STATISTICAL METHODS FOR ADVANCED ECONOMETRIC MODELS WITH APPLICATIONS TO VEHICLE HOLDING AND SPEED QUANTILES DISTRIBUTION

This dissertation proposes statistical methods to formulate, estimate and apply complex transportation models. Two main problems are part of the analyses conducted and presented in this dissertation. The first method solves an econometric problem and is concerned with the joint estimation of models that contain both discrete and continuous decision variables. The use of ordered models along with a regression is proposed and their effectiveness is evaluated with respect to unordered models. Procedure to calculate and optimize the log-likelihood functions of both discrete-continuous approaches are derived, and difficulties associated with the estimation of unordered models explained. Numerical approximation methods based on the Genz algortithm are implemented in order to solve the multidimensional integral associated with the unordered modeling structure. The problems deriving from the lack of smoothness of the probit model around the maximum of the log-likelihood function, which makes the optimization and the calculation of standard deviations very difficult, are carefully analyzed. A methodology to perform out-of-sample validation in the context of a joint model is proposed. Comprehensive numerical experiments have been conducted on both simulated and real data. In particular, the discrete-continuous models are estimated and applied to vehicle ownership and use models on data extracted from the 2009 National Household Travel Survey. The second part of this work offers a comprehensive statistical analysis of free-flow speed distribution; the method is applied to data collected on a sample of roads in Italy. A linear mixed model that includes speed quantiles in its predictors is estimated. Results show that there is no road effect in the analysis of free-flow speeds, which is particularly important for model transferability. A very general framework to predict random effects with few observations and incomplete access to model covariates is formulated and applied to predict the distribution of free-flow speed quantiles. The speed distribution of most road sections is successfully predicted; jack-knife estimates are calculated and used to explain why some sections are poorly predicted. Eventually, this work contributes to the literature in transportation modeling by proposing econometric model formulations for discrete-continuous variables, more efficient methods for the calculation of multivariate normal probabilities, and random effects models for free-flow speed estimation that takes into account the survey design. All methods are rigorously validated on both real and simulated data.

Role of climate on barn owls road-kill likelihood and the effect on population viability in future climate change

Roads represent a new source of mortality due to animal-vehicle risk of collision threatening log-term populations’ viability. Risk of road-kill depends on species sensitivity to roads and their specific life-history traits. The risk of road mortality for each species depends on the characteristics of roads and bioecological characteristics of the species. In this study we intend to know the importance of climatic parameters (temperature and precipitation) together with traffic and life history traits and understand the role of drought in barn owl population viability, also affected by road mortality in three scenarios: high mobility, high population density and the combination of previous scenarios (mixed) (Manuscript). For the first objective we correlated the several parameters (climate, traffic and life history traits). We used the most correlated variables to build a predictive mixed model (GLMM) the influence of the same. Using a population model we evaluated barn owl population viability in all three scenarios. Model revealed precipitation, traffic and dispersal have negative relationship with road-kills, although the relationship was not significant. Scenarios showed different results, high mobility scenario showed greater population depletion, more fluctuations over time and greater risk of extinction. High population density scenario showed a more stable population with lower risk of extinction and mixed scenario showed similar results as first scenario. Climate seems to play an indirect role on barn owl road-kills, it may influence prey availability which influences barn owl reproductive success and activity. Also, high mobility scenario showed a greater negative impact on viability of populations which may affect their ability and resilience to other stochastic events. Future research should take in account climate and how it may influence species life cycles and activity periods for a more complete approach of road-kills. Also it is important to make the best mitigation decisions which might include improving prey quality habitat.

Epidemiology and genetic architecture of blood pressure: a family based study of Generation Scotland

