There arise two problems when the expectation of some function with respect to a nonuniform multivariate distribution has to be computed by (quasi-) Monte Carlo integration: the integrand can have singularities when the domain of the distribution is unbounded and it can be very expensive or even impossible to sample points from a general multivariate distribution. We show that importance sampling is a simple method to overcome both problems. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

There are situations in the framework of quasi-Monte Carlo integration where nonuniform low-discrepancy sequences are required. Using the inversion method for this task usually results in the best performance in terms of the integration errors. However, this method requires a fast algorithm for evaluating the inverse of the cumulative distribution function which is often not available. Then a smoothed version of transformed density rejection is a good alternative as it is a fast method and its speed hardly depends on the distribution. It can easily be adjusted such that it is almost as good as the inversion method. For importance sampling it is even better to use the hat distribution as importance distribution directly. Then the resulting algorithm is as good as using the inversion method for the original importance distribution but its generation time is much shorter. / Series: Preprint Series / Department of Applied Statistics and Data Processing

’Flight’ is a program that uses flight mechanics to estimate the flight range of birds. This program, used by ornithologists, is only available for Windows OS. It requires manual imputation of body measurements and constants (one observation at a time) and this is time-consuming. Therefore, the first task is to implement the methods in R, a programming language that runs on various platforms. The resulting package named flying, has three advantages; first, it can estimate flight range of multiple bird observations, second, it makes it easier to experiment with different settings (e.g. constants) in comparison to Flight and third, it is open-source making contribution relatively easy. Uncertainty and global sen- sitivity analyses are carried out on body measurements separately and with various con- stants. In doing so, the most influential body variables and constants are discovered. This task would have been near impossible to undertake using ’Flight’. A comparison is made amongst the results from a crude partitioning method, generalized additive model, gradi- ent boosting machines and quasi-Monte Carlo method. All of these are based on Sobol’s method for variance decomposition. The results show that fat mass drives the simulations with other inputs playing a secondary role (for example mechanical conversion efficiency and body drag coefficient).

De nombreuses sources de variabilité impactent la fabrication des circuits intégrés analogiques et RF et peuvent conduire à une dégradation du rendement. Il est donc nécessaire de mesurer leur influence le plus tôt possible dans le processus de fabrications. Les méthodes de simulation statistiques permettent ainsi d'estimer le rendement paramétrique des circuits durant la phase de conception. Cependant, les méthodes traditionnelles telles que la méthode de Monte Carlo ne sont pas assez précises lorsqu'un faible nombre de circuits est simulé. Par conséquent, il est nécessaire de créer un estimateur précis du rendement paramétrique basé sur un faible nombre de simulations. Dans cette thèse, les méthodes statistiques existantes provenant à la fois de publications en électroniques et non-Électroniques sont d'abord décrites et leurs limites sont mises en avant. Ensuite, trois nouveaux estimateurs de rendement sont proposés: une méthode de type quasi-Monte Carlo avec tri automatique des dimensions, une méthode des variables de contrôle basée sur l'estimation par noyau, et une méthode par tirage d'importance. Les trois méthodes reposent sur un modèle mathématique de la métrique de performance du circuit qui est construit à partir d'un développement de Taylor à l'ordre un. Les résultats théoriques et expérimentaux obtenus démontrent la supériorité des méthodes proposées par rapport aux méthodes existantes, à la fois en terme de précision de l'estimateur et en terme de réduction du nombre de simulations de circuits. / Semiconductor device fabrication is a complex process which is subject to various sources of variability. These variations can impact the functionality and performance of analog integrated circuits, which leads to yield loss, potential chip modifications, delayed time to market and reduced profit. Statistical circuit simulation methods enable to estimate the parametric yield of the circuit early in the design stage so that corrections can be done before manufacturing. However, traditional methods such as Monte Carlo method and corner simulation have limitations. Therefore an accurate analog yield estimate based on a small number of circuit simulations is needed. In this thesis, existing statistical methods from electronics and non-Electronics publications are first described. However, these methods suffer from sever drawbacks such as the need of initial time-Consuming circuit simulations, or a poor scaling with the number of random variables. Second, three novel statistical methods are proposed to accurately estimate the parametric yield of analog/RF integrated circuits based on a moderate number of circuit simulations: An automatically sorted quasi-Monte Carlo method, a kernel-Based control variates method and an importance sampling method. The three methods rely on a mathematical model of the circuit performance metric which is constructed based on a truncated first-Order Taylor expansion. This modeling technique is selected as it requires a minimal number of SPICE-Like circuit simulations. Both theoretical and simulation results show that the proposed methods lead to significant speedup or improvement in accuracy compared to other existing methods.

