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7.3 Earned Schedule (ES) Theory, SV(t), and SPI(t)
AACE Planning and Scheduling Professional PSP
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1 Chapter 0: Introduction & AACE PSP Exam Structure
0.1 Current AACE PSP Exam, Eligibility, and Certification Facts 0.2 Planning and Scheduling Professional Roles and Competencies 0.3 Cost Engineering and Scheduling Terminology per RP 10S-90
2 Chapter 1: Scope Definition & Planning Fundamentals
1.1 Work Breakdown Structure (WBS) Architecture & RP 33R-15 1.2 Organization & Resource Breakdown Structures (OBS, RBS, RAM) 1.3 Project Planning and Activity-Logic Development 1.4 Contract Requirements and Delivery Constraints 1.5 Stakeholder Identification, Needs, and Plan Review 1.6 Constructability Methods and Value Engineering 1.7 Resource Identification and Project Variables 1.8 Scope, Goals, Project Plan, and Phase Definition 1.9 Cost Breakdown Structure and Cost Estimate Development 1.10 Phase Relationships, Baseline Plan, Forecasts, and Risk/Recovery Planning
3 Chapter 2: Critical Path Method Mechanics & Network Logic
2.1 Activity Definition and Logic Relationships 2.2 Activity Durations, Productivity, and Work Calendars 2.3 Forward and Backward Pass Mathematical Mechanics 2.4 Float Calculations and Critical-Path Identification
4 Chapter 3: Advanced Network Techniques & Schedule Constraints
3.1 Schedule Constraints and Their Impact on Dates and Float 3.2 Advanced Logic Modeling: Ladders and Fragnets 3.3 Schedule Levels of Detail and Schedule Basis Documentation 3.4 Schedule Scope and Schedule Specification 3.5 Breakdown-Structure Relationships and the Cost Estimate Model 3.6 Stakeholder Feedback and Types of Schedules 3.7 Activities, Milestones, Schedule Quality, and Basis Documentation
5 Chapter 4: Resource Management & Leveling
4.1 Resource Planning, Allocation, and Histograms 4.2 Resource Leveling vs. Resource Smoothing 4.3 Cumulative Resource S-Curves & Productivity Tracking
6 Chapter 5: Baseline Management & Schedule Updating
5.1 Baseline Establishment, Forecasts, and Controlled Revision 5.2 Progress Measurement and Data Date Mechanics 5.3 Out-of-Sequence Logic: Progress Override vs. Retained Logic 5.4 Schedule Update Review and Quality Verification per RP 53R-06 5.5 Cost/Resource Management, Schedule Change, and Feedback 5.6 Acceleration and Recovery Scheduling per RP 54R-07 5.7 Control Schedules, Variance Analysis, Forecasts, and Management Summaries
7 Chapter 6: Schedule Risk Analysis & Monte Carlo Simulation
6.1 Schedule Risk Principles, Risk Drivers, and Three-Point Estimates 6.2 Monte Carlo Simulation, Criticality, Correlation, and Merge Effects 6.3 Risk Outputs, Confidence Dates, Sensitivity, and Contingency
8 Chapter 7: Earned Value & Earned Schedule Management
7.1 Earned Value Foundations: PV, EV, AC, and Variances 7.2 Traditional EV Performance Indices & Late-Project Quirks 7.3 Earned Schedule (ES) Theory, SV(t), and SPI(t) 7.4 Independent Schedule Forecasting & IEAC(t)
9 Chapter 8: Forensic Schedule Analysis & Delay Claims
8.1 Delay Classification, Criticality, and Contract Questions 8.2 RP 29R-03 Taxonomy, Data Validation, and Method Selection 8.3 TIA, Windowed Analysis, and Subtractive Models 8.4 Concurrency, Pacing, and Float: Technical Analysis Before Entitlement
10 Chapter 9: Executive Communication & Practical Scenario Applications
9.1 Official PSP Memo Writing Framework 9.2 Structured Technical Problem-Solving for PSP Scenarios 9.3 Current Exam Strategy and Core Calculation Review
7.3 Earned Schedule (ES) Theory, SV(t), and SPI(t)
Key Takeaways Explain This Topic AI
Earned Schedule translates earned value onto the baseline planned-value time curve to create aggregate indicators expressed in time units.
Earned Schedule estimates the baseline time at which cumulative Planned Value equals current Earned Value, using the defined interpolation convention between status periods.
Time-based Schedule Variance ( S V ( t ) = E S − A T SV(t) = ES - AT S V ( t ) = ES − A T ) is an aggregate earned-schedule variance, not a substitute for CPM milestone or path analysis.
For a project completed late, S P I ( t ) = E S / A T SPI(t) = ES / AT SP I ( t ) = ES / A T remains below 1.00 at completion because Earned Schedule equals planned duration while actual time is longer.
