APPENDIX D

SCHEDULE ANALYSIS USING EVM DATA

D.1 Introduction

While there are limitations to using EVM data for schedule analysis, techniques have been developed which allow EVM data to be used to augment and improve the effectiveness of overall project schedule analysis.

However, consistent with long-standing EVM practice, the network schedule remains the primary source of schedule analysis. Also consistent with EVM best practice, the resource-loaded, time-phased network project schedule, should strongly correlate to the performance measurement baseline (PMB) as a prerequisite to effective “cost-schedule integration.”

The schedule analysis techniques utilizing EVM data should be used as a cross check to network-schedule-predicted durations and completion dates and to assist in identifying potential exceptions for further analysis and possible corrective action.

D.2 Average Performance to Date Versus Average Performance Required to Achieve Completion Date¹

A long standing technique utilizing EVM data is to compare average historic schedule performance and compare to the future schedule performance required to achieve an estimated duration (ED).

The formulas are:

While averages may not necessarily reflect either current planned or actual performance, this approach enabled the comparison and analysis of past average schedule efficiency achieved from an EV perspective and a comparison to the projected future efficiency required to achieve an ED.

D.3 Estimates of Duration and the Completion Date

D.3.1 Work Rate Predictions¹

Other long-standing techniques that have been used to predict an ED and the project completion date utilizing EVM data have been collectively known as the “schedule averaging” formulas. The generic formula is:

Then:

IECD = Project Start Date + ED

where IECD is the independent estimate of the completion date.

The work rates historically utilized as performance factors include:

• PV_{(current period)}
• PV_(average)
• EV_{(current period)}
• EV_(average)

Inspection of the formulas, in particular the performance factors historically utilized, reveal limitations with these techniques. When a project exceeds the planned duration (PD), the value of PV_cum equals its maximum value, the BAC. Therefore, in the case of PV_{(current period)} after the PD is exceeded there are no further current period values of PV to utilize as a work rate. In the case of EV_{(current period)} in the generally unlikely condition of zero EV being accrued in a period, the calculation also becomes indeterminate. The use of current period work rates as performance factors may produce volatile predictions over time.

However, all the work rates, with the exception of PV_{(current period)} will produce predictions which converge to the final outcome achieved and range of predicted outcomes for the project duration which can be used for further analysis.

D.3.2 Predictions Using SPI¹

An alternative approach, an independent prediction of project duration has been utilized using EVM data²:

³

where PD = planned duration.

This formula resolves to and produces the same predictions as:

While these formulas will produce reasonable predictions of the final outcome for early and on-time completion projects, the limitations of this approach mimic the limitations of the predictive capability of SPI($). The mathematically inevitable reversion of SPI($) to unity at project completion will result in predictive utility being lost when this reversion commences as the predicted duration will revert to the PD. Predictive utility using this approach is also lost when the PD is exceeded in the case of late finish projects.

D.4 Time Variance Using Graphical Method

A longstanding method to determine a measure of time variance based on EVM data is the graphical method which projects the EV accrued onto the PV curve. This is accomplished by drawing a horizontal line from the EV curve at the status date to the PV curve and reading the time increment on the X (time) axis as illustrated in the bicycle case study in Section D11.2.

D.5 Earned Schedule

Earned schedule (ES), developed by Lipke in 2003,⁴ extends the graphical method of projecting EV accrued onto the PV curve.

D.5.1 ES Concept

The ES concept as described by Lipke is as follows:

The idea of Earned Schedule is similar to Earned Value. However, instead of using cost for measuring schedule performance, we would use time. Earned Schedule is determined by comparing the cumulative EV earned to the performance baseline. The time associated with EV, i.e. Earned Schedule, is found from the PV S-curve. This concept of projecting EV onto PV is not truly new. It is illustrated in many books dealing with EVM (including Mr. Fleming's book [Fleming, 1988]⁵). The significance of using the Earned Schedule concept is that the associated schedule indicators behave appropriately throughout the entire period of project performance.⁴

The ES concept is depicted in Figure D1. While the example depicts time increments in months, ES works with the time increment of choice, for example, weeks if weekly EVM is being utilized.