Hypertension is a major risk factor for cardiovascular disease and mortality, and a growing global public health concern, with up to one-third of the world’s population affected. Despite the vast amount of evidence for the benefits of blood pressure (BP) lowering accumulated to date, elevated BP is still the leading risk factor for disease and disability worldwide. It is well established that hypertension and BP are common complex traits, where multiple genetic and environmental factors contribute to BP variation. Furthermore, family and twin studies confirmed the genetic component of BP, with a heritability estimate in the range of 30-50%. Contemporary genomic tools enabling the genotyping of millions of genetic variants across the human genome in an efficient, reliable, and cost-effective manner, has transformed hypertension genetics research. This is accompanied by the presence of international consortia that have offered unprecedentedly large sample sizes for genome-wide association studies (GWASs). While GWAS for hypertension and BP have identified more than 60 loci, variants in these loci are associated with modest effects on BP and in aggregate can explain less than 3% of the variance in BP. The aims of this thesis are to study the genetic and environmental factors that influence BP and hypertension traits in the Scottish population, by performing several genetic epidemiological analyses. In the first part of this thesis, it aims to study the burden of hypertension in the Scottish population, along with assessing the familial aggregation and heritialbity of BP and hypertension traits. In the second part, it aims to validate the association of common SNPs reported in the large GWAS and to estimate the variance explained by these variants. In this thesis, comprehensive genetic epidemiology analyses were performed on Generation Scotland: Scottish Family Health Study (GS:SFHS), one of the largest population-based family design studies. The availability of clinical, biological samples, self-reported information, and medical records for study participants has allowed several assessments to be performed to evaluate factors that influence BP variation in the Scottish population. Of the 20,753 subjects genotyped in the study, a total of 18,470 individuals (grouped into 7,025 extended families) passed the stringent quality control (QC) criteria and were available for all subsequent analysis. Based on the BP-lowering treatment exposure sources, subjects were further classified into two groups. First, subjects with both a self-reported medications (SRMs) history and electronic-prescription records (EPRs; n =12,347); second, all the subjects with at least one medication history source (n =18,470). In the first group, the analysis showed a good concordance between SRMs and EPRs (kappa =71%), indicating that SRMs can be used as a surrogate to assess the exposure to BP-lowering medication in GS:SFHS participants. Although both sources suffer from some limitations, SRMs can be considered the best available source to estimate the drug exposure history in those without EPRs. The prevalence of hypertension was 40.8% with higher prevalence in men (46.3%) compared to women (35.8%). The prevalence of awareness, treatment and controlled hypertension as defined by the study definition were 25.3%, 31.2%, and 54.3%, respectively. These findings are lower than similar reported studies in other populations, with the exception of controlled hypertension prevalence, which can be considered better than other populations. Odds of hypertension were higher in men, obese or overweight individuals, people with a parental history of hypertension, and those living in the most deprived area of Scotland. On the other hand, deprivation was associated with higher odds of treatment, awareness and controlled hypertension, suggesting that people living in the most deprived area may have been receiving better quality of care, or have higher comorbidity levels requiring greater engagement with doctors. These findings highlight the need for further work to improve hypertension management in Scotland. The family design of GS:SFHS has allowed family-based analysis to be performed to assess the familial aggregation and heritability of BP and hypertension traits. The familial correlation of BP traits ranged from 0.07 to 0.20, and from 0.18 to 0.34 for parent-offspring pairs and sibling pairs, respectively. A higher correlation of BP traits was observed among first-degree relatives than other types of relative pairs. A variance-component model that was adjusted for sex, body mass index (BMI), age, and age-squared was used to estimate heritability of BP traits, which ranged from 24% to 32% with pulse pressure (PP) having the lowest estimates. The genetic correlation between BP traits showed a high correlation between systolic (SBP), diastolic (DBP) and mean arterial pressure (MAP) (G: 81% to 94%), but lower correlations with PP (G: 22% to 78%). The sibling recurrence risk ratio (λS) for hypertension and treatment were calculated as 1.60 and 2.04 respectively. These findings confirm the genetic components of BP traits in GS:SFHS, and justify further work to investigate genetic determinants of BP. Genetic variants reported in the recent large GWAS of BP traits were selected for genotyping in GS:SFHS using a custom designed TaqMan® OpenArray®. The genotyping plate included 44 single nucleotide polymorphisms (SNPs) that have been previously reported to be associated with BP or hypertension at genome-wide significance level. A linear mixed model that is adjusted for age, age-squared, sex, and BMI was used to test for the association between the genetic variants and BP traits. Of the 43 variants that passed the QC, 11 variants showed statistically significant association with at least one BP trait. The phenotypic variance explained by these variant for the four BP traits were 1.4%, 1.5%, 1.6%, and 0.8% for SBP, DBP, MAP, and PP, respectively. The association of genetic risk score (GRS) that were constructed from selected variants has showed a positive association with BP level and hypertension prevalence, with an average effect of one mmHg increase with each 0.80 unit increases in the GRS across the different BP traits. The impact of BP-lowering medication on the genetic association study for BP traits has been established, with typical practice of adding a fixed value (i.e. 15/10 mmHg) to the measured BP values to adjust for BP treatment. Using the subset of participants with the two treatment exposure sources (i.e. SRMs and EPRs), the influence of using either source to justify the addition of fixed values in SNP association signal was analysed. BP phenotypes derived from EPRs were considered the true phenotypes, and those derived from SRMs were considered less accurate, with some phenotypic noise. Comparing SNPs association signals between the four BP traits in the two model derived from the different adjustments showed that MAP was the least impacted by the phenotypic noise. This was suggested by identifying the same overlapped significant SNPs for the two models in the case of MAP, while other BP traits had some discrepancy between the two sources

