  -Complex manufacturing systems are subject to high levels of variability that
decrease productivity, increase cycle times and severely impact the systems
tractability. As accurate modelling of the sources of variability is a
cornerstone to intelligent decision making, we investigate the consequences of
the assumption of independent and identically distributed variables that is
often made when modelling sources of variability such as down-times, arrivals,
or process-times. We first explain the experiment setting that allows, through
simulations and statistical tests, to measure the variability potential stored
in a specific sequence of data. We show from industrial data that dependent
behaviors might actually be the rule with potentially considerable consequences
in terms of cycle time. As complex industries require strong levers to allow
their tractability, this work underlines the need for a richer and more
accurate modelling of real systems. Keywords-variability; cycle time; dependent
events; simulation; complex manufacturing; industry 4.0 I. Accurate modelling
of variability and the independence assumption Industry 4.0 is said to be the
next industrial revolution. The proper use of real-time information in complex
manufacturing systems is expected to allow more customization of products in
highly flexible production factories. Semiconductor High Mix Low Volume (HMLV)
manufacturing facilities (called fabs) are one example of candidates for this
transition towards "smart industries". However, because of the high levels of
variability, the environment of a HMLV fab is highly stochastic and difficult
to manage. The uncontrolled variability limits the predictability of the system
and thus the ability to meet delivery requirements in terms of volumes, cycle
times and due dates. Typically, the HMLV STMicroelectronics Crolles 300 fab
regularly experiences significant mix changes that result in unanticipated
bottlenecks, leading to firefighting to meet commitment to customers. The
overarching goal of our strategy is to improve the forecasting of future
occurrences of bottlenecks and cycle time issues in order to anticipate them
through allocation of the correct attention and resources. Our current finite
capacity projection engine can effectively forecast bottlenecks, but it does
not include reliable cycle time estimates. In order to enhance our projections,
better forecast cycle time losses (queuing times), improve the tractability of
our system and reduce our cycle times, we now need accurate dynamic cycle time
predictions. As increased cycle-time is the main reason workflow variability is
studied (both by the scientific community and practitioners, see e.g. [1] and
[2]), what follows concentrates on cycle times. Moreover, the "variability" we
account for should be understood as the potential to create higher cycle times,
even though "variability" may be understood in a broader meaning. This choice
is made for the sake of clarity, but the methodology we propose and the
discussion we lead can be applied to any other measurable indicator. Sources of
variability have been intensely investigated in both the literature and the
industry, and tool down-times, arrivals variability as well as process-time
variability are recognized as the major sources of variability in that sense
that they create higher cycle times (see [3] for a review and discussion). As a
consequence, these factors are widely integrated into queuing formulas and
simulation models with the objective to better model the complex reality of
manufacturing facilities. One commonly accepted assumption in the development
of these models is that the variables (MTBF, MTTR, processing times, time
between arrivals, etc.) are independent and identically distributed (i.i.d.)
random variables. However, these assumptions might be the reason for models
inaccuracies as [4] points out in a literature review on queuing theory.
Several authors have studied the potential effects of dependencies, such as [5]
who studied the potential effects of dependencies between arrivals and
process-times or [6] who investigated dependent process times, [4] also gives
further references for studies on dependencies effects. In a previous work [3],
we pinpointed a few elements from industrial data that questioned the viability
of this assumption in complex manufacturing systems. Figure 1: Number of
arrivals per week from real data (A) and generated by removing dependencies (B)