Linear interpolation between adjacent cumulative Planned Value periods calculates a fractional Earned Schedule value under a piecewise-linear curve assumption.
Last updated: October 2026
7.3 Earned Schedule (ES) Theory, SV(t), and SPI(t)
AACE Professional Context: Traditional Earned Value schedule metrics ( S V SV S V and S P I SPI SP I ) are value-denominated and converge toward their planned completion values, limiting their usefulness for interpreting time performance late in a project. In 2003, American quality and project controls engineer Walt Lipke published the seminal paper Schedule is Different , creating Earned Schedule (ES) theory. Earned Schedule is an established time-based extension of EVM, and AACE RP 80R-13 discusses its use in schedule forecasting. It supplies aggregate indicators that complement rather than replace CPM milestone and path analysis. Candidates benefit from understanding the interpolation, S V ( t ) SV(t) S V ( t ) , and S P I ( t ) SPI(t) SP I ( t ) calculations and their assumptions.
The Concept of Earned Schedule (ES)
The fundamental premise of Earned Schedule is remarkably elegant:
Core Principle: Instead of measuring schedule accomplishment along the vertical cost axis (in dollars), Earned Schedule measures accomplishment along the horizontal time axis (in calendar units).
Earned Schedule asks the question: "At what point in time was the currently achieved Earned Value originally planned to be accomplished?" THE EARNED SCHEDULE (ES) DERIVATION
- Cumulative Cost (\$)
- ▲
- │ Planned Value (PV) S-Curve
- │ ┌─────────*
- │ ┌───┘
- │ ┌───┘
- EV ──┼───────────────────────────────────────►*───┘
- │ ││
- │ ││
- │ ││
- │ ││
- └───────────────────────────────────────┴┴─────────────────────► Time
- ▲▲
- ││
- ES│
- │
- AT (Actual Time / Data Date)
- ◄───────────────── ES ─────────────────►
- ◄─────────────────────── AT ────────────────────────►
- ◄── SV(t) ──►
- (Delay in Time)
- Core Definitions
Actual Time ( A T AT A T ): The elapsed calendar time from the project start date to the current Data Date (Status Date). A T AT A T is expressed in time units such as days, weeks, or months (e.g., A T = 8.0 months AT = 8.0 \text{ months} A T = 8.0 months ).
Earned Schedule ( E S ES ES ): The date or elapsed time increment on the baseline schedule when the cumulative Planned Value ( P V PV P V ) equals the current Earned Value ( E V EV E V ). E S ES ES is expressed in the identical time units as A T AT A T (e.g., E S = 6.4 months ES = 6.4 \text{ months} ES = 6.4 months ).
Mathematical Derivation and Linear Interpolation
Because project controls data is typically recorded in discrete periodic increments (e.g., weekly or monthly status periods), Earned Value ( E V EV E V ) rarely falls precisely on an exact integer time period of the Planned Value table. Therefore, linear interpolation is used to determine the exact fractional portion of E S ES ES .
- The Earned Schedule Formula
- E S = C + I \mathbf{ES = C + I} ES = C + I
Where:
C C C (Integer Time Index): The time increment where cumulative P V PV P V is less than or equal to current E V EV E V , but where the next period's P V PV P V exceeds E V EV E V : P V C ≤ E V < P V C + 1 PV_C \le EV < PV_{C+1} P V C ≤ E V < P V C + 1
I I I (Fractional Interpolation Increment): The proportional distance traversed between period C C C and period C + 1 C+1 C + 1 : I = E V − P V C P V C + 1 − P V C \mathbf{I = \frac{EV - PV_C}{PV_{C+1} - PV_C}} I = P V C + 1 − P V C EV − P V C
Full Linear Interpolation Expression:
E S = C + [ E V − P V C P V C + 1 − P V C ] \mathbf{ES = C + \left[ \frac{EV - PV_C}{PV_{C+1} - PV_C} \right]} ES = C + [ P V C + 1 − P V C EV − P V C ]
Note: If E V ≥ B A C EV \ge BAC E V ≥ B A C (project scope is complete), E S ES ES equals the baseline Planned Duration ( P D PD P D ).
Time-Based Schedule Metrics: S V ( t ) SV(t) S V ( t ) and S P I ( t ) SPI(t) SP I ( t )
With Earned Schedule ( E S ES ES ) established in pure units of time, Lipke defined time-based analogs to the traditional EVM schedule metrics:
- 1. Time-Based Schedule Variance: S V ( t ) SV(t) S V ( t )
- S V ( t ) = E S − A T \mathbf{SV(t) = ES - AT} SV ( t ) = ES − AT
Denominated in units of time (calendar days, working days, weeks, or months).
