Cost Analysis and Estimating for Engineering and Management

Cost Analysis and Estimating for Engineering and Management Chapter 5 Forecasting © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -1

Overview l Working with Data -Graphing, Statistics -Regression / Curve Fitting -Confidence / Correlation l Time Series -Moving Averages, Smoothing l Cost Indexes © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -2

Business Forecasting l Prediction -Price of Material -Cost/Amount of Labor -Market Demand/Price l Term -Short 2 Years -Medium 2 - 5 Years -Long Range > 5 Years © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -3

Graphical Analysis l Descriptive Statistics -Collect/Organize/Analyze Data -Summarize/Present -Draw Conclusions/Make Decisions l Raw Data Communicates Little Information © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -4

Simplifying Data Price, ($/roll) Obs Rel Freq Cum Freq 12. 35– 12. 75 1 0. 003 12. 75– 13. 15 6 0. 019 0. 022 13. 15– 13. 55 33 0. 102 0. 124 13. 55– 13. 95 51 0. 157 0. 281 13. 95– 14. 35 121 0. 373 0. 654 14. 35– 14. 75 50 0. 154 0. 808 14. 75– 15. 15 44 0. 136 0. 944 15. 15– 15. 65 13 0. 040 0. 984 15. 65– 16. 05 5 0. 016 1. 000 324 1. 000 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -5

Graphical Presentation © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -6

Frequency Curves © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -7

Mean l Average Eq 5. 1 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -8

Median & Mode l Median -All Data from Lowest to Highest -Number in the Middle l Mode -Data Value(s) that Appear the Most Often © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -9

Standard Deviation l Amount of Data Spread Around the Mean Eq 5. 2 l Variance Is the Square of the Standard Deviation © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -10

Graph the Data l Pure Statistics Can Be Misleading l Any Set of Numbers -Will Have Mean, Std Dev, etc. -May or May Not Be Relevant l Plot the Data -Visual Interpretation -Apply “Judgment” © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -11

Mathematical Model l Draw Line Through Data l Half of Points Above Line, Half Below l Straight Line y = a + bx l Determine a and b from Graph © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -12

Example © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -13

Why Graph? l Visual Analysis of What Is Happening l Non-Linearity May Be Exposed l Incorporates “Reasonableness” l Mathematical Methods Can Assist in Establishing the “Best Fit” Line Through the Data © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -14

Regression Analysis l Finds Dependent y for Given x l If x Is Time -Called Trend Line -Used for Forecasting © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -15

Least Squares l Minimize Variation (Error) Between -Observed (Real) Values -Fitted Curve (Predicted) Values l Minimize -Sum of the Squares of the Errors © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -16

Normal vs. Student-t Distribution © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -17

Distribution Applied to Regression © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -18

Mathematical Calculations l Error Eq 5. 4 l Sum of the Squares Eq 5. 5 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -19

The Least Squares Equation ly = a + bx Eq 5. 8 Eq 5. 9 l The Least Squares Line Goes Through (X, Y) © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -20

Example Year x Index y x 2 xy y 2 0 87 0 0 84. 875 2. 125 4. 516 1 89 87. 264 1. 736 3. 013 2 90 4 180 89. 654 0. 346 0. 120 3 92 9 276 92. 043 -0. 043 0. 002 4 93 16 372 94. 432 -1. 432 2. 051 … … … … 105 1524 1015 11337 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management 63. 168 Ch 5 -21

Example Calculations l Find l. Y a and b = 84. 875 + 2. 389 X © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -22

Confidence Limits © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -23

Equations l Variance Around Regression Line Eq 5. 19 l Degrees of Freedom Eq 5. 11 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -24

Confidence Limits l Based on Student-t Tables Eq 5. 14 l Regression Line Passes Through y -Variation of y Equals Constant Variation of regression line © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -25

In General l Variance of y Due to Variance of y Eq 5. 15 l Variance Applied to y Eq 5. 16 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -26

Compounded Variance l Variance of Predicted Value Eq 5. 17 Eq 5. 18 Eq 5. 19 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -27

Confidence vs Prediction l Confidence Interval -Variation Around Expected Y Value l Prediction Interval -Variation Around a Single Y Value -Greater In Magnitude © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -28

Variance from Intercept l. X = 0 at Intercept a Eq 5. 22 Eq 5. 20 Eq 5. 21 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Eq 5. 23 Ch 5 -29