Les études de Sûreté de Fonctionnement (SdF) sur les barrières instrumentées de sécurité représentent un enjeu important dans de nombreux domaines industriels. Afin de pouvoir réaliser ce type d'études, TOTAL développe depuis les années 80 le logiciel GRIF. Pour prendre en compte la complexité croissante du contexte opératoire de ses équipements de sécurité, TOTAL est de plus en plus fréquemment amené à utiliser le moteur de calcul MOCA-RP du package Simulation. MOCA-RP permet d'analyser grâce à la simulation de Monte-Carlo (MC) les performances d'équipements complexes modélisés à l'aide de Réseaux de Petri (RP). Néanmoins, obtenir des estimateurs précis avec MC sur des équipements très fiables, tels que l'indisponibilité, revient à faire de la simulation d'événements rares, ce qui peut s'avérer être coûteux en temps de calcul. Les méthodes standard d'accélération de la simulation de Monte-Carlo, initialement développées pour répondre à cette problématique, ne semblent pas adaptées à notre contexte. La majorité d'entre elles ont été définies pour améliorer l'estimation de la défiabilité et/ou pour les processus de Markov. Par conséquent, le travail accompli dans cette thèse se rapporte au développement de méthodes d'accélération de MC adaptées à la problématique des études de sécurité se modélisant en RP et estimant notamment l'indisponibilité. D'une part, nous proposons l'Extension de la Méthode de Conditionnement Temporel visant à accélérer la défaillance individuelle des composants. D'autre part, la méthode de Dissociation ainsi que la méthode de ``Truncated Fixed Effort'' ont été introduites pour accroitre l'occurrence de leurs défaillances simultanées. Ensuite, nous combinons la première technique avec les deux autres, et nous les associons à la méthode de Quasi-Monte-Carlo randomisée. Au travers de diverses études de sensibilité et expériences numériques, nous évaluons leur performance, et observons une amélioration significative des résultats par rapport à MC. Par ailleurs, nous discutons d'un sujet peu familier à la SdF, à savoir le choix de la méthode à utiliser pour déterminer les intervalles de confiance dans le cas de la simulation d'événements rares. Enfin, nous illustrons la faisabilité et le potentiel de nos méthodes sur la base d'une application à un cas industriel. / The dependability analysis of safety instrumented systems is an important industrial concern. To be able to carry out such safety studies, TOTAL develops since the eighties the dependability software GRIF. To take into account the increasing complexity of the operating context of its safety equipment, TOTAL is more frequently led to use the engine MOCA-RP of the GRIF Simulation package. Indeed, MOCA-RP allows to estimate quantities associated with complex aging systems modeled in Petri nets thanks to the standard Monte Carlo (MC) simulation. Nevertheless, deriving accurate estimators, such as the system unavailability, on very reliable systems involves rare event simulation, which requires very long computing times with MC. In order to address this issue, the common fast Monte Carlo methods do not seem to be appropriate. Many of them are originally defined to improve only the estimate of the unreliability and/or well-suited for Markovian processes. Therefore, the work accomplished in this thesis pertains to the development of acceleration methods adapted to the problematic of performing safety studies modeled in Petri nets and estimating in particular the unavailability. More specifically, we propose the Extension of the "Méthode de Conditionnement Temporel" to accelerate the individual failure of the components, and we introduce the Dissociation Method as well as the Truncated Fixed Effort Method to increase the occurrence of their simultaneous failures. Then, we combine the first technique with the two other ones, and we also associate them with the Randomized Quasi-Monte Carlo method. Through different sensitivities studies and benchmark experiments, we assess the performance of the acceleration methods and observe a significant improvement of the results compared with MC. Furthermore, we discuss the choice of the confidence interval method to be used when considering rare event simulation, which is an unfamiliar topic in the field of dependability. Last, an application to an industrial case permits the illustration of the potential of our solution methodology.