Modeling height-diameter relationship in pinus pinaster ait. in the forest intervention zone of Lomba, NE-Portugal

In this work, the relationship between diameter at breast height (d) and total height (h) of individual-tree was modeled with the aim to establish provisory height-diameter (h-d) equations for maritime pine (Pinus pinaster Ait.) stands in the Lomba ZIF, Northeast Portugal. Using data collected locally, several local and generalized h-d equations from the literature were tested and adaptations were also considered. Model fitting was conducted by using usual nonlinear least squares (nls) methods. The best local and generalized models selected, were also tested as mixed models applying a first-order conditional expectation (FOCE) approximation procedure and maximum likelihood methods to estimate fixed and random effects. For the calibration of the mixed models and in order to be consistent with the fitting procedure, the FOCE method was also used to test different sampling designs. The results showed that the local h-d equations with two parameters performed better than the analogous models with three parameters. However a unique set of parameter values for the local model can not be used to all maritime pine stands in Lomba ZIF and thus, a generalized model including covariates from the stand, in addition to d, was necessary to obtain an adequate predictive performance. No evident superiority of the generalized mixed model in comparison to the generalized model with nonlinear least squares parameters estimates was observed. On the other hand, in the case of the local model, the predictive performance greatly improved when random effects were included. The results showed that the mixed model based in the local h-d equation selected is a viable alternative for estimating h if variables from the stand are not available. Moreover, it was observed that it is possible to obtain an adequate calibrated response using only 2 to 5 additional h-d measurements in quantile (or random) trees from the distribution of d in the plot (stand). Balancing sampling effort, accuracy and straightforwardness in practical applications, the generalized model from nls fit is recommended. Examples of applications of the selected generalized equation to the forest management are presented, namely how to use it to complete missing information from forest inventory and also showing how such an equation can be incorporated in a stand-level decision support system that aims to optimize the forest management for the maximization of wood volume production in Lomba ZIF maritime pine stands.

Efeitos do treinamento resistido com máquinas pneumáticas e resistência elástica progressiva na força, capacidade funcional e equilíbrio em mulheres idosas : um ensaio clínico randomizado

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Educação Física, Programa de Pós-Graduação Strictu-Sensu em Educação Física, 2015.

Estudo do processo de combustão in-situ usando poços horizontais como produtores de óleo (Toe-to-Hell Air Injection)

The method "toe-to-heel air injection" (THAITM) is a process of enhanced oil recovery, which is the integration of in-situ combustion with technological advances in drilling horizontal wells. This method uses horizontal wells as producers of oil, keeping vertical injection wells to inject air. This process has not yet been applied in Brazil, making it necessary, evaluation of these new technologies applied to local realities, therefore, this study aimed to perform a parametric study of the combustion process with in-situ oil production in horizontal wells, using a semi synthetic reservoir, with characteristics of the Brazilian Northeast basin. The simulations were performed in a commercial software "STARS" (Steam, Thermal, and Advanced Processes Reservoir Simulator), from CMG (Computer Modelling Group). The following operating parameters were analyzed: air rate, configuration of producer wells and oxygen concentration. A sensitivity study on cumulative oil (Np) was performed with the technique of experimental design, with a mixed model of two and three levels (32x22), a total of 36 runs. Also, it was done a technical economic estimative for each model of fluid. The results showed that injection rate was the most influence parameter on oil recovery, for both studied models, well arrangement depends on fluid model, and oxygen concentration favors recovery oil. The process can be profitable depends on air rate

Evaluation of the risk factors contributing to the African swine fever occurrence in Sardinia, Italy

