Cost Analysis and Estimating for Engineering and Management Chapter 6 Estimating Methods Ch 6-1
Overview Introduction Non-Analytic Estimating Methods Cost & Time Estimating Relationships Learning Curves Proportional Relationships Using Probability and Statistics Ch 6-2
General Estimating Methods Preliminary Estimates Limited Information and Time Compare Alternatives Decisions (Proceed or Discontinue) Detailed Estimates More Quantitative (Solid Information) Used for Pricing Ch 6-3
Other Estimates Broad Tolerance on Accuracy ROM NTE Effort to Estimate Proportional to Use and Information Available Estimates Attempt to Forecast Actual Costs Ch 6-4
Universal Methods Opinion Uses Experience and Judgment Conference Collective Opinion Comparison Unit Ch 6-5
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 C c ( D ) C ( D ) C ( D ) c a a b b Eq 6.2 Ch 6-6
Comparison Example Ch 6-7
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 Ch 6-8
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 Ch 6-9
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 Ch 6-10
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 Ch 6-11
Data Many (12 or so) Studies Process and Arrange Data Regression Analysis Determine Variable Elements Ch 6-12
Variable Element Test 1 Is the Element Variable? Establish a Limit - P 1 (%) Check at Extremes of Range (x) Use Computed y Values Conditionally Variable if: ^ y ^ max y ^ y min ^ min 100 P1% Eq 6.4 Ch 6-13
Variable Element Test 2 Is the Variability of the Element Significant to the Overall Cost? Establish Another Limit P 2 (%) y ^ ave ^ y t 100 P2% Eq 6.5 Exceeds Both Test 1 & 2 = Variable Ch 6-14
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 Ch 6-15
Example Independent Values Element x min x ave x max 1 29 65 101 2 8 18 28 3 5 24.5 44 4 3 19.5 36 5 37 71.5 106 P 1 = 100% and = P 2 10% Ch 6-16
Regression Data Element Regression Equation 1 0.0139 + 0.0027x 1 2-0.1282 + 0.0216x 2 3 0.0642 + 0.0133x 3 4-0.1156 + 0.0608x 4 5 0.1907 + 0.0014x 5 Ch 6-17
Calculated Values Element ^ ^ y min y ave y^ max 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 Ch 6-18
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 Ch 6-19
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 Ch 6-20
Estimating Database Set Up Constant Load 3 rd Part L + W + H 1.2 hr 0.87 min 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 Ch 6-21
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 Ch 6-22
Learning Repetition Improves Performance Design Improvements Process Improvements Operator Efficiency Improvement Improvement Is Predictable Improvement Generally Decreases Exponentially Ch 6-23
The Learning Theory Time/Cost Decreases by a Constant % Each Time the Quantity Doubles u Finding the Slope s T = KN Eq 6.6 log T u = log K + s log N Eq 6.7 log ϕ = s log 2 Eq 6.8 log ϕ s = Eq 6.9 log 2 Ch 6-24
The Learning Curve Ch 6-25
Logarithmic Function Ch 6-26
Expanding Cumulative Time for N units T c = T N 1 + T 2 + L+ TN = u= 1 T u Eq 6.10 Average Time per Unit for N units T N T a ( = Tc + s) N N u u 1 a = = Eq 6.11 T 1 1 KN Eq 6.12 s Ch 6-27
More Learning Curve Notes Eq 6.12 Works for N > 20 Finding s from Known Times s = log T log Limitations N i i log Tj log N j Eq 6.13 Not for Small Items or High Production Jobs Ch 6-28
Ch 6-29 Project Estimating Power Law and Sizing Economies of Scale Correlating Exponent m m r c r Q Q C C = i r c m r c r C I I Q Q C C + = 1 = m r c r r c Q Q Q C Q C Eq 6.14 Eq 6.15 Eq 6.16
Other CERs m C = KQ Caution, Keep Scale within Factor of 5 Variable and Fixed Components Multi-Variable m Qc C = Cv + Q r Eq 6.17 C f m N s Eq 6.18 C = KQ Eq 6.19 Ch 6-30
Factor Method Mostly for Major Projects Summary Model Uses Separate Factors C = C + e fice I i ( f + 1) Eq 6.20 Includes Cost Index C r = C c I I r c Eq 6.21 Ch 6-31
Using Probability and Statistics Expected Value Range Percentile Monte Carlo Simulation Ch 6-32
Expected Value Elements of Uncertainty Assigned Probabilities Certain Events (NO Other Possibilities) Mutually Exclusive Events Probabilities Indicate the Future Expected Value C () i = n j p j x ij Eq 6.22 Ch 6-33
Range Most Likely Value Optimistic and Pessimistic Estimates Expected Cost and Variance L + 4M + H E i 6 ( C ) = var( ) C i = H 6 L 2 Eq 6.23 Eq 6.24 Ch 6-34
More on Range Central Limit Theorem Mean of the Sum = Sum of Means Variance = Sum of Variances Probability Actual Cost Will Exceed Upper Limit Z = UL E( C ) T [ var ( )] 1/ 2 C T Eq 6.27 Ch 6-35
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% Ch 6-36
Example Item Percentile Difference 10 th 50 th 90 th (50 10) (90 50) 1 $25 $33 $44 $8 $11 2 9 13 15 4 2 3 3 4 7 1 3 Ch 6-37
Square and Sum (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 Root of Sum = Contribution to Uncertainty Ch 6-38
Final Result 50th Percentile = $50 10th Percentile 50-9 = $41 90th Percentile 50 + 11.58 = $61.58 Ch 6-39
Monte Carlo Simulation Mathematical Models Repeatedly Run Using Random Input for Variables Based on Expected Probabilities Many Runs (1000s) Gives Cost Distribution Ch 6-40
Single Value vs Distribution Compare A and B Single Values - Choice is Obvious Distribution - Choices May Overlap Ch 6-41
A and B with Distributions Ch 6-42
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 6-43