ch 6-1 © 2004 pearson education, inc. pearson prentice hall, pearson education, upper saddle river,...

Ch 6-1© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Cost Analysis and Estimatingfor Engineering and Management

Chapter 6

Estimating Methods


Overview

Introduction “Non-Analytic” Estimating Methods Cost & Time Estimating Relationships Learning Curves Proportional Relationships Using Probability and Statistics


General Estimating Methods

Preliminary EstimatesLimited Information and TimeCompare AlternativesDecisions (Proceed or Discontinue)

Detailed EstimatesMore Quantitative (Solid Information)Used for Pricing


Other Estimates

Broad Tolerance on AccuracyROMNTE

Effort to Estimate Proportional to Use and Information Available

Estimates Attempt to Forecast Actual Costs


Universal Methods

OpinionUses Experience and Judgment

ConferenceCollective Opinion

Comparison Unit


Comparison Method

Bracket Unknown with KnownKnown Cost of Similar Product/ProjectFind Cost for Upper BoundCost for a Lower Bound Is Good, too

bbaacc DCDCDC Eq 6.2


Comparison Example


Unit Method

Identify a Cost Driver Use Historical Data Find “Cost per…”

Square ft., pound, kW, hp, etc. Average Cost Dependent on Quality of Model


Estimating Relationships

Cost (CER) or Time (TER) Math Models or Graphs Function of One or More Independent

Variables - Causality CERs are Considered Preliminary Best if Used Within Data Range


Performance Time Data

Extends Time Study StandardsStandard Time Good Only for Operation(s) StudiedNot Suitable Directly for Estimating

Use Algorithm to Develop Time Study Data into PTD


PTD Algorithm

Collect Data Classify Data into Common Groups Use Regression Separate into Constant and Variable Set Variable into Equation or Table Complete, Test, Publish, Implement


Data

Many (12 or so) Studies Process and Arrange Data

Regression Analysis Determine Variable Elements


Variable Element Test 1 Is the Element Variable? Establish a Limit - P1 (%) Check at Extremes of Range (x) Use Computed y Values “Conditionally” Variable if:

^

%100 1^

min

^

min

^

max P

y

yy

Eq 6.4


Variable Element Test 2

Is the Variability of the Element Significant to the Overall Cost?

Establish Another Limit P2 (%)

Exceeds Both Test 1 & 2 = Variable

%100 2^

^

ave P

y

y

t

Eq 6.5


Process the Data

Collect and Add All Constant Elements Provide Equations or Tables for Each

Variable Element Use Rules for Setting Table Divisions Include PF&D


Example

Independent Values

P1 = 100% and = P2 10%

Element xmin xave xmax

1 29 65 101

2 8 18 28

3 5 24.5 44

4 3 19.5 36

5 37 71.5 106


Regression Data

Element Regression Equation

1 0.0139 + 0.0027x1

2 - 0.1282 + 0.0216x2

3 0.0642 + 0.0133x3

4 - 0.1156 + 0.0608x4

5 0.1907 + 0.0014x5


Calculated Valuesy ave^

y^

min y^

max

Element

1 0.092 0.189 0.287

2 0.045 0.261 0.477

3 0.131 0.390 0.649

4 0.067 1.070 2.073

5 0.243 0.291 0.339

y t^

2.201


Test Results

Element Test 1 Outcome Test 2 Outcome

1 212 Variable 9 Constant

2 960 Variable 12 Constant

3 396 Variable 18 Variable

4 2995 Variable 49 Variable

5 40 Constant


Constant Elements

Elements Normal Time, Min

1 0.189

2 0.261

5 0.291

Total 0.741

STD Min. with PF&D 0.872


Estimating DatabaseSet Up 1.2 hr

Constant 0.87 min

Load 3rd Part

L + W + H Time (min)

5.0 0.16

9.4 0.22

15.6 0.32

19.7 0.38

No. Spots Time (min)