This study assesses the relation between hypothesized risk factors and African swine fever virus (ASFV) distribution in Sardinia (Italy) after the beginning of the eradication program in 1993, using a Bayesian multivariable logistic regression mixed model. Results indicate that the probability of ASFV occurrence in Sardinia was associated to particular socio-cultural, productive and economical factors found in the region, particularly to large number of confined (i.e., closed) farms (most of them backyard), high road density, high mean altitude, large number of open fattening farms, and large number of pigs per commune. Conversely, large proportion of open farms with at least one census and large proportion of open farms per commune, were found to be protective factors for ASFV. Results suggest that basic preventive and control strategies, such as yearly census or registration of the pigs per farm and better control of the public lands where pigs are usually raised, together with endanced effords of outreach and communication with pig producers should help in the success of the eradication program for ASF in the Island. Methods and results presented here will inform decision making to better control and eradicate ASF in Sardinia and in all those areas with similar management and epidemiological conditions.

Pelvic-Floor Rehabilitation, Part 1 : Comparison of Two Surface Electrode Placements During Stimulation of the Pelvic-Floor Musculature in Women Who Are Continent Using Bipolar Interferential Currents

Background and Purpose. Electrical stimulation of the pelvic floor is used as an adjunct in the conservative treatment of urinary incontinence. No consensus exists, however, regarding electrode placements for optimal stimulation of the pelvic-floor musculature. The purpose of this study was to compare two different bipolar electrode placements, one suggested by Laycock and Green (L2) the other by Dumoulin (D2), during electrical stimulation with interferential currents of the pelvic-floor musculature in continent women, using a two-group crossover design. Subjects. Ten continent female volunteers, ranging in age from 20 to 39 years (X̅=27.3, SD=5.6), were randomly assigned to one of two study groups. Methods. Each study group received neuromuscular electrical stimulation (NMES) of the pelvic-floor musculature using both electrode placements, the order of application being reversed for each group. Force of contraction was measured as pressure (in centimeters of water [cm H2O]) exerted on a vaginal pressure probe attached to a manometer. Data were analyzed using a two-way, mixed-model analysis of variance. Results. No difference in pressure was observed between the two electrode placements. Differences in current amplitude were observed, with the D2 electrode placement requiring less current amplitude to produce a maximum recorded pressure on the manometer. Subjective assessment by the subjects revealed a preference for the D2 electrode placement (7 of 10 subjects). Conclusion and Discussion. The lower current amplitudes required with the D2 placement to obtain recordings comparable to those obtained with the L2 technique suggest a more comfortable stimulation of the pelvic-floor muscles. The lower current amplitudes required also suggest that greater increases in pressure might be obtained with the D2 placement by increasing the current amplitude while remaining within the comfort threshold. These results will help to define treatment guidelines for a planned clinical study investigating the effects of NMES and exercise in the treatment of urinary stress incontinence in women postpartum.

A Microdata Analysis Approach to Transport Infrastructure Maintenance

Maintenance of transport infrastructure assets is widely advocated as the key in minimizing current and future costs of the transportation network. While effective maintenance decisions are often a result of engineering skills and practical knowledge, efficient decisions must also account for the net result over an asset's life-cycle. One essential aspect in the long term perspective of transport infrastructure maintenance is to proactively estimate maintenance needs. In dealing with immediate maintenance actions, support tools that can prioritize potential maintenance candidates are important to obtain an efficient maintenance strategy. This dissertation consists of five individual research papers presenting a microdata analysis approach to transport infrastructure maintenance. Microdata analysis is a multidisciplinary field in which large quantities of data is collected, analyzed, and interpreted to improve decision-making. Increased access to transport infrastructure data enables a deeper understanding of causal effects and a possibility to make predictions of future outcomes. The microdata analysis approach covers the complete process from data collection to actual decisions and is therefore well suited for the task of improving efficiency in transport infrastructure maintenance. Statistical modeling was the selected analysis method in this dissertation and provided solutions to the different problems presented in each of the five papers. In Paper I, a time-to-event model was used to estimate remaining road pavement lifetimes in Sweden. In Paper II, an extension of the model in Paper I assessed the impact of latent variables on road lifetimes; displaying the sections in a road network that are weaker due to e.g. subsoil conditions or undetected heavy traffic. The study in Paper III incorporated a probabilistic parametric distribution as a representation of road lifetimes into an equation for the marginal cost of road wear. Differentiated road wear marginal costs for heavy and light vehicles are an important information basis for decisions regarding vehicle miles traveled (VMT) taxation policies. In Paper IV, a distribution based clustering method was used to distinguish between road segments that are deteriorating and road segments that have a stationary road condition. Within railway networks, temporary speed restrictions are often imposed because of maintenance and must be addressed in order to keep punctuality. The study in Paper V evaluated the empirical effect on running time of speed restrictions on a Norwegian railway line using a generalized linear mixed model.