Battery electric trucks (BETs) offer environmental benefits in terms of reduced carbon emissions and enhanced energy efficiency but have been challenged with economic viability compared to conventional internal combustion engine trucks (ICETs) caused by substantial acquisition costs, limited charging infrastructure, and concerns regarding range and payload capacity.  Previous studies focus on TCO at the vehicle or policy level but overlook the system and firm-level impacts. Operational aspects like vehicle utilization, battery utilization, charging planning, and route optimization are often ignored, potentially underestimating electric freight cost-competitiveness.The research gap does not address the practical needs of fleet operators, especially in scenarios where charging infrastructure is lacking. There is therefore a need to consider the complex system level interactions, market dynamics, technology developments, and operational processes involved in freight shipping. By applying a decision-making under deep uncertainty (DMDU) framework, this study enables informed decisions in unpredictable scenarios, bridging the gap between strategic choices like battery capacity and operational optimization like route planning. This study identifies the most significant factors that affect the TCO of BET fleets and cost-competitiveness relative to ICET fleets, taking into account market-operational interfaces between unpredictable market dynamics and operational processes such as stochastic demand and feature selection from a strategic and operational perspective. 40 tonne truck-trailers for freight distribution networks with distances up to 250 km are considered in the study.  A TCO model of BET and ICET fleets was developed taking into account vehicle route optimization, vehicle selection, and vehicle utilization which was then programmatically iterated by sampling and simulating optimized vehicle routes for a total of 220 224 iterations. The parameter space was screened and reduced with Feature Scoring using Extra Trees approximation of 1st order Sobol Indices. The reduced parameter space was then sampled using Sobol sampling to conduct a Sobol Global Variance decomposition Analysis of TCO, TCO delta, and service level in order to identify the most significant factors affecting BET fleet TCO and cost-competitiveness.To identify cost-competitive scenarios, the Patient Rule Induction Method (PRIM) was used to identify parameter sub spaces to determine scenarios where BET fleets have a lower TCO than ICET fleets. Further visual analysis was done using linear and polynomial regression and kernel density estimation. The analysis shows that both TCO and cost-competitiveness of BETs are primarily affected by shipment demand, distance between distribution center and delivery sites, and battery size, and that a trade-off is made between cost-competitiveness and service level. The results show that cost-competitiveness of electric freight scales with demand, with larger fleets being better able to optimize routing and shipment allocation; balancing the shipment demand to minimize charging times that otherwise would make the fleet less competitive than their fossil-fuel counterparts. This, paired together with higher degrees of vehicle utilization and appropriate battery sizing, allow for electric freight to be cost-competitive even for long-haul distances up to 250 km.  Furthermore, optimization of the Electric Vehicle Routing Problem (E-VRP) with shifts and time windows is shown to have a highly significant effect when minimizing TCO on a fleet level, with the vast majority of optimal ICET routes not being optimal for BETs.The benefits of E-VRP optimization scales with demand and fleet size, indicating that large-scale electrification is required to make BETs cost-competitive.Electrification of road freight is therefore highly contingent on effective route planning and charging scheduling with E-VRP optimization in order to be cost-competitive, which has not been considered in previous literature. Thus previous literature have therefore likely underestimated the cost-competitiveness of electric freight, particularly at medium-long haul