Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1711.06261

A study of variability induced by events dependency in microelectronic production

Kean Dequeant·Pierre Lemaire·Marie-Laure Espinouse·Philippe Vialletelle
View original source ↗Read source document ↗Export metadata ↓

Abstract

-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)

Explore related subjects

stat.AP

Keep this discovery

BibTeXRIS

Kean Dequeant, Pierre Lemaire, Marie-Laure Espinouse, Philippe Vialletelle. 2017-11-16. A study of variability induced by events dependency in microelectronic production. https://arxiv.org/abs/1711.06261

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Privacy-Preserving Causal Meta-Mediation Analysis with Survival Outcomes

Privacy and data-governance constraints often prevent pooling individual-level data across studies, limiting the use of conventional approaches for causal media- tion analysis in multicenter settings. We propose a federated causal meta-mediation framework for right-censored time-to-event outcomes that enables collaborative es- timation without sharing individual-level data. Our framework targets natural indirect effects in a prespecified population by combining information on mediator and outcome mechanisms across distributed data sources. A site-by-site identifi- cation strategy further allows heterogeneity across data sources to be character- ized, with a variance decomposition separating outcome-related, mediator-related, and interaction components. We develop federated one-step and targeted maxi- mum likelihood estimators that accommodate data-adaptive and machine-learning methods for nuisance-function estimation. The finite-sample performance of the proposed estimators is evaluated through numerical simulations. To illustrate the practical utility of the framework, we apply it on data from the French National Health Data System to evaluate the role of methotrexate coprescription in explain- ing the effect of TNFi versus IL-12/23 inhibitor therapy on treatment persistence among psoriatic patients.

stat.AP↗
arXiv2026

Geospatial Foundation Models Capture Health-Relevant Dimensions of Place Beyond Conventional Social Risk Indices

Area-based social risk indices summarize residents' socioeconomic conditions but incompletely capture physical features of place that may affect health. We evaluated whether numerical representations of physical place produced by four geospatial foundation model families from 2022 satellite data explained residual variance in tract-level associations between the Area Deprivation Index, Social Deprivation Index, and Social Vulnerability Index with health outcomes. We used LightGBM to predict variables from the American Community Survey and 40 chronic disease and health-behavior outcomes from CDC PLACES across 82,646 census tracts in the contiguous United States, evaluating performance across 10 held-out states. Among survey variables, models were moderately predictive of some variables including housing type (R-squared up to 0.54) but weak for disability, unemployment, and income disparity. For health outcomes, models explained up to 54% of variance left unexplained by social risk indices, with the largest gains for annual checkups, arthritis, and high blood pressure. Mean total variance explained by geospatial foundation models across the 40 health-related outcomes increased from 0.31 in the smallest tract-size decile to 0.39 in the largest. Geospatial foundation models capture health-relevant features of place not represented by conventional social risk indices and may usefully augment them in epidemiological analyses.

stat.AP↗
arXiv2026

A spatiotemporal negative binomial model with dynamic dispersion: An application to Tuberculosis infections

Tuberculosis (TB) remains a critical public health concern in Brazil, characterized by pronounced spatial heterogeneity and fluctuating temporal volatility. In this paper, we study monthly TB notifications across 61 microregions of Sao Paulo state from 2001 to 2024. To do this, we introduce a negative binomial spatial integer-valued generalized autoregressive conditional heteroskedastic (INGARCH) model featuring jointly dynamic conditional means and time-varying dispersion. To capture inter-regional spillovers, we incorporate both discrete adjacency structures and a novel continuous distance-based formulation leveraging the Matern correlation function. Parameter estimation via conditional maximum likelihood employs a two-step profile-likelihood iterative scheme, demonstrating solid finite-sample performance in simulation studies. Applied to the Sao Paulo TB surveillance data, the framework substantially outperforms standard Poisson and fixed-dispersion spatiotemporal baselines in empirical fit and uncertainty quantification, maintaining nominal 95% predictive coverage across both dense metropolitan centers and rural microregions. Our results reveal marked spatial heterogeneity in baseline incidence, dynamic overdispersion driven by localized outbreaks, and short-range spatial interaction decay. By accurately modeling spatiotemporal volatility, the proposed methodology provides a robust statistical tool to support public health surveillance, policy-making, and resource allocation.

stat.AP↗