Boeing

Monte-Carlo Simulation of Large-Scale Complex Life-Cycle Product Patterns for Program Management

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Probabilities and Randomness
Monte-Carlo analysis is a simulation method named after the famous Mediterranean gambling resort. These methods are a broad class of algorithms requiring repeated random sampling, essentially using randomness to solve deterministic problems.
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Summary

By Scott D. Button, Joshua W. Brown, Tek D. Kim and Thomas E. Sherer

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Cognitive bias unfavorably affects how we make decisions under uncertainty. This is exacerbated with the increase in scale and complexity of systems that are affected by those decisions.

Methods are needed to provide decision analysis support for program managers and other engineers faced with allocating scarce resources for large-scale, complex product development.

The approach described in this summary extracts a life-cycle thread from an overall product development network and uses Monte-Carlo analysis to simulate options for resource allocation. By doing this, we can then describe the trade-offs between the resource allocation choices. Expected benefits are reductions in the cost and the elapsed time from beginning to the end of programs that contain significant product development.

An explanatory description of this methodology is described in the full paper available on Boeing.com.

This approach starts with Lean+ Systems Integration Management (LSIM), a set of tools and methods demonstrated to increase productivity and improve affordability of product development. The principle objective of LSIM is to perform the right work in the right order to reduce unplanned and out-of-sequence rework. This model-based approach improves the quality of deliverables, increases throughput, facilitates cross-functional integration, and provides management a predictive model with regular feedback on focus areas requiring their attention.

In 2015, we started developing life-cycle threads from our LSIM integration models. The context of a thread is the life-cycle maturity of information for a few functional groups—for example, how the Flight Controls team and the Stability and Control team interact to mature information from concept to deliverable. These thread features enable the use of statistical clustering to extract a life-cycle pattern of products and inputs, and to apply this life-cycle pattern to other products to establish similar patterns of inputs, without manually selecting these inputs. This has the potential to significantly speed up our modeling process.

In 2016, we enhanced these features to provide network diagram plots. We created the ability to add to a thread from a tree view of the product hierarchy, produce a network diagram with nodes and edges colored according to the responsible organization, and populate the nodes with additional helpful information.

In 2017, we added a Monte-Carlo analysis of these threads. This new approach enables functional managers to understand the expected completion distribution of their function, in the context of the overall program.

To conduct a Monte-Carlo simulation, a sample is drawn from a defined distribution representing each task. Each sample from the defined distribution constitutes a trial, and 100-1,000,000 trials are typically evaluated to determine the results.

The mainstream approach to simulation of project duration is by assuming a shape for the task distributions, then aggregating the tasks according to the project network to form a project completion distribution.

For this Monte-Carlo analysis, we selected the log normal distribution to use as the shape of the distribution for task duration. We favor the log normal distribution as it only requires our program sources to estimate the average duration and validate our assumption that the safe duration should be two standard deviations longer than the average duration.

Figure 2 illustrates a network thread for the 787 semi-levered landing gear. This is a thread excerpted from a larger, airplane-level integration model. The curve above the first two tasks in the thread represents the log-normal distribution of durations for each task.

For each task in the network, a random sample is taken from the probability density function representing that task. A finish time is computed for each task, which is the sum of the sampled task duration and the finish time of the latest predecessor to that task. The finish time of the terminal product in the network represents the finish time for the thread, for one run of the Monte-Carlo analysis.

This is repeated numerous times (1,000 to 100,000) to form the completion distribution of the thread. Figure 5 shows the histogram for the completion distribution of the terminal product in the thread. Note the completion distribution shifts towards a more normal distribution, due to effects predicted by the Central Limit Theorem.

The network diagram is shown as Figure 8: Landing Gear Network Diagram. The upper number is the uniform resource identifier, the lower number is the duration in days. The three tasks involved in the trade-off are indicated with an ellipse.

We find it rather interesting that by moving resources from 1.3.1 to 1.3.2 in this example, the project duration is reduced approximately the same amount as if you doubled the resources on 1.3.2 in isolation. This is due to sufficient slack in the non-critical path feed from 1.3.1 downstream. Although this effect is somewhat obvious for this simple network, the technique will provide non-obvious results for more complex networks.

This shows that Monte Carlo analysis methods are useful to demonstrate the trade-offs between time and resources for life-cycle threads in a commercial aircraft program. And it allows program managers and engineers to understand the role of variation and uncertainty in large-scale, complex, life-cycle product patterns. This understanding is central to meeting the flow time and cost improvement necessary to remain competitive.

    Figure 2 - Semi-levered landing gear thread, horizontal axis in units of days.

    Semi-levered landing gear thread

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    Figure 5 - Completion distribution, mode = 1,370 days.

    Completion distribution, mode

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    Figure 8 - Landing gear network diagram.

    Landing gear network diagram

    Boeing