

ctor

? Is

it c

ausa

l or

logi

cal?

•Is

fact

or u

niqu

e to

you

r pr

opos

al o

r is

it a

n al

loca

tion?

CA

S 4

01 is

sue?

2. D

ata

Col

lect

ion

Is d

ata

colle

cted

from

an

acco

untin

g al

loca

tion?

Sel

f ful

fillin

g pr

ophe

cy?

3. A

naly

sis/

Nor

mal

izat

ion

Con

sist

ency

in th

e co

nten

t of t

he

expe

nses

bei

ng e

stim

ated

in th

e nu

mer

ator

and

bas

e (d

enom

inat

or)

of

the

fact

or is

one

of t

he m

ost o

ver-

look

ed a

spec

ts o

f dev

elop

ing

and

usin

g fa

ctor

s.

4.Sp

ecifi

catio

n

Thi

s is

wha

t you

are

spe

cify

ing.

The

pric

e, c

ost,

or h

ours

are

prim

arily

va

riabl

e in

nat

ure.

Thi

s m

ust b

e tr

ue

in o

rder

for

the

mod

el to

be

robu

st

(i.e.

app

licab

le o

ver

a w

ide

rang

e of

th

e ba

se o

f the

fact

or).

The

gre

ater

the

prop

ortio

n of

fixe

d co

sts

incl

uded

with

in th

e da

ta, t

he

mor

e re

stric

tive

the

appl

icat

ion

of th

e fa

ctor

.

5.Vi

sual

Insp

ectio

n of

the

Dat

a

Dev

elop

er/R

evie

wer

:

Doe

s a

scat

terp

lot o

f the

dat

a su

ppor

t the

use

of a

fact

or? No

Yes

6.Fi

tting

the

Dat

a

Rat

io:

A r

atio

can

be

deve

lope

d us

ing

a si

ngle

dat

a po

int;

the

aver

age

of a

nu

mbe

r of

rat

ios;

or

a ra

tio o

f the

to

tal o

f the

poo

ls d

ivid

ed b

y th

e to

tal

of th

e ba

ses

(a w

eigh

ted

aver

age)

.

Reg

ress

ion:

A te

chni

que

know

n as

“re

gres

sion

th

roug

h th

e or

igin

” or

“re

gres

sion

with

a

zero

con

stan

t” c

an b

e us

ed.

7.R

elia

bilit

y of

the

Fact

or (c

ont.)

Dev

elop

er/R

evie

wer

: Ove

r w

hat r

ange

of th

e da

ta is

the

fact

or r

elia

ble?

CE

Rs

or F

acto

rs

Y

X

Y

X

Scr

ap $

Scr

ap R

ate

= M

ater

ial $

X1

X1

ˆ

y =

0 +

bx

whi

ch b

ecom

es

ˆ

y

= b

x

Y

X

Y

X

EXPE

NSE

FIXE

D

ESTI

MAT

ING

BAS

E

FAC

TOR

TRU

E C

ER

MO

RE

RO

BU

STES

TIM

ATIN

G R

ANG

E

EXPE

NSE

FIXE

D

ESTI

MAT

ING

BAS

E

FAC

TOR

TRU

E C

ER

MO

RE

LIM

ITED

ESTI

MAT

ING

RAN

GE

Low

er R

isk

in E

stim

atin

g U

sing

Fac

tor

•R

elat

ivel

y lit

tle fi

xed

cost

•A

ctua

l reg

ress

ion

(tru

e C

ER

) w

ith a

n in

terc

ept:

-clo

ser

to fa

ctor

ass

umpt

ion

of z

ero

inte

rcep

t-in

terc

ept c

oeffi

cien

t “t”

and

“pr

obab

ility

of

no

t zer

o” r

elat

ivel

y sm

alle

r •

Rel

ativ

ely

wid

er r

ange

of e

stim

atin

g us

eful

ness

Hig

her

Ris

k in

Est

imat

ing

Usi

ng F

acto

r•

Mor

e (r

elat

ive)

fixe

d co

st•

Act

ual r

egre

ssio

n (t

rue

CE

R)

with

an

inte

rcep

t:-c

ontr

adic

ts a

ssum

ptio

n of

zer

o in

terc

ept

-inte

rcep

t coe

ffici

ent “

t” a

nd “

prob

abili

ty o

f

not z

ero”

rel

ativ

ely

larg

e •

Nar

row

er r

ange

of e

stim

atin

g us

eful

ness

•U

sed

cons

iste

ntly

ove

r/un

der?