S V ( t ) > 0 SV(t) > 0 S V ( t ) > 0 (Positive): Favorable aggregate earned-schedule variance.
S V ( t ) = 0 SV(t) = 0 S V ( t ) = 0 (Zero): Earned Schedule equals Actual Time.
S V ( t ) < 0 SV(t) < 0 S V ( t ) < 0 (Negative): Unfavorable aggregate earned-schedule variance.
Example: If E S = 5.2 months ES = 5.2 \text{ months} ES = 5.2 months and A T = 7.0 months AT = 7.0 \text{ months} A T = 7.0 months , then: S V ( t ) = 5.2 − 7.0 = − 1.8 months SV(t) = 5.2 - 7.0 = \mathbf{-1.8 \text{ months}} S V ( t ) = 5.2 − 7.0 = − 1.8 months The project controls manager can immediately inform project leadership: "Aggregate Earned Schedule variance is -1.8 months; CPM determines milestone impact." Compare this clarity against traditional EVM reporting: "Schedule Variance is -$142,000," which leaves stakeholders wondering how much time was lost.
- 2. Time-Based Schedule Performance Index: S P I ( t ) SPI(t) SP I ( t )
- S P I ( t ) = E S A T \mathbf{SPI(t) = \frac{ES}{AT}} SPI ( t ) = AT ES
Represents the time efficiency factor of the project.
S P I ( t ) > 1.00 SPI(t) > 1.00 SP I ( t ) > 1.00 : Favorable. Project is converting calendar time into earned schedule at an accelerated rate.
S P I ( t ) = 1.00 SPI(t) = 1.00 SP I ( t ) = 1.00 : On schedule.
S P I ( t ) < 1.00 SPI(t) < 1.00 SP I ( t ) < 1.00 : Unfavorable. Project is experiencing time slippage (e.g., S P I ( t ) = 0.75 SPI(t) = 0.75 SP I ( t ) = 0.75 indicates the project is earning only 0.75 months of schedule for every 1.0 calendar month expended).
Why S P I ( t ) SPI(t) SP I ( t ) avoids traditional SPI convergence at late completion
The breakthrough achievement of Earned Schedule is solving the late-project mathematical distortion that plagues traditional S P I SPI SP I .
Recall from Section 7.2 that when a delayed project reaches final completion ( A T > P D AT > PD A T > P D ):
Traditional E V EV E V reaches B A C BAC B A C , and P V = B A C PV = BAC P V = B A C , forcing traditional S P I = E V / P V = 1.00 SPI = EV / PV = 1.00 SP I = E V / P V = 1.00 .
Now, analyze the behavior of Earned Schedule under the identical late-project scenario:
At project finish, all scope is complete, so E V = B A C EV = BAC E V = B A C .
Because E V = B A C EV = BAC E V = B A C , the earned time on the baseline PV curve is the full Planned Duration: E S = P D ES = PD ES = P D .
However, because the project was late, the elapsed Actual Time exceeds Planned Duration: A T > P D AT > PD A T > P D .
Substituting these values into the time-based formulas:
S V ( t ) final = E S − A T = P D − A T final < 0 \mathbf{SV(t)_{\text{final}} = ES - AT = PD - AT_{\text{final}} < 0} SV ( t ) final = ES − AT = PD − A T final < 0
S P I ( t ) final = E S A T final = P D A T final < 1.00 \mathbf{SPI(t)_{\text{final}} = \frac{ES}{AT_{\text{final}}} = \frac{PD}{AT_{\text{final}}} < 1.00} SPI ( t ) final = A T final ES = A T final PD < 1.00 BEHAVIOR AT COMPLETION OF A DELAYED PROJECT
(Planned Duration = 10 Months | Actual Completion Date = 14 Months | BAC = \$1.0M)
- Metric Traditional EVM Earned Schedule (ES)
- ──────────────────────────────────────────────────────────────────────────────────
- Schedule Variance SV = EV - PV SV(t) = ES - AT
- SV = \$1.0M - \$1.0M = \$0 SV(t) = 10 - 14 = -4.0 Months
- (Falsely indicates on plan!) (Correctly shows 4 months late!)
- Schedule Index SPI = EV / PV SPI(t) = ES / AT
- SPI = \$1.0M / \$1.0M = 1.00 SPI(t) = 10 / 14 = 0.714
- (Falsely indicates 100% on time!) (Correctly preserves 71.4% efficiency!)
Key takeaway: At completion, a late project has ES equal to planned duration and AT equal to actual duration, so SPI(t) remains below 1.00 and SV(t) expresses the duration variance in the chosen time units. CPM remains necessary for milestone and path analysis.