distances. / Battery electric trucks (BETs), även kända som batterielektriska lastbilar, erbjuder miljömässiga fördelar genom minskade koldioxidutsläpp och förbättrad energieffektivitet. Men de har utmanats när det kommer till ekonomisk konkurrenskraft jämfört med konventionella lastbilar med förbränningsmotor (ICETs) på grund av höga inköpskostnader, begränsad laddinfrastruktur och oro över räckvidd och lastkapacitet. Tidigare studier har fokuserat på TCO (totala ägandekostnader) på fordon- eller policynivå men har inte betraktat TCO på nätverksnivå och från det enskilda företagets perspektiv. Operativa aspekter som fordonssutnyttjande, batteriutnyttjande, laddningsplanering och ruttoptimisering ignoreras ofta, vilket potentiellt leder till en underskattning av elektrisk frakts kostnadskonkurrenskraft. Forskningsluckan tar inte upp de praktiska behoven hos fordonsflottoperatörer, särskilt i scenarier där laddinfrastrukturen är bristfällig. Det finns därför ett behov av att granska komplexa systemnivåinteraktioner, marknadens dynamik, teknikutveckling och operativa processer som är involverade i godstransport. Genom att tillämpa \textit{decision-making under deep uncertainty} (DMDU) möjliggör denna studie informerade beslut i scenarier präglade av osäkerhet och studerar interaktionseffecter mellan strategiska val som batterikapacitet och operativ optimering som t.ex.\ ruttplanering. Denna studie identifierar de mest betydande faktorer som påverkar TCO för BET-flottor och deras kostnadskonkurrenskraft jämfört med ICET-flottor, med beaktande av gränssnitten mellan marknadsdynamik och operativa processer såsom stokastisk efterfrågan och urval av funktioner ur såväl strategisk som operativ synvinkel. 40-ton lastbilssläp för nätverk med avstånd upp till 250 km beaktas inom omfånget för studien. En TCO-modell för BET- och ICET-flottor utvecklades med hänsyn till ruttoptimering, fordonsval och fordonsutnyttjande, vilket sedan programmässigt itererades genom provtagning och simulering av optimerade fordonsrutter för sammanlagt 220 224 iterationer. Parameterrummet granskades och minskades med hjälp av funktionsskattning med hjälp av Extra Trees-approximation av Sobol-indices av första ordningen. Det reducerade parameterrummet provtogs sedan med Sobol-provtagningsmetod för att genomföra en global variansdekomponering av TCO, TCO-delta och servicenivå för att identifiera de mest betydande faktorerna som påverkar BET-flottans TCO och kostnadskonkurrenskraft. För att identifiera kostnadskonkurrenskraftiga scenarier användes Patient Rule Induction Method (PRIM) för att identifiera parametrarum som visar scenarier där BET-flottor har lägre TCO än ICET-flottor. Vidare utfördes visuell analys med linjär och polynomisk regression samt kärnskattning. Analysen visar at kostnadskonkurrenskraft för tunga elektriska fordon primärt påverkas av efterfrågan, köravstånder och batteristorlek, och att det görs en avvägning mellan kostnadskonkurrenskraft och servicenivå. Resultaten visar at kostnadskonkurrenskraft ökar i takt med efterfrågan, då större flottor kan mer fördelaktigt optimera rutter och allokering av leveranser till varje fordon genom att transportefterfrågan balanseras sådan att tiden för laddning minimeras, vilket hade annars gjort de elektriska flottorna mindre konkurrenskraftiga gentemot fossildrivna flottor av tunga fordon. Detta i samband med högre utnyttjandegrad av fordonen och val av rätt batteristorlek gjör att elektrisk godstransport kan vara kostnadskonkurrenskraftig även vid längre körsträckor upp till 250 km. Vidare visar ruttoptimering för BETs (E-VRP) sig vara av stor betydelse när det gäller att minimera TCO på flottnivå, medan majoriteten av optimala ICET-rutter inte är optimala för BETs.Fördelarna med E-VRP optimering skalar med ökande efterfrågan och flottstorlek, vilket tyder på att storskalig elektrifiering behövs för att göra BETs kostnadskonkurrenskraftigaElektrifiering av godstransport är därför starkt beroende av effektiv rutt- och laddningsplanering med E-VRP-optimering. Tidigare litteratur har sannolikt underskattat kostnadskonkurrenskraften för elektrisk godstransport, särskilt vid medellånga och långa transportavstånd.