Ave

rage

s ou

t?•

Con

side

r al

tern

ativ

e es

timat

ing

met

hodo

logy

?ve

rsio

n 1.

0

Y0

bX

or

YbX∴b

Y X

25

Det

erm

ine

If C

ER

s W

ere

Pro

perly

Dev

elop

ed a

nd A

pplie

d.

To d

eter

min

e if

cost

est

imat

ing

rela

tions

hips

(C

ER

s) u

sed

in th

e pr

opos

al w

ere

prop

erly

de

velo

ped

and

appl

ied,

ask

que

stio

ns r

elat

ed to

the

issu

es a

nd c

once

rns

asso

ciat

ed w

ith C

ER

dev

elop

men

t.

•D

oes

the

avai

labl

e in

form

atio

n ve

rify

the

exis

tenc

e an

d ac

cura

cy o

f th

e pr

opos

ed r

elat

ions

hip?

•Is

ther

e an

y tr

end

in th

e re

latio

nshi

p?•

Is th

e C

ER

use

d co

nsis

tent

ly?

•H

as th

e C

ER

bee

n co

nsis

tent

ly a

ccur

ate

in th

e pa

st?

•H

ow c

urre

nt is

the

CE

R?

•W

ould

ano

ther

inde

pend

ent v

aria

ble

be b

ette

r fo

r de

velo

ping

and

app

lyin

g a

CE

R?

•Is

the

CE

R a

sel

f-fu

lfilli

ng p

roph

ecy?

•W

ould

use

of a

det

aile

d es

timat

e or

dire

ct c

ost c

ompa

rison

with

act

uals

from

a

prio

r ef

fort

pro

duce

mor

e ac

cura

te r

esul

ts?

•D

oes

the

CE

R e

stim

ate

cons

ider

the

chan

ging

val

ue o

f the

dol

lar?

Fro

m th

e F

ive-

Vol

ume

Pric

ing

Gui

des

Vol

3, C

hap

6.2

26

vers

ion

2.0

1.Id

entif

icat

ion

of C

ost D

river

s

2.D

ata

Col

lect

ion

3.A

naly

sis/

Nor

mal

izat

ion

4.Sp

ecifi

catio

n

5.Vi

sual

Insp

ectio

n of

the

Dat

a

6.Fi

tting

the

Dat

a (N

onlin

ear)

a)T

rans

form

atio

n on

X

b)Q

uadr

atic

Equ

atio

n

c)P

ower

Equ

atio

n

The

se a

ppro

ache

s ar

e so

met

imes

ca

lled

“intr

insi

cally

line

ar”

in th

at th

e da

ta is

tran

sfor

med

or

mod

eled

usi

ng

linea

r re

latio

nshi

ps. S

ome

“non

linea

r”

tren

ds a

re “

not l

inea

r” in

that

the

data

ca

n’t b

e tr

ansf

orm

ed o

r m

odel

ed w

ith

a lin

ear

func

tion

(e.g

. ste

p fu

nctio

ns).

Non

linea

r R

egre

ssio

n

Whe

n w

ould

we

cons

ider

a N

onlin

ear a

ppro

ach?