Step-by-Step Worked Calculation of E S ES ES , S V ( t ) SV(t) S V ( t ) , and S P I ( t ) SPI(t) SP I ( t )
A municipal light rail infrastructure project has a contract baseline budget B A C BAC B A C = $12,000,000 and a Planned Duration of 10 months ( P D = 10 PD = 10 P D = 10 ).
Cumulative Baseline Planned Value Table (Monthly Periods):
Period ( n n n ) Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 ( B A C BAC B A C )
- Period P V PV P V ($) 400k 600k 1,000k 1,400k 1,800k 2,200k 2,000k 1,400k 800k 400k
- Cumulative P V PV P V ($) 400k 1,000k 2,000k 3,400k 5,200k 7,400k 9,400k 10,800k 11,600k 12,000k
Status at Data Date = End of Month 7 ( A T = 7.0 AT = 7.0 A T = 7.0 months):
The field survey confirms physical progress corresponding to an Earned Value ( E V EV E V ) of $6,300,000 .
The accounting system books an Actual Cost ( A C AC A C ) of $7,000,000 .
Step 1: Identify Integer Time Increment C C C
Search the Cumulative P V PV P V row to locate the interval that bounds E V EV E V = $6,300,000:
- P V 5 PV_5 P V 5 = $5,200,000
- P V 6 PV_6 P V 6 = $7,400,000
Since P V 5 PV_5 P V 5 ($5.2M) ≤ E V \le EV ≤ E V ($6.3M) < P V 6 < PV_6 < P V 6 ($7.4M), the integer period is C = 5 C = 5 C = 5 .
Step 2: Compute Fractional Interpolation Increment I I I
I = E V − P V C P V C + 1 − P V C = $ 6,300,000 − $ 5,200,000 $ 7,400,000 − $ 5,200,000 = $ 1,100,000 $ 2,200,000 = 0.50 I = \frac{EV - PV_C}{PV_{C+1} - PV_C} = \frac{\text{\textdollar}6{,}300{,}000 - \text{\textdollar}5{,}200{,}000}{\text{\textdollar}7{,}400{,}000 - \text{\textdollar}5{,}200{,}000} = \frac{\text{\textdollar}1{,}100{,}000}{\text{\textdollar}2{,}200{,}000} = \mathbf{0.50} I = P V C + 1 − P V C E V − P V C = $ 7 , 400 , 000 − $ 5 , 200 , 000 $ 6 , 300 , 000 − $ 5 , 200 , 000 = $ 2 , 200 , 000 $ 1 , 100 , 000 = 0.50
Step 3: Compute Earned Schedule ( E S ES ES )
E S = C + I = 5 + 0.50 = 5.50 months ES = C + I = 5 + 0.50 = \mathbf{5.50 \text{ months}} ES = C + I = 5 + 0.50 = 5.50 months Physical Meaning: The work accomplished by the end of Month 7 was originally planned to be reached at Month 5.50.
Step 4: Compute Time-Based Schedule Variance ( S V ( t ) SV(t) S V ( t ) )
S V ( t ) = E S − A T = 5.50 − 7.00 = − 1.50 months SV(t) = ES - AT = 5.50 - 7.00 = \mathbf{-1.50 \text{ months}} S V ( t ) = ES − A T = 5.50 − 7.00 = − 1.50 months Physical Meaning: The project is 1.50 months behind schedule in elapsed calendar time.
Step 5: Compute Time-Based Schedule Performance Index ( S P I ( t ) SPI(t) SP I ( t ) )
S P I ( t ) = E S A T = 5.50 7.00 = 0.786 SPI(t) = \frac{ES}{AT} = \frac{5.50}{7.00} = \mathbf{0.786} SP I ( t ) = A T ES = 7.00 5.50 = 0.786 Physical Meaning: The project is progressing at 78.6% of the planned temporal schedule rate (earning 0.786 months of schedule per actual month worked).
Step 6: Comparison with Traditional EV Metrics
Traditional Planned Value at Month 7: P V 7 PV_7 P V 7 = $9,400,000.
Traditional Schedule Variance: S V = E V − P V SV = EV - PV S V = E V − P V = $6.3M - $9.4M = -$3,100,000.
Traditional Schedule Index: S P I = E V / P V = 6.3 / 9.4 = 0.670 SPI = EV / PV = 6.3 / 9.4 = 0.670 SP I = E V / P V = 6.3/9.4 = 0.670 .
Cost Performance Index: C P I = E V / A C = 6.3 / 7.0 = 0.900 CPI = EV / AC = 6.3 / 7.0 = 0.900 CP I = E V / A C = 6.3/7.0 = 0.900 .
Analytical Insight: While traditional EVM reports an alarming -$3,100,000 variance, Earned Schedule reports an aggregate S V ( t ) SV(t) S V ( t ) of -1.50 months and S P I ( t ) SPI(t) SP I ( t ) of 0.786; the CPM network determines the forecast effect on milestones.