The ES concept includes a time-based computation, called the earned schedule which calculates the time increment where the EV at the status date should have been accrued.

⁶

D.5.2 ES Indicators

From the ES calculation, a set of time-based schedule indicators are formed from the EVM data which behave in the same way as the EVM cost indicators:

Schedule Variance (time): SV(t) = ES – AT

Schedule Performance Index (time): SPI(t) = ES / AT

where AT is the actual time (in time increments) at the project status date.

When the ES exceeds AT, the SV(t) is positive and negative when it lags. The SPI(t) is greater than 1.0 when ES exceeds AT, and less than 1.0 when ES is less than AT. SV(t) will only revert to zero and SPI(t) to unity at project completion when the project completes on time.

The ES indicators, calculated by reference to the unconstrained actual time, behave appropriately and consistently as per the EVM cost counterparts for all phases of the project, including early and late finish projects.

D.5.3 ES Computation

The ES computation is expressed as:

ES_cum = C + I

where C is the number of time increments of the PMB for which EV is greater than or equal to PV.

I is the calculation for the fraction of the subsequent PV increment. The calculation is a linear interpolation using the following formula:

I = (EV – PV_C) / (PV_C+1 – PV_C)

Using the example shown in Figure D1, the ES accrued is 6 months. The periodic measure of ES is derived from successive cumulative values:

ESperiod_(n) = EScum _(n) – EScum _(n–1)

where the subscript n is the number of time periods from the beginning of the project.

D.5.4 ES “To Complete” Indexes

The ES concept has been developed to provide similar metrics for the schedule to those provided by EVM for cost. The ES planned duration for work remaining (PDWR) is:

PDWR = PD – ES cum

where PD is the planned duration for the project.

To determine the future schedule efficiency required to achieve projected schedule outcomes, the ES “to complete” indices which are similar to the EVM TCPI for cost are:

TSPI = (PD – ES) / (PD – AT) and

TSPI = PD – ES) / (ED – AT)

where ED is the project manager's estimated completion duration.

The use of the TSPI for schedule analysis is similar to the TCPI for cost. Recent research indicates that, when the TSPI is greater than 1.1, the projected outcome (PD or ED) is also likely to be unachievable.⁷

D.6 ES Completion Estimates

D.6.1 ES Completion Prediction⁸

ES provides two formulas for statistically predicting an independent estimate at complete time (IEAC(t)):

IEAC(t) = PD / SPI(t)

which is often referred to as the “short form” formula which is similar to BAC/CPI for cost and

IEAC(t) = ES cum + PDWR / PF(t)

where PF(t) is a time-based performance factor.

The latter is often referred to as the “long form” formula and enables the development and testing of PF(t) other than SPI(t) to ascertain where alternatives might more reliably predict project duration earlier in the project lifecycle.

From the IEAC(t), an independent prediction of project completion date can be calculated:

IECD = Project Start Date + IEAC(t)

where IECD is the independent estimate of completion date.

D.6.2 Future Performance

Consistent with the behavior of the EVM IEAC cost predictors, the ES IEAC(t) predictor projects the schedule future performance based on the historic schedule performance as represented in the SPI(t). Just as for cost forecasting, past project performance, while useful for initial prediction, may not continue into the future.

D.7 ES Analysis

Similar to EVM for cost, ES analysis is usually conducted as a “top-down” analysis process aimed at identifying adverse variances for further analysis and evaluation for corrective action.

Reliance on “high-level” ES metrics without further detailed analysis introduces the risk, which is the same as for EVM cost analysis, whereby lower-level positive and negative variances may be masked at the summary level.

As previously stated, the network schedule should remain as the primary source of schedule analysis augmented by the ES indicators and predictors.

D.8 Critical Path Analysis⁹

D.8.1 Introduction

The EVM data does not, in current practice, identify activities that form part of the critical path (or critical chain if critical chain scheduling is being utilized). Therefore, the network schedule should be utilized as the primary source for critical path analysis.

In practice, it has sometimes been noted that, when the project manager is actively managing activities on the critical path, the EVM (and ES) schedule indicators may indicate delay when the network schedule critical path analysis does not, or vice versa.