Pelvic-Floor Rehabilitation, Part 1 : Comparison of Two Surface Electrode Placements During Stimulation of the Pelvic-Floor Musculature in Women Who Are Continent Using Bipolar Interferential Currents

Background and Purpose. Electrical stimulation of the pelvic floor is used as an adjunct in the conservative treatment of urinary incontinence. No consensus exists, however, regarding electrode placements for optimal stimulation of the pelvic-floor musculature. The purpose of this study was to compare two different bipolar electrode placements, one suggested by Laycock and Green (L2) the other by Dumoulin (D2), during electrical stimulation with interferential currents of the pelvic-floor musculature in continent women, using a two-group crossover design. Subjects. Ten continent female volunteers, ranging in age from 20 to 39 years (X̅=27.3, SD=5.6), were randomly assigned to one of two study groups. Methods. Each study group received neuromuscular electrical stimulation (NMES) of the pelvic-floor musculature using both electrode placements, the order of application being reversed for each group. Force of contraction was measured as pressure (in centimeters of water [cm H2O]) exerted on a vaginal pressure probe attached to a manometer. Data were analyzed using a two-way, mixed-model analysis of variance. Results. No difference in pressure was observed between the two electrode placements. Differences in current amplitude were observed, with the D2 electrode placement requiring less current amplitude to produce a maximum recorded pressure on the manometer. Subjective assessment by the subjects revealed a preference for the D2 electrode placement (7 of 10 subjects). Conclusion and Discussion. The lower current amplitudes required with the D2 placement to obtain recordings comparable to those obtained with the L2 technique suggest a more comfortable stimulation of the pelvic-floor muscles. The lower current amplitudes required also suggest that greater increases in pressure might be obtained with the D2 placement by increasing the current amplitude while remaining within the comfort threshold. These results will help to define treatment guidelines for a planned clinical study investigating the effects of NMES and exercise in the treatment of urinary stress incontinence in women postpartum.

Forage peanut (Arachis spp.) genetic evaluation and selection.

Forage peanut improvement for use in grass?legume mixtures is expected to have a great impact on the sustainability of Brazilian livestock production. Eighteen cloned Arachis spp. ecotypes were evaluated under clipping in a Brazilian Cerrado region and results analysed using a mixed model methodology. The objective was to estimate genetic and phenotypic parameters and to select the best ecotypes based on selection index applied on their predicted genotypic value. The traits of total dry-matter (DM) and leaf DM yield presented moderate (0_30 < h2g < 0_50) to high (>0_50) broad-sense heritability, in contrast to the low genetic variability in nutritional quality-associated traits. Ecotypes of Arachis spp. contained average crude protein concentrations of 224 g kg _1 DM in leaves and 138 g kg _1 DM in stems, supporting the potential role of these species to overcome the low protein content in Cerrado pastures. The correlations between yield traits and traits associated with low nutritional value in leaves were consistently significant and positive. Genetic correlations among all the yield traits evaluated during the rainy or dry seasons were significant and positive. The ecotypes were ranked based on selection index. The next step is to validate long-term selection of grass?Arachis in combination with pastures under competition and adjusted grazing in the Cerrado region.

A single nucleotide polymorphism in NEUROD1 is associated with production traits in nelore beef cattle.

Feed efficiency and carcass characteristics are late-measured traits. The detection of molecular markers associated with them can help breeding programs to select animals early in life, and to predict breeding values with high accuracy. The objective of this study was to identify polymorphisms in the functional and positional candidate gene NEUROD1 (neurogenic differentiation 1), and investigate their associations with production traits in reference families of Nelore cattle. A total of 585 steers were used, from 34 sires chosen to represent the variability of this breed. By sequencing 14 animals with extreme residual feed intake (RFI) values, seven single nucleotide polymorphisms (SNPs) in NEUROD1 were identified. The investigation of marker effects on the target traits RFI, backfat thickness (BFT), ribeye area (REA), average body weight (ABW), and metabolic body weight (MBW) was performed with a mixed model using the restricted maximum likelihood method. SNP1062, which changes cytosine for guanine, had no significant association with RFI or REA. However, we found an additive effect on ABW (P ≤ 0.05) and MBW (P ≤ 0.05), with an estimated allele substitution effect of -1.59 and -0.93 kg0.75, respectively. A dominant effect of this SNP for BFT was also found (P ≤ 0.010). Our results are the first that identify NEUROD1 as a candidate that affects BFT, ABW, and MBW. Once confirmed, the inclusion of this SNP in dense panels may improve the accuracy of genomic selection for these traits in Nelore beef cattle as this SNP is not currently represented on SNP chips.

