Join me on an adventure down a rabbit hole into the wonderland of Conditional Branching. I presented a paper at ADIPEC1 back in Nov. 2024 in Abu Dhabi where I work as a PSM.
My paper made the case that integrated Cost & Schedule Risk Analysis (iCSRA) can enhance both predictability & project outcomes and touched on how iCSRA can also serve as a powerful tool for Decision Analysis/Quality (DA/DQ). I believe this DA/DQ tool topic is worth exploring further by using a worked example in Safran Risk.
‘Carryover’ worked example
Your team is overseeing construction of a processing platform at a contractor’s fabrication yard that is going to be installed in the North Sea. Progress has fallen well behind plan and the likelihood of meeting the planned sailaway date appears low without a dramatic improvement in the performance trend over a sustained period. You have been tasked with making a recommendation: should we keep the contracted sailaway date so we can install the topside deck in the summer window (before October), and accept carryover work from onshore to offshore, or should we delay the transport & installation (T&I) window to the next spring to maximise the completion status in the yard where productivity is far higher?
This sounds like a relatively easy trade-off between schedule vs cost drivers, but such a decision will usually be based on the highest value proposition to the project business case and so the net present value (NPV) should really be taken into consideration as a late start-up date will erode a lot of value due to the discounting effects of deferred revenue streams.
I developed a deliberately simple iCSRA model based on the following assumptions and input parameters:
- Topside processing module weighing 10,000 tonnes with cost & durations benchmarked against Performance Forum (Turner & Townsend database) in the North Sea region, translating -/+ uncertainty ranges from as-built risk-impacted data into corresponding Estimate Uncertainty ranges in the iCSRA model
- Weather window preventing offshore T&I over Q4/Q1 winter period each year
- Conditional Branch criteria: carryover work not to exceed 10% of planned construction scope in the onshore yard (Construction/ Commissioning Manager would advise threshold limits based on punch list categories).
This decision point could occur at any point in a project lifecycle from concept selection until weeks before the platform is due to sail and so I have deliberately disregarded many factors that would typically enter the equation, e.g. contractual implications, or even contract strategy if T&I not yet awarded.
We often talk about biases in QRA, but offshore carryover takes our hubris to a stratospheric level! Carryover work always materializes but is very rarely planned for. It is also very easy to bury in the heroic legends of project delivery as there is so much focus on the sailaway date – a key milestone that is often publicised in the public domain, distorting our benchmarking (to most observers a platform that is 90% complete looks no different to the finished article). One manhour onshore can easily become 3-5 manhours offshore, with a cost multiplier that is also proportionate.
I first started playing with Probabilistic & Conditional Branching after I was trained by Pertmaster in 2007. I struggled with both approaches for years. How is it possible to preordain the probability of going down one branch vs another? I must confess I have abandoned Probabilistic branching as I feel a lot more comfortable applying What-if logic statements to simple conditions for the path taken in each iterative simulation run. The condition set in this worked example could not be simpler: if construction progress – duration %complete used as a coarse proxy – is more than or equal to 90% complete at the planned sailaway date then stick to Plan A, if not switch to Plan B and sail the following spring.
The iCSRA model comprises two Conditional Branches, or paths:
- Plan A: Carryover work ≤10% enabling platform to be installed in 2028
- Plan B: Carryover work >10% postponing platform installation to 2029, or 2030 in extreme cases of further construction delays.
One of the most prominent experts in the field of iCSRA, David Hulett, Ph.D. FAACE, submitted a technical paper, RISK-3111, in 2019 to the AACE2 in collaboration with Samuel Steiman, P.E. titled ‘Identifying the Most Probable Cost – Schedule Values from a Joint Confidence Level (JCL) Risk Analysis’. The writers were able to render 3D histograms and surface plots thanks to support from Michael Saitta who used MathWorks® MATLAB® R2018a software to convert 2D xy scatterplot data from Polaris v1.10.1 iCSRA software into 3D xyz graphs where the frequency of Monte Carlo simulation run occurrences were plotted on the z-axis.
I do not have such resources at my disposal, but I do have the world’s greatest iCSRA, and spreadsheet software (Safran Risk, and Microsoft Excel); I imagine most readers of this blog will also have access to both applications.
The 3D surface plot below shows the iCSRA results from my simple worked model with the hydrocarbon production Start-up date on the x-axis, the NPV impact on the y-axis, and the frequency of model output occurrences on the z-axis.
The PDF3 is essentially split into three discrete modes. Plan A resembles the shape of a dolphin, whilst the 2 PDF modes for Plan B look more like the fins of a mother and baby shark. Plan A and Plan B follow mutually exclusive paths, automatically determined by the conditional branch algorithm for the 10% carryover exceedance criteria. To use my animal analogy, you will either be swimming with a Dolphin or with a Shark since there is no known breed of mammalfish as a Dolhark, or a Sholphin at the time of writing this blog:
The chart below shows the Joint Confidence Level (JCL) bands in 10% increments from JCL-P10 to JCL-P90:
Hulett & Steiman recommend identifying the most likely cost/schedule values at any JCL based on the highest frequency of occurrences. The mode average is simply the value that occurs most in the set, but this is highly sensitive to the subjective choice made on bin sizing, e.g. do you divide the total range of risked xy outcomes into 10x10 bins, 50x50 bins, 100x100 bins, or 13x97 bins or…?
