The Mysterious S Curve

Introduction

The first time most project managers become aware of the existence of S Curves is when they are requested by the client or senior management to include one in their next progress report. The following explains what the mysterious S Curve is, why it is an important project management tool, and how to generate one.

What is a S Curve?

A S Curve is defined as "a display of cumulative costs, labour hours or other quantities plotted against time. The name derives from the S-like shape of the curve, flatter at the beginning and end and steeper in the middle, which is typical of most projects. The beginning represents a slow, deliberate but accelerating start, while the end represents a deceleration as the work runs out."
Source: Wideman Comparative Glossary of Common Project Management Terms v2.1 Copyright R. Max Wideman, May 2001

Types of S Curves

There are a variety of S Curves that are applicable to project management applications, including...

Man Hours versus Time S Curve

The Man Hours versus Time S Curve is appropriate for projects that are labour intensive. It shows cumulative man hours expended over time for the duration of the project. As man hours are a product of man power and working hours, these may be adjusted together or individually in an attempt to keep the project on schedule. Projects may require additional man hours to finish on time due to low productivity, delays and disruptions, rework, variations, etc.

 Figure 1: Man Hours versus Time S Curve

Costs versus Time S Curve

The Costs versus Time S Curve is appropriate for projects that contain labour and non-labour (e.g. material supply / hire / subcontract) tasks. It shows cumulative costs expended over time for the duration of the project, and may be used to assist in the calculation of the project's cashflow, and cost to complete.

 Figure 2: Costs versus Time S Curve

Baseline S Curve

Prior to project commencement, a schedule is prepared outlining the proposed allocation of resources and the timing of tasks necessary to complete the project within a set time frame and budget. This schedule is referred to as the Baseline Schedule. From this schedule, a Baseline S Curve is generated. This S Curve reflects the planned progress of the project. If the project requirements change prior to commencement (eg. change of scope, delayed start), the Baseline Schedule may require revision to reflect the changed requirements.

 Figure 3: Baseline S Curve

Target S Curve

Following project commencement, modification of the Baseline Schedule is usually required. Changes are continually made to the Production Schedule (which is originally the same as the Baseline Schedule). The production schedule reflects the actual progress of the project to date, and any revisions made to tasks yet to commence or not yet completed. From this schedule, a Target S Curve may be generated. This S Curve reflects the ideal progress of the project if all tasks are completed as currently scheduled. In an ideal world, the Target S Curve will meet the Baseline S Curve at the end of the project (On Time, On Budget) or finish below and to the left of the Baseline S Curve (Early, Under Budget). In reality, it is not uncommon for the Target S Curve to finish above and to the right of the Baseline S Curve (Late, Over Budget).

 Figure 4: Target S Curve

Actual S Curve

The production schedule is updated on a regular basis throughout the duration of the project. These updates include the revision of percentage complete for each task to date. Using this information, an Actual S Curve may be generated. This S Curve reflects the actual progress of the project to date, and may be compared with the Baseline and Target S Curves to determine how the project is progressing. During the project, the Actual S Curve will terminate at the Cut Off Date. This is the date the Production Schedule was last updated. At the completion of the project, the Actual S Curve will meet the Target S Curve.

 Figure 5: Actual S Curve

Value and Percentage S Curves

S Curves may be graphed as absolute values (i.e. Man Hours or Costs) versus Time, or as percentage values versus Time. Value S Curves are useful for determining Man Hours or Costs expended to date, and Man Hours or Costs to complete. Percentage S Curves are useful for calculating the project's actual percentage complete against target and baseline percentage complete, and for calculating the project's percentage growth (or contraction).


Why Use a S Curve?

S Curves are an important project management tool. They allow the progress of a project to be tracked visually over time, and form a historical record of what has happened to date. Analysis of S Curves allow project managers to quickly identify project growth, slippage, and potential problems that could aversely impact the project if no remedial action is taken.

Determining Growth

Comparison of the Baseline and Target S Curves quickly reveals if the project has grown (Target S Curve finishes above Baseline S Curve) or contracted (Target S Curve finishes below Baseline S Curve) in scope. A change in the project's scopes implies a re-allocation of resources (increase or decrease), and the very possible requirement to raise contract variations. If the resources are fixed, then the duration of the project will increase (finish later) or decrease (finish earlier), possibly leading to the need to submit an extension of time claim.