Confidence Intervals © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -30

Non-Linear Relationships l Curvilinear Regression Exponential Eq 5. 24 Power Eq 5. 25 Polynomial Eq 5. 26 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -31

Non-Linear Calculations l Convert to Log Representation l For y = abx (Exponential Function) Eq 5. 27 Eq 5. 28 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -32

Another Version l For y = axb (Power Function) Eq 5. 29 Eq 5. 30 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -33

Example x y log x log y 10 510 1. 0000 2. 7076 30 210 1. 4771 2. 3222 2. 1819 3. 4302 100 190 2. 0000 2. 2788 4. 0000 4. 5575 150 125 2. 1761 2. 0969 4. 7354 4. 5631 300 71 2. 4771 1. 8513 6. 1361 4. 5858 9. 1303 11. 2567 18. 0534 19. 8441 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management (log x)2 log x log y Ch 5 -34

Finding a and b Eq 5. 29 Eq 5. 30 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -35

Polynomial Regression l Linear Relationship Unknown Eq 5. 31 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -36

Correlation © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -37

Correlation l Sometimes There Isn’t Any l Quantitative Measure Eq 5. 33 1 l Farther from 0, Stronger Correlation l -1 r © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -38

Multiple Linear Regression l More than 1 Independent Variable l Graphical Representation Difficult l Mathematical Form Eq 5. 34 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -39

Finding Constants Eq 5. 35 l Solve Simultaneously © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -40

Regression Assumptions l The Values of x Are Controlled l Regression is Linear l Deviations are Mutually Independent l Deviations Are Not a Function of x l Deviations Are Normally Distributed l Model Contains ALL Relevant Variables © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -41

Time Series Models l Used for Forecasting l Fundamentals -Consistent Data Collection -Types of Behavior -Moving Average -Smoothing l Data Added on Revolving Basis © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -42

Time Series Data l Collected at Successive Periods l Usually Equally Spaced l Is the Underlying Process -Constant -Variable -Trend-Cycle -Seasonal -Regular © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -43

Typical Time Series Models © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -44

Moving Average l Places More Reliance on Recent Data l Recent Data Better Predicts Future Eq 5. 36 l. N Determines Rate of Response © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -45

Smoothing l “Weighted” Moving Average l Exponential Smoothing Eq 5. 38 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -46

Smoothing Constant Variations in values Drift in data Small, = 0 Little, = 0. 5 None Moderate Very small Small Moderate Large © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Large, = 1 Ch 5 -47

Cost Index l Dimensionless Number l Represents Change in Cost l Over a Period of Time l Relative to a “Benchmark” Period l What is Costed Remains Constant l Used to Forecast © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -48

Using Cost Index l Compares Known Cost at Period r l Using Current Ic and Reference Ir Indexes Eq 5. 39 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -49

Figuring Cost Indexes l Benchmark Cost Used as Denominator l Index for Benchmark Period = 1 or 100 l Costs for Other Periods Divided by Benchmark Cost © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -50

Rate of Change l Differences Between Periods -Percent Change Current index, period 5 106. 8 Less previous index, period 4 102. 3 Index point change Divide by previous index Equals © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management +4. 5 102. 3 +0. 044 = + 4. 4% Ch 5 -51

Change Rate l Figuring Average Rate of Change Eq 5. 40 l Using Rate of Change to Find Index Eq 5. 41 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -52

Composite Index Material 0* 1 2 3 Laser glass $26, 117 $24, 027 $22, 345 $21, 228 Steel tubing 1913 2008 2129 2278 Al extrusion 418 426 439 456 Printed circuits 637 643 656 657 Harness cable 2103 2124 2134 2305 Glass tubing 4317 4187 4103 4185 $35, 505 $33, 415 $31, 806 $31, 119 100. 0 94. 1 89. 6 87. 6 Total Index, % * Benchmark Period © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -53

Indexes l Basis Changes (Qty, Qual, Mix, etc) l Technology Creep l Kinds of Indexes -Material -Labor Geographical l Index Specific for Time and Location © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -54

Caveats l Results Depend on Good Data l Cause and Effect Relationship l Eliminating Spurious Data l Backcast Period Forecast Period l Limit Number of Variables l Use Judgment l Test for “Reasonableness” © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -55

Summary l Objective - Forecasting l Methods for Working with Data -Graphing, Statistics, Regression l Data In Time Periods (Time Series) l Cost Indexes -Applications, Calculations, Caveats © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and Mc. Laren / Cost Analysis and Estimating for Engineering and Management Ch 5 -56