D.8.2 Critical Path Analysis Using ES

In addition to overall analysis of schedule performance, ES provides the ability to allow comparison to critical path performance. By treating the critical path activities (including completed critical path activities) as a separate project, the duration of the critical path can be forecast and compared to the planned duration as well as the overall project forecast.

From this comparison, the project manager can determine the relative performance of executing the critical and non-critical tasks and activities. If the ES metrics as applied to the critical path are better than the overall project ES metrics, this indicates that critical path is being protected and critical path activities are being properly prioritized during project execution. It may also be another indicator, provided that the critical path performance is sustainable during the execution of the project that the overall project ES metrics may improve over time.

Conversely, if the overall project ES metrics are less favorable than the ES metrics being applied at what is currently being analyzed and managed as the critical path, this may be a macro level indicator that the critical path has changed. Detailed analysis of the network scheduled is required to ascertain the actual status of the critical path and the critical path calculated project completion date.

D.8.3 Conclusion

These methods are recommended to further supplement the network analysis of the project schedule and the critical path.

D.9 “P” Factor¹⁰

D.9.1 Introduction

Following up from the development of the ES additional advances to practice have been developed. One of the most significant advances is the “P” factor measure of schedule adherence. In developing the tasks and interrelationships between the tasks required to be executed by the project, the project schedule is also modeling the processes planned to be used by the project.

The “P” factor is a measure of the conformance of the actual process execution to the planned processes as embodied in the project schedule. It is important to note that that the “P” factor is not a measure of the efficiency of project execution. The “P” factor also provides, for the first time, important information on the sequence in which earned value has been accrued.

D.9.2 Concept

The idea of schedule adherence is embodied in the “P” factor measure. The “P” factor is the ratio of the EV accrued in accordance with the project schedule compared to the total EV. Therefore the “P” factor measure will be a value between zero (if schedule tasks are being executed completely at random) and one (if the conformance of the EV accrued during execution is perfectly aligned to the schedule).

ES facilitates the “P” factor calculation by enabling the identification of tasks in the schedule where work and EV accrued should have been accomplished in conformance with the schedule.

¹¹

To illustrate these points, the shaded tasks in Figure D2 represent the EV accrued at the status date AT. The ES line depicts the ES accrued at the AT status date. It is apparent that the SV(t) is negative indicating a project that is executing behind schedule in ES terms. It is important to note that the purpose of Figure D2 is limited to depicting the:

• Relationship between the network schedule and the PV curve (PMB)
• Distribution of the EV accrued on the project as at the status date, actual time (AT)

The shaded areas represent where work and EV were actually accomplished. If the project was executing in perfect conformance to the schedule achieving a “P” factor of 1, all of the shading that indicates a task completion would be to the left of and up to the vertical ES line. Therefore, only tasks 1 through 6 should be executed and have EV accrued. It can be seen from Figure D2 that:

• Tasks 2, 4 and 6 are incomplete and to the left of the ES line, and
• Tasks 7 and 8 have commenced to the right of ES line.

Therefore the process execution and EV accrued has not been achieved in complete adherence to the schedule.

D.9.3 Calculation

The “P” factor formula is:

P = ΣEV_j /ΣPV_j = ΣEV_j /EV

where the subscript “j” denotes the identity of the tasks from the schedule which comprise the planned accomplishment (i.e., to the left of the ES line).

The sum of the EV in the shaded areas of tasks 1 through 6 up to the ES line is the value of the numerator for P.

Notional data is used to further illustrate this. Where the sum of the EV accrued to the left of the ES line is $900 (ΣEV_j) and the total EV accrued is $1000, the “P” factor is 0.90 ($900/$1,000). This means that 90% of the EV accrued by the project has occurred in adherence to the project schedule. Conversely 10% of the EV accrued (to the right of the ES line) has been accrued out of agreement with the process sequence detailed in the schedule.

D.9.4 Impediments, Constraints, and Rework

The “P” factor construct also facilitates the development of additional useful information.

Where the difference between the EV – PV value for each task is negative, (identification can be automated) there is possibility of a process impediment or constraint impeding completion.