 Figure 6: Calculating Project Growth using S Curves

Determining Slippage

Slippage is defined as "the amount of time a task has been delayed from its original baseline schedule. The slippage is the difference between the scheduled start or finish date for a task and the baseline start or finish date. Slippage can occur when a baseline plan is set and the actual dates subsequently entered for tasks are later than the baseline dates or the actual durations are longer than the baseline schedule durations".
Source: Wideman Comparative Glossary of Common Project Management Terms v2.1 Copyright R. Max Wideman, May 2001

Comparison of the Baseline S Curve and Target S Curve quickly reveals any project slippage (ie. the Target S Curve finishes to the right of the Baseline S Curve). Additional resources will need to be allocated or additional hours worked in order to eliminate (or at least reduce) the slippage. An extension of time claim may need to be submitted if the slippage can not be eliminated or reduced to an acceptable level.

 Figure 7: Calculating Project Slippage using S Curves

Determining Progress

Comparison of the Target S Curve and Actual S Curve reveals the progress of the project over time. In most cases, the Actual S Curve will sit below the Target S Curve for the majority of the project (due to many factors, including delays in updating the production schedule). Only towards the end of the project will the curves converge and finally meet. The Actual S Curve can never finish above the Target S Curve. If the Actual S Curve sits above the Target S Curve at the Cut Off Date, the Production Schedule should be examined to determine if the project is truly ahead of schedule, or if the Production Schedule contains unrealistic percentage complete values for ongoing tasks.

Figure 8: Calculating Project Progress using S Curves

Project Benchmarks

Percentage S Curves may be used to calculate important project benchmarks on an ongoing basis, including:

How is a S Curve Generated?

To generate a Baseline S Curve, a Baseline Schedule is required.
The Baseline Schedules should contain the following information for each task...


To generate Actual and Target S Curves, a Production Schedule is required.
The Production Schedules should contain the following information for each task...

Worked Example

To better understand how S Curves are generated, consider a simple project comprising three tasks.
A Baseline Schedule prepared using MS Project for this project is shown below.

Figure 9: Sample Baseline Schedule

Baseline Man Hours versus Time S Curve

To generate a Basline Man Hours versus Time S Curve, two sets of calculations are performed.
The first set of calculations are performed for each task in the Baseline Schedule.
(1) Calculate the duration in days for each task.
ie. Baseline Duration = Baseline Finish Date - Baseline Start Date + 1
(2) Calculate Man Hours per day for each task.
ie. Baseline MHs per Day = Baseline Man Hours / Baseline Duration

These calculations are shown in the following table.

Figure 10: Baseline S Curve Calculation 1/2

The second set of calculations are performed for each day in the Baseline Schedule.
(3) Calculate the total Man Hours per Day for all tasks.
(4) Calculate the Year To Date Total for Man Hours per Day for all tasks.

These calculations are shown in the following table.

Figure 11: Baseline S Curve Calculation 2/2

The S Curve is constructed by assigning the Dates to the X Axis, and the YTD values to the Y Axis.
The resulting Baseline Man Hours versus Time S Curve is shown below.

Figure 12: Baseline Man Hours versus Time S Curve

Target Man Hours versus Time S Curve

To generate the Actual and Target S Curves, a Production Schedule is required.
A Production Schedule for this project is shown below.

Figure 13: Production Schedule

To generate a Target Man Hours versus Time S Curve, two sets of calculations are performed.
The first set of calculations are performed for each task in the Production Schedule.
(1) Calculate the duration in days for each task.
ie. Duration = Finish Date - Start Date + 1
(2) Calculate Man Hours per day for each task.
ie. MHs per Day = Man Hours / Duration

These calculations are shown in the following table.

Figure 14: Target S Curve Calculation 1/2

The second set of calculations are performed for each day in the Production Schedule.
(3) Calculate the total Man Hours per Day for all tasks.
(4) Calculate the Year To Date Total for Man Hours per Day for all tasks.

These calculations are shown in the following table.

Figure 15: Target S Curve Calculation 2/2

The resulting Target Man Hours versus Time S Curve is shown below.

Figure 16: Target Man Hours versus Time S Curve

Actual Man Hours versus Time S Curve

To generate an Actual Man Hours versus Time S Curve, two sets of calculations are performed.
Before these calculations may be performed, the Cut Off Date needs to be defined. This is the date the Production Schedule was last updated. For this example a Cut Off Date of 3rd November, 2008 will be used.