1. T

he e

xpec

tatio

n or

spe

cific

atio

n by

sub

ject

mat

ter

expe

rt

2.O

bser

vatio

n ba

sed

on g

raph

ical

ana

lysi

s of

the

data

X Tr

ansf

orm

atio

ns

Incr

easi

ng a

t an

incr

easi

ng ra

te

Incr

easi

ng a

t a d

ecre

asin

g ra

te

Dec

reas

ing

at a

dec

reas

ing

rate

0102030405060708090100

020

0040

0060

0080

00

SqFt

Price 3.A

s a

rem

edy

for

a:

Pre

dict

ion

Pro

blem

Influ

entia

l Obs

erva

tion

Non

linea

rity

in th

e R

esid

ual P

lots

1 X

X

X

Qua

drat

ic E

quat

ion

Y=

b0

+ b

1X

1+

b2X

12

…th

is w

hen

b 2is

pos

itive

…

…an

d th

is w

hen

b 2is

neg

ativ

e

27

The

Stan

dard

Err

or (S

E) in

“U

nit S

pace

” fo

r the

Pow

er M

odel

Pow

er M

odel

a.k

.a. L

og-L

og M

odel

X a

nd Y

tran

sfor

mat

ion

usin

g ei

ther

Lo

g X

, Log

Y o

r us

ing

LN X

, LN

Y

Com

mon

Log

arith

m (

LOG

)-

uses

bas

e 10

-th

e LO

G o

f a n

umbe

r is

the

pow

er

to w

hich

10

mus

t be

rais

ed to

obt

ain

that

num

ber

Nat

ural

Log

arith

m (

LN)

-us

es b

ase

e (2

.718

28…

)-

the

LN o

f a n

umbe

r is

the

pow

er to

w

hich

“e”

mus

t be

rais

ed to

obt

ain

that

num

ber

Cre

atin

g th

e Po

wer

Mod

el –

Reg

ress

Log

X, L

og Y

or

LN X

, LN

Y s

uch

as:

Equ

atio

n in

“Lo

g” S

pace

Con

vert

ing

an e

quat

ion

from

Log

Spa

ce to

Uni

t Spa

ce

Tak

e th

e an

tilog

of t

he in

terc

ept (

e -0

.010

2=

0.9

899)

Slo

pe in

log

spac

e 1.

9069

LN

(X)

beco

mes

the

expo

nent

in u

nit s

pace

X1.

9069

Equ

atio

n in

“U

nit”

spac

e (i.

e. P

ower

Mod

el):

Y=

0.9

899

(X)1.

9069

1000

)

10 (i.

e. 3

10

00

LOG

100)

10

(i.e.

2

100

LO

G3

2

10

00)

2.

7182

8

(i.e.

6.

9078

1000

LN

10

0)

2.71

828

(i.

e.

4.60

5

10

0

LN6.

9078

4.60

5

The

Pow

er M

odel

Y

bX

Incr

easi

ng a

t an

incr

easi

ng ra

te

b 1>

1

Incr

easi

ng a

t a d

ecre

asin

g ra

te

0 <

b1

< 1

Dec

reas

ing

at a

dec

reas

ing

rate

b 1<

0

YX

LN(Y

)LN

(X

)

42

1.38

630.

6931

428

3.73

772.

0794

225

165.

4161

2.77

26

450

256.

1092

3.21

89

750

326.

6201

3.46

57

LN Y

= -

0.01

02 +

1.9

069

LN (

X)

(X)

(Y)

YY

YY

YIn

depe

nden

tD

epen

dent

Pre

dict

edR

esid

ual

Res

idua

l2

24

3.71

0.29

0.08

842

52.2

0-1

0.20

104.

0416

225

195.

7629

.24

854.

9825

450

458.

48-8

.48

71.9

132

750

734.

1115

.89

252.

