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Cost Analysis and Estimating for Engineering and Management

Cost Analysis and Estimating for 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.

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Cost Analysis and Estimating for Engineering and Management

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  1. Cost Analysis and Estimatingfor Engineering and Management Chapter 6 Estimating Methods

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

  3. General Estimating Methods • Preliminary Estimates • Limited Information and Time • Compare Alternatives • Decisions (Proceed or Discontinue) • Detailed Estimates • More Quantitative (Solid Information) • Used for Pricing

  4. Other Estimates • Broad Tolerance on Accuracy • ROM • NTE • Effort to Estimate Proportional to Use and Information Available • Estimates Attempt to Forecast Actual Costs

  5. Universal Methods • Opinion • Uses Experience and Judgment • Conference • Collective Opinion • Comparison • Unit

  6. Comparison Method • Bracket Unknown with Known • Known Cost of Similar Product/Project • Find Cost for Upper Bound • Cost for a Lower Bound Is Good, too Eq 6.2

  7. Comparison Example

  8. 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

  9. 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

  10. Performance Time Data • Extends Time Study Standards • Standard Time Good Only for Operation(s) Studied • Not Suitable Directly for Estimating • Use Algorithm to Develop Time Study Data into PTD

  11. 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

  12. Data • Many (12 or so) Studies • Process and Arrange Data • Regression Analysis • Determine Variable Elements

  13. 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: ^ Eq 6.4

  14. 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 Eq 6.5

  15. 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

  16. 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 Example • Independent Values • P1 = 100% and = P2 10%

  17. 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 Regression Data

  18. 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 Calculated Values

  19. 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   Test Results

  20. Elements Normal Time, Min 1 0.189 2 0.261 5 0.291 Total 0.741 STD Min. with PF&D 0.872 Constant Elements

  21. Set 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 Estimating Database

  22. 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

  23. Learning • Repetition Improves Performance • Design Improvements • Process Improvements • Operator Efficiency Improvement • Improvement Is Predictable • Improvement Generally Decreases Exponentially

  24. 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 The Learning Theory • Time/Cost Decreases by a Constant % • Each Time the Quantity Doubles • Finding the “Slope” Eq 6.6 Eq 6.7 Eq 6.8 Eq 6.9

  25. The Learning Curve

  26. Logarithmic Function

  27. Expanding • Cumulative Time for N units • Average Time per Unit for N units Eq 6.10 Eq 6.12 Eq 6.11

  28. More Learning Curve Notes • Eq 6.12 Works for N > 20 • Finding s from Known Times • Limitations • Not for Small Items or High Production Jobs Eq 6.13

  29. Project Estimating • Power Law and Sizing • Economies of Scale • Correlating Exponent m Eq 6.14 Eq 6.15 Eq 6.16

  30. Other CERs • Caution, Keep Scale within Factor of 5 • Variable and Fixed Components • Multi-Variable Eq 6.17 Eq 6.18 Eq 6.19

  31. Factor Method • Mostly for Major Projects • Summary Model • Uses Separate Factors • Includes Cost Index Eq 6.20 Eq 6.21

  32. Using Probability and Statistics • Expected Value • Range • Percentile • Monte Carlo Simulation

  33. Expected Value • Elements of Uncertainty Assigned Probabilities • Certain Events (NO Other Possibilities) • Mutually Exclusive Events • Probabilities Indicate the Future • Expected Value Eq 6.22

  34. Range • Most Likely Value • Optimistic and Pessimistic Estimates • Expected Cost and Variance Eq 6.23 Eq 6.24

  35. More on Range • Central Limit Theorem • Mean of the Sum = Sum of Means • Variance = Sum of Variances • Probability Actual Cost Will Exceed Upper Limit Eq 6.27

  36. 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%

  37. 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 Example

  38. (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 Square and Sum • Square Root of Sum = Contribution to Uncertainty

  39. Final Result • 50th Percentile = $50 • 10th Percentile 50 - 9 = $41 • 90th Percentile 50 + 11.58 = $61.58

  40. Monte Carlo Simulation • Mathematical Models • Repeatedly Run Using Random Input for Variables • Based on Expected Probabilities • Many Runs (1000s) Gives Cost Distribution

  41. Single Value vs Distribution • Compare A and B • Single Values - Choice is Obvious • Distribution - Choices May Overlap

  42. A and B with Distributions

  43. 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

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