The first set of calculations are performed for each task in the Production Schedule.
(1) Determine the Task Status: Complete, Ongoing, Not Started.
Complete: Tasks that have a Finish Date prior to the Cut Off Date.
Ongoing: Tasks that have commenced and have a Finish Date on or after the Cut Off Date.
Not Started: Tasks that have a Start Date after the Cut Off Date.
(2) Calculate the Duration to Date based on the Task Status.
Complete: Duration To Date = Finish Date - Start Date + 1
Ongoing: Duration To Date = Cut Off Date - Start Date + 1
Not Started: Duration To Date = 0.
(3) Calculate Man Hours to Date for Complete and Ongoing Tasks.
ie. Man Hours to Date = Man Hours x % Complete / Duration to Date.

These calculations are shown in the following table.

Figure 17: Actual S Curve Calculation 1/2

The second set of calculations are performed for each day in the Production Schedule up to the Cut Off Date.
(4) Calculate the total Man Hours to Date per Day for all tasks.
(5) Calculate the Year To Date Total for Man Hours to Date per Day for all tasks.

These calculations are shown in the following table.

Figure 18: Actual S Curve Calculation 2/2

The resulting Actual Man Hours versus Time S Curve is shown below.

Figure 19: Actual Man Hours versus Time S Curve

The Baseline, Actual, and Target S Curves are usually combined, as shown below.

Figure 20: Man Hours versus Time S Curves

S Curve Analysis

Initial analysis of the S Curves generated above reveal the following about the status of the project...

Project Growth

Analysis of the Baseline and Target S Curve data reveals the project has grown in scope by 12 man hours, or 14.29%.
ie. Growth = Target MHs - Baseline MHs = 96 - 84 = 12
ie. Growth % = (Target MHs / Baseline MHs - 1) x 100% = (96 / 84 - 1) x 100% = 14.29%

Project Slippage

Analysis of the Baseline and Target S Curve data reveals the project has slipped by 1 day, or 20.00%.
ie. Slippage = Target Duration - Baseline Duration = 6 - 5 = 1
ie. Slippage % = (Target Duration / Baseline Duration - 1) x 100% = (6 / 5 - 1) x 100% = 20.00%

Project Progress

According to MS Project, based on the Production Schedule the project is 50% complete. MS Project calculates percentage complete based on durations, and does not take into account man hours assigned to each task.
Analysis of the Actual and Target S Curve data reveals the project is 53.13% complete as of the Cut Off Date, while the project should be 59.38% complete.
ie. Actual % Complete = (Actual YTD Man Hours @ Cut Off Date / Target Man Hours) x 100% = (51 / 96) x 100% = 53.13%
ie. Target % Complete = (Target YTD Man Hours @ Cut Off Date / Target Man Hours) x 100% = (57 / 96) x 100% = 59.38%

Project Summary

The project will finish late and over budget compared to the Baseline Schedule. Progress to date (ie. the Cut Off Date) is behind schedule compared to the Production Schedule. Detailed analysis of the project is required to determine why the project will be completed late and over budget. Project growth and/or slippage may be due to a number of factors, including underestimation of effort in the Baseline Schedule, low productivity, rework, variations (approved or not), etc. In this example, varations may need to be raised to account for the extra man hours expended, and an extension of time claim raised for the later than planned completion. The Production Schedule may need review to ensure tasks have been updated accurately (especially with respect to true percentage complete values), and ongoing and future tasks may require revising.

Generating S Curves

Some software scheduling packages automatically generate S Curves. On the other hand, some (including MS Project) do not. In this case, a third party software application is required to process the Baseline and Production Schedule data to generate the required S Curves.

Midori Media's myPM SCG: S Curve Generator is a MS Windows application that integrates with MS Excel to generate the various types of S Curves discussed above. MS Project users will need to export their schedule data to a MS Excel file (easily accomplished using MS Project's File Save As option).

myPM SCG processes the resulting export file, and creates a MS Excel Output file containing the required S Curves.
These may be copy-pasted to MS Word for inclusion in Project Progress Reports.

Conclusion

The S Curve is an important but often overlooked and misunderstood project management tool. A variety of S Curves exist, the most common being Man Hours versus Time and Costs versus Time. By creating a Baseline Schedule, a Baseline S Curve may be generated. Baseline S Curves provide a basis on which to compare a project's actual status to its planned status. They may also assist in the planning of manpower and financial resources required to complete the project. A Production Schedule allows Actual and Target S Curves to be generated. These allow the progress of a project to be monitored, and quickly reveal any divergence from the Baseline Schedule. S Curves may be used to determine project growth, slippage, and progress to date.