Examples of this from Figure D2 are Tasks 2, 4, and 6 which are incomplete and to the left of the ES line. Investigation by the project manager of these tasks with a view to implementing corrective action aimed at resolving the impediment or constraint is indicated.

Additionally, when the difference between EV and PV is positive, (identification also automatable), the task may be at risk of experiencing rework.

Examples from Figure D2 are Tasks 7 and 8, which have commenced and are to the right of the ES line. These tasks have commenced in advance of the schedule and with incomplete inputs from the preceding:

• Tasks 2 and 4 are incomplete in the case of Task 7
• Task 6 is incomplete, in the case of Task 8.

Tasks commencing with incomplete inputs are at risk of requiring rework after the preceding tasks are completed. This may also be evidence of poor process discipline, all of which indicate the need for investigation with a view to corrective action by the project manager.

D.9.5 Conclusion

This discussion highlights the benefits of ES and the “P” factor in facilitating analysis of the network project schedule by providing a list of tasks which can be used to prioritize the detailed analysis using the network schedule.

Furthermore, the “P” factor permits calculation of the EV accrued that is not in conformance with the correct process sequence. This facilitates the ability to forecast the rework resulting from out-of-sequence performance. The importance and value of maintaining the task precedence relationships in the network project schedule are also highlighted.

D.10 Summary

While EVM is oftentimes viewed as primarily being a method focused on project cost analysis and management, time conversion techniques to augment network schedule analysis have been a historic part of the EVM methodology.

Recent developments in the use of EVM data for schedule analysis, which is based on ES, has resulted in time-based indicators and predictors that parallel the EVM metrics for cost and can be used to further augment network schedule analysis.

The “P” factor measure of schedule (and process) adherence is an additional development which provides, for the first time, important information on the sequence in which EV is accrued.

Additional useful information obtained from the “P” factor includes the identification of activities which may be the subject of impediments, constraints, or “at risk of rework,” which can be used to prioritize areas for analysis in the network schedule itself.

These developments further augment the core EVM claim and benefit of being a methodology which achieves cost-schedule integration.

D.11 Bicycle Case Study

This section extends the bicycle case study from Chapter 9 of this practice standard to demonstrate the application of the concepts presented in this appendix.

D.11.1 Average Performance to Date Versus Average Performance Required To Achieve Completion Date

Table D1 assembles the periodic data, in this case weekly, and tabulates the average and required performance (using an ED of 22 weeks, which is also the PD) for the bicycle project as, at the end of Period 6, the status date in Chapter 9 of this practice standard.

While the average EV to date has been consistently less that the average projected performance required to achieve the ED of 22 weeks, the trend has been week on week improvements in the average performance and a reduction in the gap between actual and projected future performance required. This indicates progressively improving performance by the bicycle project since commencement.

D.11.2 Work Rate Estimates of Duration

Figure D3 assembles the periodic data, in this case weekly, and charts the estimates of duration utilizing the “work rates” for the bicycle project as at the end of Period 6, the status date in Chapter 9 of this practice standard.

The work rates utilizing the planned value measures (average and current period) predict project duration in line with the planned duration of 22 weeks. The EV performance factors predict a late finish project of around 30 weeks from Week 1 with progressively improving performance to an “on time” finish project (EV average) of around 22 weeks and early finish at around 17 weeks with the EV current period performance factor.

¹²

These estimates, consistent with all schedule predictions based on EVM data, need to be analyzed in conjunction with the network project schedule including the critical path and near-critical path activities. Analysis of the work rate performance factor that is most likely to best represent future schedule performance also assists in determining the best current estimate of project duration.

D.11.2.1 Time Variance Using Graphical Method Analysis¹³

Figure D4 shows the EVM graphical analysis of schedule delay as applied to the bicycle project. The time variance is approximately negative 1 week.

It has been suggested that the time variance be added to the planned duration to provide an EVM-based forecast of the schedule duration compared to the “planned earned value schedule.”¹⁴

D.11.2.2 Earned Schedule Analysis

Figure D5 assembles the periodic data, in this case weekly, and charts the planned schedule and earned schedule for the bicycle project as at the end of Period 6, the status date in Chapter 9 of this practice standard.

