PM 587 Week 3 Quantitative Risk Analysis Example

A Twenty-Two Percent Chance of Month Fourteen: Monte Carlo Schedule Analysis and a Decision Tree for a Composite Panel Launch

[Student Name]

University of Phoenix

PM/587: Project Risk Management and Quality Assurance

Week 3 Assignment

[Instructor Name]

[Date]

Plainsview Aerostructures, its distributions, simulation results and figures are composites written for a model paper.

Last week's ranking sent five of Plainsview's thirty launch risks on for modeling. The plan's single-point schedule shows the first shipset delivered in month 14. The general manager wants to know how likely that date is and what drives the uncertainty. This paper builds and runs the model.

Why Quantify

Qualitative scores rank risks one at a time. Quantitative analysis shows their combined effect on objectives. Kwak and Ingall (2007) reviewed the use of Monte Carlo simulation in project management and found it useful for estimating the likelihood of meeting schedule and cost targets, while noting that its value depended on the quality of inputs and on managers' understanding of the method. The current standard similarly describes simulation as a way to represent the combined effect of individual risks and other sources of uncertainty on project outcomes (Project Management Institute [PMI], 2021).

The Model's Structure

The full schedule has about 400 activities, but the path to first delivery is driven by a few chains. The model keeps eight summary activities: customer drawing release for six late parts; tool design for those parts; invar tool fabrication; process qualification, including autoclave cure trials; first article inspection on the coordinate measuring machine; customer source inspection; the first production run; and shipping. Parallel chains for the other 16 parts, which have drawings and simpler tools, are included as one summary path that rarely becomes critical.

Input Ranges

Each activity received a three-point range from the people who own the work, using a triangular distribution. Examples: drawing release for the six late parts, 2 to 10 weeks after month 2, most likely 8; invar tool fabrication, 20 to 30 weeks, most likely 22; process qualification, 6 to 14 weeks, most likely 8; first article inspection, 5 to 9 weeks, most likely 6.

Discrete Risk Events

Four risks from the register were added as events that either happen or do not in each iteration:

Prepreg supply cut: 30 percent probability; adds 4 to 10 weeks to qualification and production.

Autoclave slots unavailable: 50 percent probability; adds 2 to 6 weeks to qualification.

Out-time scrap of qualification panels: 30 percent; adds 1 to 3 weeks.

Customer source inspector rejects report format: 20 percent; adds 1 to 2 weeks.

Correlation

Late drawings and late tools are related: when drawings slip, tool design starts late and tool builders often lose their slot. Treating them as independent would understate the chance that both run long. Williams (2004) argued that Monte Carlo simulations of project networks can mislead when they ignore how managers respond to delays and how activities depend on each other, producing ranges that are too narrow. The model applies a correlation of 0.6 between drawing release and tool fabrication and 0.4 between autoclave availability and out-time scrap.

Leaving out correlation makes a model optimistic in exactly the cases the sponsor most needs to see.

Results

After 5,000 iterations:

Probability of first delivery by month 14: about 22 percent.

Median (P50) first delivery: early month 15.

P80 first delivery: mid-month 16.

Worst 5 percent of outcomes: later than month 17.5.

The sensitivity ranking, based on how strongly each input's variation correlated with the delivery date, placed drawing release first, autoclave availability second, prepreg supply third and tool fabrication fourth. First article inspection mattered less than the team had feared, because its range was narrow.

Cost was modeled with the same events plus cost ranges for overtime, expedited tooling and scrap. Against a launch budget of $6.2 million, the P50 cost was about $6.55 million and the P80 about $7.1 million.

How the Model Was Checked

Before the results were shown to anyone, the team tested the model in three ways. First, with all risk events switched off and every activity set to its most likely duration, the model reproduced the plan's month 14, confirming that the logic matched the schedule. Second, the scheduler compared the simulated range for tool fabrication with the tool builder's delivery record on its last eight invar tools, which had run from 21 to 29 weeks, close to the input range. Third, the team ran the model with correlations set to zero and found that the P80 date moved about three weeks earlier, which showed how much the correlated drawing and tooling delays mattered and why leaving them out would have misled the general manager.

Presenting the Results

The results were presented as an S-curve of cumulative probability against delivery month, with month 14, the P50 and the P80 marked, and as a short ranked list of drivers. The team avoided presenting a single date. It also showed the same curve with the two proposed management actions applied, so that the general manager could see what each action was worth in probability terms: early release of the four largest drawings raised the chance of month 14 from about 22 to about 38 percent, and secured autoclave time raised it further to about 47 percent.

What the Results Mean

Month 14 is a target with about a one-in-five chance. Committing it to the customer without action would be imprudent. The analysis points to where action pays: the drawing release and autoclave access, which together explain most of the variance. The general manager decided to negotiate early drawing release for the four largest late parts in exchange for a temporary design freeze on interfaces and to secure autoclave time through the military program's manager, then re-run the model. Contingency was set near the P80 cost, about $0.9 million above the base budget.

A Decision Tree for an Opportunity

The out-of-autoclave material could move the smaller panels off the constrained autoclave, but it needs customer approval. Qualification would cost about $380,000. The team estimated a 40 percent chance of approval. If approved, the savings in overtime, avoided rental of outside autoclave time and earlier delivery are worth about $1.2 million; if not, the qualification cost is lost.

Expected monetary value of qualifying: 0.4 × $1.2 million minus $380,000 = $480,000 minus $380,000 = about $100,000. Not qualifying has an expected value of zero. Qualifying is marginally better, but the result depends heavily on the 40 percent estimate. The team identified a cheaper first step: asking the customer's materials engineers for a preliminary view, costing about $20,000 in engineering time, which would sharpen the probability before committing the full amount. That information is worth buying.

Limits of the Model

The model depends on input ranges from people with incentives and biases; Week 2's silent scoring helped, but the ranges are still judgments. Correlations are estimates. The model does not capture management responses, such as overtime ordered when work slips, which in reality would shorten some outcomes and raise costs. The results are a guide to decisions, not a forecast to be quoted to the customer to the day.

Conclusion

Quantitative analysis showed that Plainsview's month 14 delivery has about a 22 percent chance and that drawings, autoclave access and prepreg supply drive most of the uncertainty. Those findings led to two management actions, a contingency near the P80 cost and a staged approach to the out-of-autoclave opportunity. The model will be re-run after the drawing negotiation and each month as data replace estimates.

References

Kwak, Y. H., & Ingall, L. (2007). Exploring Monte Carlo simulation applications for project management. Risk Management, 9(1), 44-57. https://doi.org/10.1057/palgrave.rm.8250017

Project Management Institute. (2021). A guide to the project management body of knowledge (PMBOK guide) (7th ed.). Project Management Institute.

Williams, T. (2004). Why Monte Carlo simulations of project networks can mislead. Project Management Journal, 35(3), 53-61. https://doi.org/10.1177/875697280403500307