Triangular Probability Distribution Research Articles

Impact of Alcohol Consumption on Multiple Sclerosis Using Model-based Standardization and Misclassification Adjustment Via Probabilistic Bias Analysis.

The etiology of multiple sclerosis (MS) is still not well-demonstrated, and assessment of some risk factors like alcohol consumption has problems like confounding and measurement bias. To determine the causal effect of alcohol consumption on MS after adjusting for alcohol consumption misclassification bias and confounders. In a population-based incident case-control study, 547 patients with MS and 1057 healthy people were recruited. A minimally sufficient adjustment set of confounders was derived using the causal directed acyclic graph. The probabilistic bias analysis method (PBAM) using beta, logit-logistic, and triangular probability distributions for sensitivity/specificity to adjust for misclassification bias in self-reporting alcohol consumption and model-based standardization (MBS) to estimate the causal effect of alcohol consumption were used. Population attributable fraction (PAF) estimates with 95% Monte Carlo sensitivity analysis (MCSA) intervals were calculated using PBAM and MBS analysis. Bootstrap was used to deal with random errors. The adjusted risk ratio (95% MCSA interval) from the probabilistic bias analysis and MBS between alcohol consumption and MS using the three distribution was in the range of 1.93 (1.07 to 4.07) to 2.02 (1.15 to 4.69). The risk difference (RD) in all three scenarios was 0.0001 (0.0000 to 0.0005) and PAF was in the range of 0.15 (0.010 to 0.50) to 0.17 (0.001 to 0.47). After adjusting for measurement bias, confounding, and random error alcohol consumption had a positive causal effect on the incidence of MS.

Risk assessment in railway rolling stock planning

Rolling stock planning is one of the steps in the traffic planning process considered from the railway undertaking's point of view. It is directly related to the efficiency of rolling stock utilisation, which should be ensured at the highest possible level in the case of rail transport. The planning work stage is subject to certain risks (threats and opportunities), which, if they materialise, will impact it. It, therefore, makes sense to carry out analyses that can anticipate specific events in good time and introduce appropriate countermeasures in advance. This article aims to conduct a risk assessment process concerning rolling stock planning. It was assumed that the considerations were carried out based on the M_o_R (Management of Risk) methodology. Based on this methodology, risk identifica-tion and risk analysis (estimation of risk impact) were carried out. Risk assessment was carried out using the Monte Carlo simulation method. The work identified sixteen risks that represent threats. The principle of risk description was used to identify risks. It requires indicating for each risk the reason for its occurrence and the effect it may have. As a part of risk estimation, variables were selected to assess each risk's impact on the objectives of the stage. Publicly available statistical data were used to define the variables. The variables were expressed in monetary units. The work identified five variables describing impact, which were assigned to the individual risks. As a trian-gular probability distribution was used for the variability of impact description, the variable's minimum, most likely, and maximum value was identified. A risk assessment was carried out for only two impact description varia-bles (for those variables used to describe the impact of the most significant number of risks). For each variable, statistical parameters were indicated and analysed. The resulting value of the variable describing the impact was then read out for each percentile, and the expected value of the risk was calculated. A detailed risk assessment was made for the lower, middle and upper quartiles. A histogram of the incidence of each variable value was presented, and an assessment was made.

К ВОПРОСУ ОБ ОПРЕДЕЛЕНИИ ПЛОТНОСТИ ВЕРОЯТНОСТИ ТИПОВЫХ РАСПРЕДЕЛЕНИЙ ПО ЭКСПЕРИМЕНТАЛЬНЫМ ДАННЫМ

The article discusses the issues of determining errors in determining the type of distributions. The type of distributions is expressed in the form of probability densities of unimodal distribution laws of the K. Pearson system. Analytical dependences are obtained to determine the necessary volumes of sample data to ensure the required accuracy of identification and approximation of these distribution laws. Specific analytical dependences and graphs are given for determining such distribution laws as simple laws (normal, uniform, triangular) probability distributions, oneparameter laws (gamma distributions, lognormal distribution, Weibull distribution), twoparameter beta distribution.

