h i g h l i g h t s • A tolerance analysis approaches overview is proposed. • A linearization procedure of the behavior model is required for both approaches. • Some linearization strategies provide conservative probability of failure results. • A confidence interval is obtained using two different linearization strategies. • The order of magnitude of the probability has an effect on the convergence speed. All manufactured products have geometrical variations which may impact their functional behavior. Tolerance analysis aims at analyzing the influence of these variations on product behavior, the goal being to evaluate the quality level of the product during its design stage. Analysis methods must verify whether specified tolerances enable the assembly and functional requirements. This paper first focuses on a literature overview of tolerance analysis methods which need to deal with a linearized model of the mechanical behavior. Secondly, the paper shows that the linearization impacts the computed quality level and thus may mislead the conclusion about the analysis. Different linearization strategies are considered, it is shown on an over-constrained mechanism in 3D that the strategy must be carefully chosen in order to not overestimate the quality level. Finally, combining several strategies allows to define a confidence interval containing the true quality level.

Tolerance verification permits to check the product conformity and to verify assumptions made by the designer. For conformity assessment, the uncertainty associated with the values of the measurands must be known. In fact, to evaluate form characteristics of large aircraft structure workpieces, sampling is required, so a measurement error is present: exact estimation of form characteristics would require complete knowledge of the surface. To minimise this measurement error, this paper presents a Krigingbased procedure to identify the minimum of measured points to check the conformity with a given confidence level. The proposed method is validated on a simple example of orientation tolerance and then performed to inspect the form defect on three large aircraft workpieces.

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International audienceThe goal of tolerance analysis is to verify whether design tolerances enable amechanism to be functional. The current method consists in computing a probabilityof failure using Monte Carlo simulation combined with an optimizationscheme called at each iteration. This time consuming technique is not appropriatefor complex overconstrained systems. This paper proposes a transformationof the current tolerance analysis problem formulation into a parallel systemprobability assessment problem using the Lagrange dual form of the optimizationproblem. The number of events being very large, a preliminary selectivesearch algorithm is used to identify the most contributing events to the probabilityof failure value. The First Order Reliability Method (FORM) for systemsis eventually applied to compute the probability of failure at low cost. Theproposed method is tested on an overconstrained mechanism modeled in threedimensions. Results are consistent with those obtained with the Monte Carlosimulation and the computing time is significantly reduced

Background The novel coronavirus (COVID-19) has presented a significant and urgent threat to global health and there has been a need to identify prognostic factors in COVID-19 patients. The aim of this study was to determine whether chest CT characteristics had any prognostic value in patients with COVID-19. Methods A retrospective analysis of COVID-19 patients who underwent a chest CT-scan was performed in four medical centers. The prognostic value of chest CT results was assessed using a multivariable survival analysis with the Cox model. The characteristics included in the model were the degree of lung involvement, ground glass opacities, nodular consolidations, linear consolidations, a peripheral topography, a predominantly inferior lung involvement, pleural effusion, and crazy paving. The model was also adjusted on age, sex, and the center in which the patient was hospitalized. The primary endpoint was 30-day in-hospital mortality. A second model used a composite endpoint of admission to an intensive care unit or 30-day in-hospital mortality. Results A total of 515 patients with available follow-up information were included. Advanced age, a degree of pulmonary involvement ≥ 50% (Hazard Ratio 2.25 [95% Cl: 1.378 to 3.671], p= 0.001), nodular consolidations and pleural effusions were associated with lower 30-day in-hospital survival rates. An exploratory subgroup analysis showed a 60.6% mortality rate in patients over 75 with ≥ 50% lung involvement on a CT-scan. Conclusions Chest CT findings such as the percentage of pulmonary involvement ≥ 50%, pleural effusion and nodular consolidation were strongly associated with 30-day mortality in COVID-19 patients. CT examinations are essential for the assessment of severe COVID-19 patients and their results must be considered when making care management decisions.

Tolerance analysis consists of analyzing the impact of variations on the mechanism behavior due to the manufacturing process. The goal is to predict its quality level at the design stage. The technique involves computing probabilities of failure of the mechanism in a mass production process. The various analysis methods have to consider the component's variations as random variables and the worst configuration of gaps for over-constrained systems. This consideration varies in function by the type of mechanism behavior and is realized by an optimization scheme combined with a Monte Carlo simulation. To simplify the optimization step, it is necessary to linearize the mechanism behavior into several parts. This study aims at analyzing the impact of the linearization strategy on the probability of failure estimation; a highly over-constrained mechanism with two pins and five cotters is used as an illustration for this study. The purpose is to strike a balance among model error caused by the linearization, computing time, and result accuracy. In addition, an iterative procedure is proposed for the assembly requirement to provide accurate results without using the entire Monte Carlo simulation.

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