49

26.7

412

83.5

0

VarianceMSE

SSE

DF

∑Y

Yn

21283.50

3427.83

StandardErrorSE

in

Variance

427.83

20.68

Y294.20CV

SE Y20.68

294.20

.0703or7.03%

Dat

a is

non

linea

r in

“U

nit S

pace

”…

…bu

t is

linea

r in

“Lo

g S

pace

”…

…so

per

form

line

ar r

egre

ssio

n on

Lo

g X

, Log

Y o

r LN

X, L

N Y

…

LN Y

= b

0+

b1

LN (

X)

…th

en c

onve

rt th

e eq

uatio

n ba

ck to

X a

nd Y

in “

Uni

t Spa

ce”.

Yb

X

28

1.Id

entif

icat

ion

of C

ost D

river

s

2.Sp

ecifi

catio

n

3.D

ata

Col

lect

ion

4.N

orm

aliz

atio

n

5.G

raph

ical

Ana

lysi

s

6.Fi

tting

the

data

7.C

onfid

ence

or S

igni

fican

ce

8.A

ccur

acy

of th

e Eq

uatio

n

9.Va

riatio

n in

Y e

xpla

ined

by

X

10.X

and

Y O

utlie

rs

11.P

redi

ctio

n Pr

oble

ms

12.I

nflu

entia

l Obs

erva

tions

13.R

esid

uals

14.W

hen

shou

ld I

cons

ider

usi

ng

addi

tiona

l ind

epen

dent

var

iabl

es?

(1) E

xpec

tatio

n. T

he s

ubje

ct m

atte

r ex

pert

says

that

you

nee

d to

con

side

r dr

iver

s A

, B, a

nd C

in y

our e

quat

ion.

(2) D

esire

to h

ave

an e

quat

ion

that

ca

ptur

es m

ultip

le c

hara

cter

istic

s of

w

hat y

ou a

re e

stim

atin

g.

(3) I

mpr

ove

the

stat

istic

s of

mod

el

(e.g

. low

erin

g th

e S

E a

nd C

V).

(4) A

s a

rem

edy

for…

•O

bser

vatio

n yo

u di

dn’t

pred

ict w

ell

•R

educ

ing

or re

mov

ing

the

effe

ct o

f an

influ

entia

l obs

erva

tion

Mul

tiple

or M

ultiv

aria

te

Reg

ress

ion

X 2

Y

X 1

22

11

0X

Xb

X

b

b

Y

15.A

re th

ere

any

cons

trai

nts

with

re

gard

to h

ow m

any

inde

pend

ent

varia

bles

I us

e?

•Sam

ple

size

and

,

•Deg

rees

of F

reed

om

Eac

h ad

ditio

nal i

ndep

ende

nt v

aria

ble

in th

e eq

uatio

n ac

ts a

s an

add

ition

al

cons

train

t in

bein

g ab

le to

gen

eral

ize

abou

t the

pop

ulat

ion.

You

sho

uld

mai

ntai

n so

me

min

imum

nu

mbe

r of d

egre

es o

f fre

edom

, tha

t be

ing

the

(n –

p) d

egre

es o

f fre

edom

as

soci

ated

with

the

SS

E.

16.A

re th

ere

any

com

plic

atio

ns

whe

n us

ing

two

or m

ore

X va

riabl

es in

the

sam

e eq

uatio

n?

Col

linea

rity

or m

ulti-

collin

earit

y is

the

pres

ence

of c

orre

latio

n be

twee

n th

e in

depe

nden

tvar

iabl

es.

Som

e re

fere

nces

spe

cific

ally

refe

r to

colli

near

ity a

s th

e co

nditi

on th

at

exis

ts w

hen

the

corr

elat

ion

betw

een

the

X v

aria

bles

is h

igh.

Coe

ffici

ent o

f Cor

rela

tion

(R)

-1 ≤

R ≤

+ 1

Pai

rwis

e C

orre

latio

n M

atrix

The

R v

alue

(0.9

331)

is a

mea

sure

of

the

corr

elat

ion

betw

een

the

two

inde

pend

ent v

aria

bles

Thr

ust a

nd

Wei

ght.