By zooming into the JCL-P90 as illustrated below it is clear the mode average (highest frequency) is significantly more conservative than the median average. In the Oil & Gas industry, we tend to select the P50 median as the selected confidence level for both cost and schedule when running the economics for our business cases and when setting contingency levels to bridge the gaps from the respective deterministic targets to our risked P50 values. For this reason, my personal preference is to identify the median average point for the selected JCL:
The 3D plots above can be useful to help conceptualise these principles as a visual aid, but they are not required for the purpose of identifying the mode or median average from a selected JCL scatter plot.
The conventional 2D scatter plot below provides everything we need for the entire data set, or for a selected JCL:
- The mode average represents the single most congested or densest point in the dataset. This centre of convergence can be identified in Excel with relative ease by finding the point that has the least amount of space around it, much like identifying the person at a rock concert that is the most tightly squeezed in by the congested crowd around them. The advantage of this simple objective technique is that the identified mode average is not affected by the highly subjective determination of bin sizing.
- The median average identifies the intersection of the median values in both the x-axis & y-axis, i.e. on either side of the identified cost & schedule values, half the outcomes will be underruns & half will be overruns in each axis.
Whether selecting the mode or median average, or using the 2D or 3D methodologies outlined above, my personal preference is to follow a 2-stage process. I am ultimately looking for a concise set of assumptions when communicating any results or recommendations to senior management, and so the narrative needs to be crystal clear. When identifying a single cost &/or schedule value I want to know which conditional branch it fell on so I can filter out the other branch(es) from the dataset before progressing to the second stage where I identify the median (or mode) average values for time and money combined.
Safran Risk makes it is possible to embed simple tracer markers in the script which facilitates the first stage of separation. In my worked example, the 3D plots are now shown as 2D scatterplots with the data split into 3 colours. The blue data points follow the conditional branch for Plan A with offshore installation of the platform in 2028. The green data points follow the conditional branch for Plan B with offshore installation of the platform in 2029 and the red data points show installation in 2030. I have ringfenced two areas with dotted lines where these coloured data sets overlap. The first area contains outcomes which represent a hybrid mixture of Plan A (platform installed in 2028, but hook-up & commissioning delays impacted the start-up date) and Plan B (platform installed in 2029, but shorter hook-up & commissioning durations accelerated the start-up date). The data points in the second ringfenced area are all from Plan B, with the majority of outcomes based on offshore installation in 2030, but there is also a cloud of green points from installation in 2029:
If your selected JCL band straddles one of these hybrid areas, I would recommend making a conscious decision to filter out all values associated with the conditional branch that you wish to screen out, e.g. the JCL-P40 band for the worked example crossed the first ringfenced area above and so before calculating the median (or mode) average cost & schedule values, I would either filter out the Plan A or Plan B dataset based on which Plan (or conditional branch) contained the highest count of data points):
So, to conclude, what would be my recommendation based on the worked example above?
If I worked for an organisation like NASA that has a standardised JCL percentile value, I would simply pick the data point using the 2-stage technique above, opting for the median as a personal preference. If, like the companies I have worked for, there is no prescribed JCL rulebook I might select the mode average (densest point in a 2D scatterplot, or highest peak in a 3D plot) and then back-calculate the corresponding JCL & CLs (Confidence Level for Cost, and for Schedule) as I would argue this is the best representation of the most likely and expected outcomes. Furthermore, using the multi-modal worked example, I would recommend the economist ran three cases:
- Mode #1 (47% of data points): the tip of the dolphin’s fin (upside case), which corresponds to the densest blue data point in the 2D scatterplot above
- Mode #2 (44% of data points): the tip of the mother shark’s fin (most likely), which corresponds to the densest green point above
- Mode #3 (9% of data points): the tip of the baby shark’s fin (trainwreck stress test), which corresponds to the densest red point above
It is interesting to note the difference in perception when interpreting the 2D scatterplot vs the 3D surface plot. The height of the peak of Mode #2 (mother shark’s fin) grabs our attention as the most likely outcome, but the 2D view graph helps us see there are in fact more blue points in Mode #1 (47% of data) than there are green points in Mode #2 (44%); they are just more evenly spread out. However, on the overall balance of probability the likelihood of following Plan A (47%) is slightly lower than Plan B (53%) and so I would recommend judicious further evaluation of keeping the option open to delay the sailaway date.
Footnotes:
- Abu Dhabi International Petroleum Exhibition and Conference (ADIPEC) is the world's largest and most inclusive gathering for the energy industry. I was also given the privilege of co-presenting with Safran at the Project Controls Expo at Wembley Stadium, London in 2022.
- AACE is the Association for the Advancement of Cost Engineering (often incorrectly dubbed the Association of American Cost Engineers in the Eastern Hemisphere).
- Probability Density Functions (PDFs) describe the expected values of random variables drawn from a sample. The shape of the PDF explains how likely it is that an observed value might occur.