Graphically, it can readily be seen that the project is behind schedule with a planned schedule and actual time of 6 weeks and ES of 5.04 weeks. This results in an SV(t) of negative 0.96 weeks and SPI(t) of 0.84, both of which indicate a behind-schedule condition.

The IEAC(t) calculated using SPI(t) as the performance factor is projecting a period of project execution of 25.82 weeks with a corresponding IECD of 3 July 20XX compared to the baseline completion date of 4 June 20XX.

This analysis assumes, similar to EVM cost prediction, that the historic schedule efficiency as reflected in SPI(t) will continue into the future. In contrast to critical path method analysis which typically extends the project end date by the period of current delay, the projection of historic performance reflected in SPI(t) also explains the predicted delay at project completion of 3.82 weeks (IEAC(t) of 25.82 weeks minus planned duration of 22 weeks).

For the period ending 15 Feb, the TSPI indicator has been calculated by reference to an EAC(t) of 22 weeks (the planned duration). Its value of 1.061 suggests, as the value is less than 1.1 (subject to analysis of the network schedule and overall project) that the schedule delay may be recoverable if timely and effective corrective action is implemented.

While the ES analysis of the bicycle project at the AT status date is indicating project delay, the trend analysis indicates that a significant improvement in project performance has occurred since commencement.

In Period 1, the SPI(t) of 0.62 indicated an IEAC(t) of 35.03 weeks which has improved to SPI(t) of 0.96 and an IEAC(t) of 25.82 weeks, respectively.

Determining the ability of the project to sustain the improvement in project performance to date into the future is ultimately a matter of detailed analysis of all aspects of the project. This should include the network schedule which may highlight future schedule constraints and technical performance measures that may also indicate future constraints to ongoing performance improvement.

D.11.2.3 Earned Schedule Analysis Applied to the Critical Path⁹

While the previous discussion applies ES analysis to the overall project, ES analysis can be applied to any area of interest within the project. This is achieved by treating the area of interest as a project in its own right for ES analysis purposes. The application of ES to the critical path (including critical path activities which have been completed) and comparing to the overall project ES metrics is a useful area for further analysis.

Figure D6 assembles the data for the bicycle project critical path technical activities (excluding engineering and project management).

Comparing the critical path versus overall project ES metrics at the end of Period 6 shows a slightly improved set of measures and indicators:

• ES of 5.29 for the critical path compared to 5.04 for the overall project
• SPI(t) of 0.882 compared to 0.840 overall
• SV(t) of negative 0.71 weeks compared to negative 0.96 weeks overall
• IEAC(t) of 24.6 weeks compared to 25.82 weeks overall.
• IECD of 25 Jun XX compared to 3 Jul XX overall.

These metrics indicate that the project manager is appropriately managing the critical path and prioritizing the allocation of work to critical path activities.

Provided the critical path performance is sustainable for the remainder of the project, which would need to be determined from analysis of the network project schedule, a slight (1 week) improvement on the overall project projected completion may be achievable.

D.11.3 “P” Factor Analysis

The “P” factor calculations for the bicycle demonstrate a very high level of conformance to the project schedule and the process adherence represented by the project schedule (see Table D2).

At the end of Period 6, 97.2% of the accrued EV has occurred in adherence to the schedule and only 2.8% of the EV accrued has occurred out of the correct process sequence. In addition, the trend since the start of the project has been progressive improvement in the schedule adherence achieved.

The estimated amount of accrued rework by Period 6 resulting from poor process adherence is estimated to be $565, with a forecast for the total amount of rework for the overall project equal to $2,263.

The benefit of the “P” factor is further illustrated by notionally reducing the “P” factor value so that, at Period 6, P equals 0.6. The recalculation of the estimated rework occurring from poor process adherence yields significantly different values. The estimated value for the accrued rework is $4,965 by Period 6, while the overall forecast for the project has increased dramatically to $29,216.

This demonstrates the importance of schedule adherence and being able to measure this performance characteristic using the “P” factor.

D.11.4 Comparison of EVM and ES Schedule Indicators

In order to fully show the benefits of the ES schedule indicators compared to their EVM counterparts, it is necessary to extend the bicycle project to become a “late finish project” and compare the respective EVM and ES schedule indicators.