Cost

Thrust

Weight

Cost

1.0000

Thrust

0.9760

1.0000

Weight

0.9779

0.9331

1.0000

R0.70

Col

linea

rity

or M

ulti-

colli

near

ity

Wha

t is

high

cor

rela

tion?

Effe

cts

of h

igh

corre

latio

n?•I

ncre

ases

err

or in

the

coef

ficie

nts

•Una

ble

to a

ccur

atel

y st

ate

mar

gina

l co

ntrib

utio

ns o

f eac

h va

riabl

e•M

ay p

recl

ude

sign

ifica

nt d

river

from

ap

pear

ing

sign

ifica

nt•C

ould

cha

nge

the

sign

of o

ne o

f the

va

riabl

es

Wha

t do

I do?

•Av

oid

usin

g th

e X

var

iabl

es in

the

sam

e eq

uatio

n•

Con

side

r usi

ng th

e X

var

iabl

es

toge

ther

if th

e eq

uatio

n is

logi

cal

and

the

T st

atis

tic p

roba

bilit

ies

are

acce

ptab

le•

Cou

ld tr

y to

“cor

rect

” for

the

corr

elat

ion

Unc

orre

late

d X

varia

bles

ver

sus

Cor

rela

ted

X v

aria

bles

vers

ion

2.0

29

17. H

ow c

onfid

ent a

m I

ther

e is

a

rela

tions

hip

betw

een

the

Y va

riabl

e an

d al

l the

X’s

in th

e eq

uatio

n?

The

F st

atis

tic o

r F “r

atio

” loo

ks a

t the

“fu

ll” e

quat

ion,

i.e.

all

the

inde

pend

ent

varia

bles

in th

e eq

uatio

n.

Sho

uld

I con

side

r usi

ng th

e eq

uatio

n,

or n

ot?

18. H

ow d

o I d

ecid

e up

on th

e op

timal

com

bina

tion

of v

aria

bles

?

(1) J

udgm

ent o

f the

ana

lyst

: des

ire

for a

mod

el w

ith a

n ec

onom

y of

va

riabl

es v

ersu

s de

sire

to c

aptu

re o

r m

odel

mul

tiple

cha

ract

eris

tics

of w

hat

is b

eing

est

imat

ing.

(2) C

orre

latio

n be

twee

n X

var

iabl

es.

(3) T

sta

tistic

for e

ach

inde

pend

ent

varia

ble

in th

e m

odel

mus

t pas

s th

e cr

iteria

for d

esire

d co

nfid

ence

leve

l.

Wha

t doe

s th

e T

stat

istic

act

ually

m

easu

re in

an

equa

tion

with

mul

tiple

X

var

iabl

es?

The

T s

tatis

tic is

a

mea

sure

of t

he m

argi

nalc

ontri

butio

n th

at a

var

iabl

e m

akes

to th

e eq

uatio

n.

19. C

an I

still

use

the

R2

to c

ompa

re e

quat

ions

, ev

en w

hen

the

equa

tions

hav

e di

ffere

nt n

umbe

rs

of in

depe

nden

t var

iabl

es?

(Adj

uste

d R

2 ) (A

djus

ts fo

r deg

rees

free

dom

)

R2 a

shou

ld b

e us

ed a

nytim

e yo

u ar

e co

mpa

ring

equa

tions

with

diff

erin

g nu

mbe

rs o

f deg

rees

of

freed

om a

s w

ould

occ

ur in

equ

atio

ns w

ith d

iffer

ing

num

bers

of i

ndep

ende

nt v

aria

bles

and

equ

atio

ns

base

d on

diff

erin

g sa

mpl

e si

zes.

R2

can

still

be

used

for d

escr

iptiv

e pu

rpos

es fo

r a

give

n eq

uatio

n.

2 aR

p -n

1 -n

SS

T

SS

E - 1

aR

2

20. H

ow d

o I q

uant

ifya

qual

itativ

ech

arac

teris

tic o

r par

amet

er?

