# Presentation: 224764

## An Analytical Approach to Calculating Probabilistic Estimates at Completion

- Steven L. Van Drew, PhD, PE
- Naval Air Systems Command
- Gary J. Clor, PhD
- Army Logistics Management College

## DSMC Gold Card

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## DSMC Gold Card

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Outline

- Background
- Requirement for EACs
- Calculation of EACs
- EAC formulas in wInsight
- Common EAC Formulae Usage
- The Challenge
- Derivation of Transformed EAC ProbabilityDistributions
- Uniformly Distributed CPI
- Triangularly Distributed CPI
- Example Using Hypothetical Contract
- Summary

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Requirement for EACs

- Contractor:
- reports management estimate at completion (EAC)—also known as latest revised estimate (LRE)—whether submitting Cost Performance Report (CPR) or Cost/Schedule Status Report (C/SSR)
- comprehensive EAC developed at least annually and reviewed monthly
- Government:
- earned value analyst assesses realism of contractor EAC/LRE
- calculates independent EAC

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Cost Performance Report (CPR)

- The most likely EAC “is the value that the contractor's management believes is the most likely outcome based on a knowledgeable estimate of all authorized work, known risks and probable future conditions.”

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Calculation of EACs

- EAC = Actuals to Date + [(Remaining Work) / (Efficiency Factor)]
- EACCPI = ACWPCUM 	+ [(BAC – BCWPCUM) / CPICUM ]
- 	    = BAC / CPICUM
- EACComposite	= ACWPCUM + [(BAC – BCWPCUM) / (CPICUM * SPICUM)]
- May replace BAC with TAB
- ACWP – Actual Cost of Work Completed
- BAC – Budget at Completion
- BCWP – Budgeted Cost of Work Performed
- CPI – Cost Performance Index
- EAC – Estimate at Completion
- SPI – Schedule Performance Index

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## EAC formulas in wInsight

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Common EAC Formulae Usage

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## A-12 EACs

- Source:  Chester Paul Beach, Jr. 28 NOV 90 Memorandum for SECNAV, Subject: A-12 Administrative Inquiry

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## The Challenge

- 	To provide earned value analysts with an approach to EAC calculation that allows them to answer questions such as, What is the probability of under running the contractor’s LRE?
- not meant to be a substitute for analyst’s knowledge of contract
- must be understandable, explainable, defensible

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Uniformly Distributed CPI

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Uniformly Distributed CPI (cont.)

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Uniformly Distributed CPI (cont.)

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Uniformly Distributed CPI (cont.)

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Triangularly Distributed CPI

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Triangularly Distributed CPI (cont.)

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Triangularly Distributed CPI (cont.)

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Triangularly Distributed CPI (cont.)

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Triangularly Distributed CPI (cont.)

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Triangularly Distributed CPI (cont.)

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Triangularly Distributed CPI (cont.)

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Triangularly Distributed CPI (cont.)

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Transformed EAC Probability Distributions Summary Table

- g(y) =

- G(y) =

- A / ~U(a,b)

- A / ~Triang(a,b,c)

- pdf

- cdf

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Transformed EAC Probability Distributions Summary Table (cont.)

- G-1(y) =

- E(y) =

- A / ~U(a,b)

- A / ~Triang(a,b,c)

- cdf-1

- 

- E(y2) –
- [E(y)]2 =

- 2

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Example Using Hypothetical Contract

- Consider a development contract with:
- Budget at completion of $100M
- Total allocated budget of $110M
- Contractor’s latest revised estimate of $102M
- Relevant efficiency factors (e.g., CPIcum) ranging from  0.95 to 1.01, with 0.99 as efficiency factor contractor, program office, and earned value analyst all consider “most likely”
- What are the probabilities of under running BAC and LRE?
- What EACs are associated with 0.50 and 0.70 probabilities of under run?

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Excel EAC CDF Tool

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Summary

- Developed and demonstrated an analytical approach to calculating a probabilistic EAC
- Given a constant such as BAC and an uncertain efficiency factor such as  CPIcum whose distribution is assumed to follow either a uniform or triangular distribution, approach provides earned value analysts with a set of equations capable of answering questions such as, What is the probability of under running the contractor’s LRE?