The bicycle project EVM data has been extended to show a project that has completed seven weeks late. Figure D7 compares SPI($) and SPI(t) on a single axis which is generally the more useful for comparison while Figures D8 compares the EVM SV($) with the time-based SV(t) graphed on the second Y axis.

SPI($) and SPI(t) in Figure D7 shows a strong correlation up until the planned completion of the project in Week 22. In subsequent periods which is also roughly the final one-third period of project execution, SPI($) loses predictive utility as it begins the inevitable reversion to unity at project completion. In contrast the SPI(t) values of less than 1 continue to show a project executing behind schedule.

The analysis of SV($) and SV(t) in Figure D8 is consistent with the EVM and indices. After Period 22, SV($) begins the process of reverting to zero at completion while SV(t) correctly shows the periodic actual delay experienced and the 7-week delay at project completion.

In addition to ES providing intuitive time-based schedule metrics, the improved utility of the ES metrics for portraying and analyzing schedule performance compared to the EVM counterparts is demonstrated.

D.11.4 Further Discussion Regarding Rework

Rework occurs from a portion of the out of sequence work that is not useable:

Rw = f(r) · (1 – P) · EV

Rework is performed over the remainder of the project at the rate:

β = Rw / (BAC – EV)

Using the rework rate at the beginning and end of a performance period the rework for period n can be calculated:

where C = EV/BAC

The sum of the periodic values is the cumulative rework through period n :

Rcum (n) = ΣRp

Using the Rcum and the present value of β, a forecast can be made for the total rework the project is expected to experience from the lack of schedule adherence:

RT = Rcum + β · (BAC – EV)

Using the above formulas the rework for period six may be demonstrated:

Rw(6) = 0.813 · (1 – 0.972) · $74544

= $1697

Rw(5) = 0.862 · (1 – 0.959) · $56767

= $2006

β(6) = $1697 / ($277040 – $74544)

        = 0.0084

β(5) = $2006 / ($277040 – $56767)

        = 0.0091

Rp(6) = 1/2 · $277040 · (0.0084 + 0.0091) · (0.269 – 0.205)

          = $155

Rcum(6) = Rcum(5) + Rp(6)

              = $410 + $155

              = $565

RT = $565 + (0.0084) · ($277040 – $74544)

      = $2263

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¹ Adapted from “Pocket Guide to Program Management using an Earned Value Management System.” July 2009. Humphreys & Associates, Inc.

² PMI. 2005. Practice Standard for Earned Value Management. Newtown Square, PA: Author.

³ SPI($) is the traditional EVM SPI. The ($) suffix is used to distinguish from the earned schedule, schedule performance index (time) (SPI(t)) which is described later in this appendix.

⁴ Lipke, W. March 2003. Schedule is Different. The Measurable News, REDUX, Summer 2003.

⁵ Fleming, Q. 1988. Cost/Schedule Control Systems Criteria: The Management Guide to C/SCSC. Chicago, IL: Probus.

⁶ Stratton, Ray, 2005. Not Your Father's Earned Value. Projects @ Work: http://www.projectsatwork.com

Figure D1. Earned Schedule Concept ⁶

⁷ Lipke, W. 2009. The To Complete Performance Index—An Expanded View. The Measurable News, Spring 2009.

⁸ Adapted from Henderson, K. 2004. Further Developments in Earned Schedule. The Measurable News, Spring 2004.

⁹ Adapted from Lipke, W. 2006. Applying Earned Schedule to the Critical Path and More. The Measurable News, Fall 2006.

¹⁰ Adapted from Lipke, W. 2004. Connecting Earned Value to the Schedule. The Measurable News, Winter 2004.

¹¹ Lipke, Walt “Connecting Earned Value to the Schedule,” The Measurable News, Winter 2004

¹² The units of measure in this table are of value ($) per period.

¹³ Adapted from Fleming, Q. 1988. Cost/Schedule Control Systems Criteria: The Management Guide to C/SCSC. Chicago, IL: Probus.

¹⁴ Fleming, Q. & Koppleman, J. Earned Value Project Management, 2^nd Edition (Chapter 10). Newtown Square, PA: Project Management Institute.