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-Complex manufacturing systems are subject to high levels of variability thatdecrease productivity, increase cycle times and severely impact the systemstractability. As accurate modelling of the sources of variability is acornerstone to intelligent decision making, we investigate the consequences ofthe assumption of independent and identically distributed variables that isoften made when modelling sources of variability such as down-times, arrivals,or process-times. We first explain the experiment setting that allows, throughsimulations and statistical tests, to measure the variability potential storedin a specific sequence of data. We show from industrial data that dependentbehaviors might actually be the rule with potentially considerable consequencesin terms of cycle time. As complex industries require strong levers to allowtheir tractability, this work underlines the need for a richer and moreaccurate modelling of real systems. Keywords-variability; cycle time; dependentevents; simulation; complex manufacturing; industry 4.0 I. Accurate modellingof variability and the independence assumption Industry 4.0 is said to be thenext industrial revolution. The proper use of real-time information in complexmanufacturing systems is expected to allow more customization of products inhighly flexible production factories. Semiconductor High Mix Low Volume (HMLV)manufacturing facilities (called fabs) are one example of candidates for thistransition towards "smart industries". However, because of the high levels ofvariability, the environment of a HMLV fab is highly stochastic and difficultto manage. The uncontrolled variability limits the predictability of the systemand thus the ability to meet delivery requirements in terms of volumes, cycletimes and due dates. Typically, the HMLV STMicroelectronics Crolles 300 fabregularly experiences significant mix changes that result in unanticipatedbottlenecks, leading to firefighting to meet commitment to customers. Theoverarching goal of our strategy is to improve the forecasting of futureoccurrences of bottlenecks and cycle time issues in order to anticipate themthrough allocation of the correct attention and resources. Our current finitecapacity projection engine can effectively forecast bottlenecks, but it doesnot include reliable cycle time estimates. In order to enhance our projections,better forecast cycle time losses (queuing times), improve the tractability ofour system and reduce our cycle times, we now need accurate dynamic cycle timepredictions. As increased cycle-time is the main reason workflow variability isstudied (both by the scientific community and practitioners, see e.g. [1] and[2]), what follows concentrates on cycle times. Moreover, the "variability" weaccount for should be understood as the potential to create higher cycle times,even though "variability" may be understood in a broader meaning. This choiceis made for the sake of clarity, but the methodology we propose and thediscussion we lead can be applied to any other measurable indicator. Sources ofvariability have been intensely investigated in both the literature and theindustry, and tool down-times, arrivals variability as well as process-timevariability are recognized as the major sources of variability in that sensethat they create higher cycle times (see [3] for a review and discussion). As aconsequence, these factors are widely integrated into queuing formulas andsimulation models with the objective to better model the complex reality ofmanufacturing facilities. One commonly accepted assumption in the developmentof these models is that the variables (MTBF, MTTR, processing times, timebetween arrivals, etc.) are independent and identically distributed (i.i.d.)random variables. However, these assumptions might be the reason for modelsinaccuracies 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 andprocess-times or [6] who investigated dependent process times, [4] also givesfurther references for studies on dependencies effects. In a previous work [3],we pinpointed a few elements from industrial data that questioned the viabilityof this assumption in complex manufacturing systems. Figure 1: Number ofarrivals per week from real data (A) and generated by removing dependencies (B)

A study of variability induced by events dependency in microelectronic production