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Backup Slides

## Glossary of Selected EVM Terms

**Actual Cost of Work Performed (ACWP).** The costs actually incurred and recorded in accomplishing the work performed within a given time period
**Budget at Completion (BAC).** The sum of all budgets established for the contract. (See Total Allocated Budget).
**Budgeted Cost for Work Performed (BCWP). **The sum of the budgets for completed work packages and completed portions of open work packages, plus the applicable portion of the budgets for level of effort and apportioned effort.
**Budgeted Cost for Work Scheduled (BCWS).** The sum of the budgets for all work packages, planning packages, etc., scheduled to be accomplished (including in-process work packages), plus the amount of level of effort and apportioned effort scheduled to be accomplished within a given time period.
**Cost Performance Report (CPR).** A contractually required report, prepared by the contractor, containing information derived from the internal system. Provides status of progress on the contract.
**Cost/Schedule Status Report (C/SSR). **A performance measurement report established to capture information on smaller contracts.
**Estimate at Completion (EAC).** Actual direct costs, plus indirect costs allocable to the contract, plus the estimate of costs (direct and indirect) for authorized work remaining.
**Estimate to Complete (ETC).** That portion of the EAC that addresses total expected costs for all work remaining on the contract.
**Performance Measurement Baseline (PMB).** The time-phased budget plan against which contract performance is measured. It is formed by the budgets assigned to scheduled cost accounts and the applicable indirect budgets. For future effort, not planned to the cost account level, the performance measurement baseline also includes budgets assigned to higher level CWBS elements, and undistributed budgets. It equals the total allocated budget less management reserve.
**Total Allocated Budget (TAB).** The sum of all budgets allocated to the contract. Total allocated budget consists of the performance measurement baseline and all management reserve. The total allocated budget will reconcile directly to the contract budget base. Any differences will be documented as to quantity and cause.

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## CPR DID

- 10.2.2.2 Estimated Cost at Completion. These blocks will present the contractor's range of estimated costs at completion. The range of estimates is intended to allow contractor management flexibility to express possible cost outcomes. Contractors are encouraged to provide the most accurate EACs possible through program-level assessments of factors that may affect the cost, schedule or technical outcome of the contract. Where possible, such program-level assessments should include consideration of known or anticipated risk areas, and planned risk reductions or cost containment measures. EACs should be reported without regard to contract ceiling, if applicable. The methods used to develop worst case, best case and most likely management estimates at completion need not be described in the contractor's C/SCSCcompliant management control system description or CPR-No Criteria management procedures.
- 10.2.2.2.1 Management Estimate at Completion - Best Case. Enter in Block 6.a.1 the contractor's best case estimate at completion. The best case estimate is the one that results in the lowest cost to the Government. This estimate should be based on the outcome of the most favorable set of circumstances. If this estimate is different from the most likely estimate at completion (Block 6.c.1), the assumptions and conditions underlying this estimate should be explained briefly in Format 5. This estimate is for informational purposes only; it is not an official company estimate. There is no requirement for the contractor to prepare and maintain backup data beyond the explanation provided in Format 5.
- 10.2.2.2.2 Management Estimate at Completion - Worst Case. Enter in Block 6.b.1 the contractor's worst case estimate at completion. The worst case estimate is the one that results in the highest cost to the Government. This estimate should be based on the outcome of the least favorable set of circumstances. If this estimate is different from the most likely estimate at completion (Block 6.c.1), the assumptions and conditions underlying this estimate should be explained briefly in Format 5. This estimate is for informational purposes only; it is not an official company estimate. There is no requirement for the contractor to prepare and maintain backup data beyond the explanation provided in Format 5.
- 10.2.2.2.3 Management Estimate at Completion - Most Likely. Enter in Block 6.c.1 the contractor's most likely estimate at completion. This estimate is the contractor's official contract EAC and, as such, takes precedence over the estimates presented in Column (15) of Formats 1 and 2 and Blocks 6.a.1 and 6.b.1. This EAC is the value that the contractor's management believes is the most likely outcome based on a knowledgeable estimate of all authorized work, known risks and probable future conditions. This value need not agree with the total of Column (15) (Block 8.e). However, any difference should be explained in Format 5 in such terms as risk, use of management reserve, or higher management knowledge of current or future contract conditions. This EAC need not agree with EACs contained in the contractor's internal data, but must be reconcilable to them. The most likely EAC also will be reconcilable to the contractor's latest statement of funds required as reported in the Contract Funds Status Report, or its equivalent, if this report is a contractual requirement.

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## C/SSR

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## C/SSR DID

- 10.3.6 Management Estimate at Completion. Enter in Block 6.f. the contractor's most likely EAC. The estimate should include actual costs to date plus a knowledgeable projection of future performance. The estimate should be based on the agreed work scope as reflected in the CBB (Block 6.e.). The contractor may include an estimate for management reserve (MR), if applicable. The contractor also may include a realistic estimate for program risk or probable future business conditions. If the management EAC differs from the value in Column (8) of Block 7.e., the difference shall be discussed in the Narrative Explanation section.

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Why don’t I get an EAC that’s uniformly distributed when I divide TAB by a CPI that’s uniformly distributed?

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Alternate Approaches?

- Norden-Rayleigh model
- RACM
- Data-based approaches
- Simulation using Mike Popp’s DSMC study
- NGC-TASC’s regression equations

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Uniformly Distributed CPI (cont.)

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04

## Derivation of Transformed EAC Probability Distributions:  Triangularly Distributed CPI (cont.)

- 37th DoDCAS  Van Drew & Clor

- 13 Feb 04