Completion of sub-projects in complex engineering projects
Paul Davies (Thales UK), Thomas House (Mathematics)
Design engineering processes of complex projects are typically decomposed into subprojects and distributed over different companies or parts of a company. Each sub-process
has its own estimate for completion, usually expressed as a “3-point estimate”, a triangular
probability distribution of expected duration (min, median, max). Variations around the
expected time are due to influences such as risk, complexity and competence of the
estimator. Start times for sub-processes are dependent on completion of other subprocesses that are logically chained.
From a complexity science point of view, such a process can be represented as a dynamic
process on a network/graph. As a first approximation, sub-projects can either run in parallel
or in series, with probabilistic completion dynamics representing the influence of external
influences.
In the limit of a very large number of components, one can use general properties of extreme
value statistics or the central limit theorem to make analytical predictions which are
independent of the individual completion time distributions of sub-projects. It may also be
possible to apply the theory of ‘phase type’ distributions [1], provided one is prepared to
accept that each process is internally of phase type, and thereby make use of several strong
results from Markov chain theory [2]. However, when the sub-processes have significantly
different means and variances, different techniques may need to be simulated. Examples
include simulations of simplified models of noisy dynamical systems on complex networks,
and System Dynamics [3].
The project:
The aim of the project is to study different theoretical foundations to modelling of the project
completion, and to compare and contrast (and ideally explain) the results given by different
models. An extra goal, if time allows, would be to start to answer the questions:


How robust is the system against external perturbations (such as shortage of
resources)?
How does the average and variance of the overall completion time depend on the
completion of sub-processes?
This is expected to lay the groundwork for a subsequent funded PhD. Thales can provide
training data for several reference projects to seed the models.
[1] M. F. Neuts. Probability distributions of phase type. In Liber amicorum Professor emeritus
Dr. H. Florin, pages 173–206. Katholieke Universiteit Leuven, Departement Wiskunde, 1975.
[2] Norris J (1997) Markov chains. Cambridge: Cambridge University Press.
[3] Sterman JD (2000) Business Dynamics, MIT Press.