Robust Optimization of Natural Laminar Flow Airfoil Based on Random Surface Contamination

Natural laminar-flow (NLF) airfoils are one of the most promising technologies for extending the range and endurance of aircrafts. However, there is a lack of methods for the optimization of airfoils based on the surface contamination that destroys the laminar flow. In order to solve this problem, a robust optimization process is proposed using the Non-dominated Sorting genetic algorithm- II (NSGA-II) evolutionary algorithm, and Monte Carlo simulation combined with an aerodynamic calculation software Xfoil. Firstly, the airfoil is optimized normally and the aerodynamic performance of optimized airfoil under surface contamination is analyzed. Then, the original airfoil is robustly optimized under random surface contamination based on the assumption that its locations follow triangular and uniform probability distributions. Finally, all the optimized results and original airfoil are compared. It is found that robust optimization reduces the sensitivity of the airfoil to random surface contamination, hence, improving the robustness of the airfoil. The proposed methods make it possible to improve the aerodynamic performance of NLF airfoils considering surface contamination.

Uncertainty analysis in solid mechanics with uniform and triangular distributions using stochastic perturbation-based Finite Element Method

In this paper theoretical formulation and computational implementation of the Stochastic perturbation-based Finite Element Method (SFEM) for uncertainty analysis in solid mechanics with symmetric non-Gaussian input parameters are presented. Theoretical foundations of the method are based on the general order Taylor expansions of all uncertain input parameters and state functions including even orders only. The first four probabilistic characteristics of the structural responses have been derived for symmetrical triangular and uniform probability distributions of random input including probability distribution truncation effect. The Stochastic Finite Element Method implementation has been completed for the displacement version of the FEM using statistically optimized nodal polynomial response bases, and their coefficients are determined using the Least Squares Method using the weighted and non-weighted schemes. Structural responses of several mechanical systems are analyzed using their basic probabilistic characteristics, which have been validated using the probabilistic semi-analytical approach, and also the crude Monte-Carlo simulation. A relatively good coincidence of three probabilistic numerical techniques confirms the applicability of the Stochastic perturbation-based Finite Element Method to study boundary and initial problems in mechanics with uncertainties having uniform and/or triangular probability distributions.

Investigation of the British pendulum calibration uncertainty by Monte Carlo simulation

The paper presents the evaluation of the calibration uncertainty of the British pendulum slip resistance tester using Monte Carlo simulation method. A mathematical model was produced which describes pendulum behavior based on its calibration parameters. The Monte Carlo simulation, programmed in Python, was used for simulating the effect of each of the calibration parameters adjustment within their tolerance intervals, with uniform and triangular probability distribution. Four different tolerance limits were compared: limits from a current international standard, a proposition with reduced limits from recent literature, and two novel propositions, one with reduced but easily achievable limits, and a second one for best practically achievable limits. The results of the simulation show a fundamental standard uncertainty contribution of about 2.8% for pendulum calibration according to current standard limits. Furthermore, they suggest a possible improvement to 0.5%–0.7% as its best practical direct calibration standard uncertainty for reduced limits.

Assessment of distribution center locations using a multi-expert subjective\u2013objective decision-making approach

Distribution is a strategic function of logistics in different companies. Establishing distribution centers (DCs) in appropriate locations helps companies to reach long-term goals and have better relations with their customers. Assessment of possible locations for opening new DCs can be considered as an MCDM (Multi-Criteria Decision-Making) problem. In this study, a decision-making approach is proposed to assess DC locations. The proposed approach is based on Stepwise Weight Assessment Ratio Analysis II (SWARA II), Method based on the Removal Effects of Criteria (MEREC), Weighted Aggregated Sum Product Assessment (WASPAS), simulation, and the assignment model. The assessment process is performed using the subjective and objective criteria weights determined based on multiple experts’ judgments. The decision matrix, subjective weights and objective weights are modeled based on the triangular probability distribution to assess the possible alternatives. Then, using simulation and the assignment model, the final aggregated results are determined. A case of DC locations assessment is addressed to show the applicability of the proposed approach. A comparative analysis is also made to verify the results. The analyses of this study show that the proposed approach is efficient in dealing with the assessment of DC locations, and the final results are congruent with those of existing MCDM methods.