Kno

wn

as D

umm

y va

riabl

es, I

ndic

ator

va

riabl

es, Q

ualit

ativ

e va

riabl

es, o

r Bin

ary

varia

bles

.

Dum

my

varia

bles

can

be

used

whe

n yo

u ha

ve c

lass

es o

r cat

egor

ies

with

in th

e da

ta s

et

that

you

wan

t to

capt

ure

in th

e eq

uatio

n.

# D

umm

y va

riabl

es =

# C

lass

es –

1

X 1X 2

C1

0

0C

2 0

1

C3

1

0

Estim

atin

g in

the

“rel

evan

t” ra

nge

of th

e C

ERTh

e ra

nge

over

whi

ch a

n es

timat

ing

rela

tions

hip

is v

alid

for u

se, r

ough

ly d

efin

ed b

y th

e up

per a

nd

low

er b

ound

s of

the

inde

pend

ent v

aria

ble.

The

pa

ram

eter

s of

wha

t is

bein

g es

timat

ing

shou

ld b

e w

ithin

the

rang

e of

the

data

. A

lso,

if th

ere

is

corr

elat

ion

betw

een

the

X v

alue

s in

the

data

set

, th

en w

hat i

s be

ing

estim

atin

g m

ust e

xhib

it th

e sa

me

rela

tions

hips

.

Fora

Xequationy

bb

XtheT‐statisticcanbecalculatedas:

Tb S

orT

Fstatistic

MSR

MSE

Fora

Xequationsuchasy

bb

Xb

X

TheT‐statisticforaparticularXvariablecanbecalculatedas:

Tb S

orT

F∗F∗isthe

FforaparticularXvariable

F∗SSR

SSR

MSE

SSR

,SSR

MSE

,

“Full”referstotheequationthatincludestheXvariableyouareevaluating.

“Reduced”referstotheequation“without”theXvariableyouareevaluating.

ThedifferencebetweentheSSRFullandSSRReducedisthemarginalcontribution.

Con

fiden

ce

Sig

nific

ance

30

CO

NC

EPT

FO

RM

UL

AT

ION

#

Des

crip

tion

Uni

t C

umul

ativ

e A

vera

ge

1

Cos

t of

any

sing

le, s

peci

fic

unit

X

Y� X=

A

XB

A

[XB

+1 -

(X

-1)B

+1]

2 C

um T

otal

(C

T)

cost

for

X u

nits

fro

m u

nit 1

th

roug

h th

e la

st u

nit (

L)

CT

X =

Alte

rnat

e Fo

rmul

a (

No

tabl

e re

quir

ed)

AX

BX

o

r

AX

B+1

3 A

vera

ge c

ost o

f th

e fi

rst X

uni

ts

=

AX

B

* 4

Tot

al C

ost (

TC

) fo

r any

lot g

iven

a fi

rst u

nit (

F)

and

a la

st u

nit (

L)

T

CF,

L =

Alte

rnat

e Fo

rmul

a (

No

tabl

e re

quir

ed)

A [

LB

+1 -

(F-

1)B

+1]

F

= Fi

rst u

nit n

umbe

r un

der

cons

ider

atio

n, L

= L

ast u

nit n

umbe

r un

der

cons

ider

atio

n

X =

may

be

eith

er th

e un

it nu

mbe

r or

cum

ulat

ive

num

ber

of X

uni

ts

A =

T1

= Y

1 =

Cos

t of

Uni

t 1

can

be

dete

rmin

ed u

sing

the

Cum

ulat

ive

Prog

ress

Cur

ve T

able

s (a

.k.a

. – th

e B

oein

g T

able

s).

Not

e: ta

bles

are

use

d on

ly w

ith th

e U

nit f

orm

ulat

ion,

not

the

Cum

ulat

ive

Ave

rage

for

mul

atio

n.

∑L 1

bX

A

xY

CT X

X

()

X

- X

A

1

F- 1

bL 1

b∑

∑

∑b

X

see

botto

m o

f pa

ge

see

botto

m o

f pa

ge

Qu

an

tity L

$ o

r H

rs. 1

Qu

an

tity L

$ o

r H

rs.