3 0.08

5 0.22

7 0.36


Using the TER Database

Select Set-Up Time Get Constant Unit Time Determine Value of Independent x Get Time Value from Equation or Table If x Is Between Table Values

Use Higher Value


Learning

Repetition Improves PerformanceDesign ImprovementsProcess ImprovementsOperator Efficiency Improvement

Improvement Is Predictable Improvement Generally Decreases

Exponentially


The Learning Theory

Time/Cost Decreases by a Constant % Each Time the Quantity Doubles

Finding the “Slope”

su KNT Eq 6.6

log log log NsKTu

2 log log s 2 log

log

s

Eq 6.7

Eq 6.8 Eq 6.9


The Learning Curve


Logarithmic Function


Expanding

Cumulative Time for N units

Average Time per Unit for N units

Eq 6.10

Eq 6.12

1

21

N

u

uNc TTTTT

1

N

T

N

T

T c

N

u

u

a

s

a KNs

T

1

1

Eq 6.11


More Learning Curve Notes

Eq 6.12 Works for N > 20 Finding s from Known Times

LimitationsNot for Small Items or High Production Jobs

Eq 6.13 log log

log log

ji

ji

NN

TTs


Project Estimating

Power Law and Sizing Economies of Scale

Correlating Exponent m

m

r

cr Q

QCC

i

r

cm

r

cr C

I

I

Q

QCC

1

m

r

c

r

r

c Q

Q

Q

C

Q

C

Eq 6.14 Eq 6.15 Eq 6.16


Other CERs

Caution, Keep Scale within Factor of 5 Variable and Fixed Components

Multi-Variable

Eq 6.17

Eq 6.18

mKQC

f

m

r

cv CQ

QCC

smNKQC Eq 6.19


Factor Method

Mostly for Major Projects Summary Model Uses Separate Factors

Includes Cost Index

Eq 6.20

Eq 6.21

1

I

i

eie fCfCC

c

rcr I

ICC


Using Probability and Statistics

Expected Value Range Percentile Monte Carlo Simulation


Expected Value

Elements of Uncertainty Assigned Probabilities

Certain Events (NO Other Possibilities) Mutually Exclusive Events Probabilities Indicate the Future Expected Value

Eq 6.22 n

j

ijjxpiC


Range

Most Likely Value Optimistic and Pessimistic Estimates Expected Cost and Variance

Eq 6.23

6

4 HMLCE i

6var

2

LH

Ci

Eq 6.24


More on Range

Central Limit TheoremMean of the Sum = Sum of MeansVariance = Sum of Variances

Probability Actual Cost Will Exceed Upper Limit

Eq 6.27

var 2/1T

T

C

CEULZ


Percentile

Three Costs Best Case 10% (1 in 10 Cost Is Lower)Best Value 50%Worst Case 90% (1 in 10 Cost Is Higher)

Find the 3 Estimates Express (10% and 90%) as

Differences from 50%


Example

Item

Percentile Difference

10th 50th 90th (50 – 10) (90 – 50)

1 $25 $33 $44 $8 $11

2 9 13 15 4 2

3 3 4 7 1 3


Square and Sum

Square Root of Sum = Contribution to Uncertainty

(50 – 10)2 Midvalue (90 – 50)2

$64 $33 $121 16 13 4 1 4 9

Total 81 50 134

Square root $9 $11.58


Final Result

50th Percentile = $50 10th Percentile

50 - 9 = $41 90th Percentile

50 + 11.58 = $61.58


Monte Carlo Simulation

Mathematical Models Repeatedly Run Using Random Input

for Variables Based on Expected Probabilities Many Runs (1000s) Gives Cost

Distribution


Single Value vs Distribution

Compare A and B Single Values - Choice is Obvious Distribution - Choices May Overlap


A and B with Distributions


Summary

How to Use Non-Analytic Methods About CERs and TERs Effects of Learning on Estimating Various Ways of Using Proportionality Impact and Uses of Probability and

Statistics for Estimates

ch 6-1 © 2004 pearson education, inc. pearson prentice hall, pearson education, upper saddle river,...

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