Variation in myogenic differentiation 1 mRNA abundance is associated with beef tenderness in Nelore cattle.

The myogenic differentiation 1 gene (MYOD1) has a key role in skeletal muscle differentiation and composition through its regulation of the expression of several muscle-specific genes. We first used a general linear mixed model approach to evaluate the association of MYOD1 expression levels on individual beef tenderness phenotypes. MYOD1 mRNA levels measured by quantitative polymerase chain reactions in 136 Nelore steers were significantly associated (P ? 0.01) with Warner?Bratzler shear force, measured on the longissimus dorsi muscle after 7 and 14 days of beef aging. Transcript abundance for the muscle regulatory gene MYOD1 was lower in animals with more tender beef. We also performed a coexpression network analysis using whole transcriptome sequence data generated from 30 samples of longissimus muscle tissue to identify genes that are potentially regulated by MYOD1. The effect of MYOD1 gene expression on beef tenderness may emerge from its function as an activator of muscle-specific gene transcription such as for the serum response factor (C-fos serum response element-binding transcription factor) gene (SRF), which determines muscle tissue development, composition, growth and maturation.

Prevention of binge drinking in young adolescents through the promotion of a balanced level of psychological well-being: be-dry

This doctoral thesis presents a project carried out in secondary schools located in the city of Ferrara with the primary objective of demonstrating the effectiveness of an intervention based on Well-Being Therapy (Fava, 2016) in reducing alcohol use and improving lifestyles. In the first part (chapters 1-3), an introduction on risky behaviors and unhealthy lifestyle in adolescence is presented, followed by an examination of the phenomenon of binge drinking and of the concept of psychological well-being. In the second part (chapters 4-6), the experimental study is presented. A three-arm cluster randomized controlled trial including three test periods was implemented. The study involved eleven classes that were randomly assigned to receive well-being intervention (WBI), lifestyle intervention (LI) or not receive intervention (NI). Results were analyzed by linear mixed model and mixed-effects logistic regression with the aim to test the efficacy of WBI in comparison with LI and NI. AUDIT-C total score increased more in NI in comparison with WBI (p=0.008) and LI (p=0.003) at 6-month. The odds to be classified as at-risk drinker was lower in WBI (OR 0.01; 95%CI 0.01–0.14) and LI (OR 0.01; 95%CI 0.01–0.03) than NI at 6-month. The odds to use e-cigarettes at 6-month (OR 0.01; 95%CI 0.01–0.35) and cannabis at post-test (OR 0.01; 95%CI 0.01–0.18) were less in WBI than NI. Sleep hours at night decreased more in NI than in WBI (p = 0.029) and LI (p = 0.006) at 6-month. Internet addiction scores decreased more in WBI (p = 0.003) and LI (p = 0.004) at post-test in comparison with NI. Conclusions about the obtained results, limitations of the study, and future implications are discussed. In the seventh chapter, the data of the project collected during the pandemic are presented and compared with those from recent literature.

Coupled reliability and boundary element model for probabilistic fatigue life assessment in mixed mode crack propagation

Fatigue and crack propagation are phenomena affected by high uncertainties, where deterministic methods fail to predict accurately the structural life. The present work aims at coupling reliability analysis with boundary element method. The latter has been recognized as an accurate and efficient numerical technique to deal with mixed mode propagation, which is very interesting for reliability analysis. The coupled procedure allows us to consider uncertainties during the crack growth process. In addition, it computes the probability of fatigue failure for complex structural geometry and loading. Two coupling procedures are considered: direct coupling of reliability and mechanical solvers and indirect coupling by the response surface method. Numerical applications show the performance of the proposed models in lifetime assessment under uncertainties, where the direct method has shown faster convergence than response surface method. (C) 2010 Elsevier Ltd. All rights reserved.