F

COST IMPROVEMENT CURVE EQUATIONS

𝐵𝐵=

log (𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠)

log (

2) 𝑠𝑠𝑜𝑜

ln (𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

)ln

(2)

𝑆𝑆𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

%=

2𝐵𝐵

Lot

Siz

e =

[L

– (

F –

1)]

Solv

ing

Impr

ovem

ent C

urve

Pro

blem

s Pe

rhap

s yo

u ha

ve b

een

aske

d fo

r a

cost

est

imat

e fo

r an

item

kno

wn

to b

e ex

peri

enci

ng (

or is

rea

sona

bly

expe

cted

to e

xper

ienc

e) s

ome

lear

ning

. So

w

hat a

re y

ou b

eing

ask

ed to

fin

d? T

he c

ost o

f a

spec

ific

uni

t? T

he c

ost o

f a

spec

ific

lot?

The

cum

ulat

ive

tota

l cos

t fro

m th

e be

ginn

ing

of

prod

uctio

n?

Exa

mpl

e: L

ets

say

DC

MA

rep

orts

that

the

cont

ract

or is

exp

erie

ncin

g an

85%

cos

t im

prov

emen

t cur

ve u

nder

the

unit

for

mul

atio

n. T

he E

VM

da

ta in

dica

tes

thei

r la

test

rev

ised

est

imat

e (L

RE

) of

the

25th

uni

t cos

t is

$45,

000.

You

hav

e be

en a

sked

to e

stim

ate

the

cost

of

the

26th

uni

t.

1) D

eter

min

e w

hat f

orm

ulat

ion

best

mod

els t

he c

ontr

acto

r’s p

rodu

ctio

n en

viro

nmen

t. In

this

exa

mpl

e, D

CM

A h

as r

epor

ted

that

this

con

trac

tor’

s pr

oduc

tion

env

iron

men

t on

this

item

is b

est m

odel

ed u

sing

a u

nit f

orm

ulat

ion

rath

er th

an a

cum

ulat

ive

aver

age

form

ulat

ion.

2)

Det

erm

ine

wha

t (ex

actly

) you

hav

e be

en a

sked

to e

stim

ate.

Y

ou h

ave

been

ask

ed to

est

imat

e th

e co

st o

f a

spec

ific

, sin

gle

unit

. T

his

is d

escr

ibed

as

the

conc

ept f

or

, con

cept

#1

on th

e fo

rmul

a sh

eet.

You

wil

l sol

ve f

or th

e co

st o

f th

e 26

th u

nit,

or

.

3) I

dent

ify w

hich

equ

atio

n w

ill p

rovi

de th

e an

swer

. U

nder

the

“Uni

t” f

orm

ulat

ion

colu

mn

we

find

the

equa

tion

ass

ocia

ted

wit

h co

ncep

t #1

()

to b

e A

Xb .

Thu

s ou

r eq

uati

on w

ill b

e =

AX

b . 4)

Ide

ntify

wha

t add

ition

al in

form

atio

n (if

any

) you

nee

d to

solv

e th

e eq

uatio

n.

To

solv

e fo

r th

e 26

th u

nit c

ost (

), w

here

X=

26, t

he e

quat

ion

beco

mes

=

A(2

6)b .

But

you

see

that

the

firs

t uni

t cos

t (A

) an

d th

e sl

ope

coef

fici

ent (

b) a

re s

till

nee

ded

to s

olve

the

equa

tion

.

5) U

se w

hate

ver

else

you

hav

e to

cal

cula

te a

ny a

dditi

onal

info

rmat

ion

you

may

nee

d.

DC

MA

rep

orts

an

85%

impr

ovem

ent c

urve

slo

pe is

bei

ng e

xper

ienc

ed.

Thu

s th

e sl

ope

coef

fici

ent (

b) c

an b

e ca

lcul

ated

fro

m th

e eq

uati

on b

=

log(

slop

e)/l

og(2

) =

log(

.85)

/log

(2),

or

b =

-.2

3446

5.

Als

o, th

e L

RE

for

the

25th

uni

t cos

t (25

Y)

is $

45,0

00.

Whe

re X

= 2

5, th

e eq

uati

on

= A

Xb b

ecom

es

25Y

= A

(25)

b . B

y su

bsti

tuti

ng

25Y

=

$45,

000

and

b=-.

2344

65 in

to th

e eq

uati

on, i

t bec

omes

$45

,000

=A

(25)

-.23

4465

whi

ch c

an b

e so

lved

for

A w

here

A =

$95

,715

.

6) S

olve

the

equa

tion

for

wha

t you

hav

e be

en a

sked

to e

stim

ate.

Now

we

can

solv

e th

e eq

uati

on

= A

Xb to

est

imat

e th

e co

st o

f the

26th

uni

t ()

whe

re

A =

$95

,715

, X =

26,

and

b=

-.23

4465

. =

$95

,715

(26)

-.23

4465

= $

44,5

88.

XY

26Y

XY

XY

26Y

26Y

XY

XY

26Y

26Y

Version 1.0

Calculating Lot Costs under the Unit Formulation The text discusses one means (algebraic lot midpoint or ALM) by which midpoints or plot points can be derived from lot data for the purpose of developing the slope and the intercept for the unit learning curve formulation. A second application of the midpoint calculation is in estimating the cost of a future lot given a predetermined slope. We first determine the lot midpoint by using a midpoint formula, we then estimate the unit cost at that midpoint using the given slope, and then determine the lot cost by multiplying the cost at the midpoint by the lot size. This teaching note will demonstrate three techniques for calculating the cost of a lot using midpoint techniques.

Given: T1 = 1000 Slope = 80% .321928- = 2log

slopelog = B B + 1 = .678072

Task: Determine the lot cost for units 26 – 50 (lot size of 25)

Using the Exact Midpoint Calculation

37.0709 = 25

813118.7 =

1-26-50

X =

1-F-L

X =Midpoint

-.321928

1-.321928

150 = X

26 = X

BB

1L = X

F = X

B

Yx = AXB

Y37.0709 = (1000)(37.0709)-.321928 = 312.5247

Cost of Units 26-50 = 312.5247 x 25 = 7813.12

Note 1: This approach required the use of a progress curve table or Boeing table in order to

calculate the summation value (7.813118) of 26-50 XB .

Note 2: This approach is a variation of the lot cost formula provided in the equation tables:

iA -iA TC1-F

1 i

bL

1 i

bLF,

33

Version 1.0

Using Approximation Approach #1

Midpoint =

L + .5 - F - .5

B + 1 L - F + 1

B+1 B+11

B

-.321928

1.678072.678072

1 + 26 - 50.678072

.5 - 26 - .5 + 50 =Midpoint

= (.312529) -3.106284 = 37.0693

Y37.0693 = (1000)(37.0693)-.321928 = 312.5290

Cost of Units 26-50 = 312.5290 x 25 = 7813.23

Note: This approach did not require the use of any tables.

Lot Cost Variation of Approximation Approach #1:

TC =

L + .5 - F - .5

B + 1 * T1F,L

B+1 B+1

TC =

50 + .5 - 26 - .5

.678072 * 1000 = 7813.23F,L

.678072 .678072

Using Approximation Approach #2: Algebraic Lot Midpoint

ALM = F + L + 2 F*L

437.0278 =

4

50*262 + 50 + 26 =

Y37.0278 = (1000)(37.0278)-.321928 = 312.6417

Cost of Units 26-50 = 327.5885 x 25 = 7816.04

Note: This approach did not require the use of any tables.

34

job aids for con 370 - dau€¦ · job aids for con 370 . evm, statistics, regression, & cost...

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