Stress–Strain Behavior of FRC in Uniaxial Tension Based on Mesoscopic Damage Model

Fiber-reinforced concrete (FRC) is widely used in the field of civil engineering. However, the research on the damage mechanism of FRC under uniaxial tension is still insufficient, and most of the constitutive relations are macroscopic phenomenological. The aim is to provide a new method for the investigation of mesoscopic damage mechanism of FRC under uniaxial tension. Based on statistical damage theory, the damage constitutive model for FRC under uniaxial tension is established. Two kinds of mesoscopic damage mechanisms, fracture and yield, are considered, which ultimately determines the macroscopic nonlinear stress–strain behavior of concrete. The yield damage mode reflects the potential bearing capacity of materials and plays a key role in the whole process. Evolutionary factor is introduced to reflect the degree of optimization and adjustment of the stressed skeleton in microstructure. The whole deformation-to-failure is divided into uniform damage phase and local failure phase. It is assumed that the two kinds of damage evolution follow the independent triangular probability distributions, which could be represented by four characteristic parameters. The validity of the proposed model is verified by two sets of test data of steel fiber-reinforced concrete. Through the analysis of the variation law of the above parameters, the influence of fiber content on the initiation and propagation of micro-cracks and the damage evolution of concrete could be evaluated. The relations among physical mechanism, mesoscopic damage mechanism, and macroscopic nonlinear mechanical behavior of FRC are discussed.

Effect of reliability on varying demand and holding cost on inventory system incorporating probabilistic deterioration

<p style='text-indent:20px;'>This paper presents a mathematical framework to derive an inventory model for time, reliability, and advertisement dependent demand. This paper considers the demand rate is high initially, and then the demand rate reduces later stage, which reflects the situation related to cash in hand. The uncertain deterioration of the product presents through Uniform, Triangular, and Double Triangular probability distributions. The holding cost of the proposed inventory system is dependent on the reliability of the item to make this study a more realistic one. This proposed inventory system allows the situation of shortage and partially backlogged at a fixed rate. Numerical examples, along with managerial implications and sensitivity analysis of the inventory parameters, discuss to examine the effect of changes on the optimal total inventory cost.</p>

Research on the Mechanical Properties of Recycled Aggregate Concrete under Uniaxial Compression Based on the Statistical Damage Model.

In this paper, uniaxial compression tests were carried out for recycled aggregate concrete with water cement ratios of 0.38, 0.49, and 0.66 and replacement ratios of 0%, 25%, 50%, 75%, and 100%, respectively. The influence of the replacement ratio of recycled aggregate and water cement ratio on the strength, elastic modulus, and deformation characteristics of concrete was discussed. The results show that the replacement rate of recycled aggregate has a significant effect on the macro stress–strain behavior of concrete. In the case of a constant water cement ratio, the peak nominal stress first decreases and then increases with the increase of the replacement rate; while the water cement ratios equal 0.38, 0.49, and 0.66, the corresponding transition states are 25%, 50%, and 50% of the replacement rate, respectively. The deformation and failure is characterized by two stages: distributed damage and local failure. Combined with the statistical damage mechanics, the influence of the aggregate replacement rate on the damage evolution mechanism of recycled concrete on a mesoscopic scale was explored. Two mesoscopic damage modes, fracture and yield, are considered. Their cumulative evolutions are assumed to follow triangular probability distributions, which could be characterized by four parameters. The peak nominal stress state and the critical state are distinguished, and the latter is defined as a precursor to local failure. With the increase of the replacement rate of recycled aggregate, the inhomogeneous evolution of mesoscopic damage shows obvious regular change, which is consistent with the internal chemical and physical mechanism and macro nonlinear stress–strain behavior.

Technical-economic analysis for a green ammonia production plant in Chile and its subsequent transport to Japan

Green ammonia can be produced using fossil fuels or any renewable energy source combined with heat or electricity. Chile has one of the highest rates of solar irradiation and also the environmental conditions that support the development of solar industry. Other renewable sources of energy are the wind and the hydraulic dams. These energies could be used to generate ammonia by a standard method such as the Haber-Bosch process, which transforms hydrogen and nitrogen using high temperatures and a catalyst. The ammonia has several desirable characteristics that suggest its use as a way to store hydrogen. Firstly, it can be liquified under mild conditions. Secondly, the ammonia has a high weight fraction of hydrogen. Thus, it is deemed necessary to study technical and economic variables that may support the use of green ammonia as an energy carrier for hydrogen. The aim of this work is to develop a technical-economic analysis about the production of ammonia using hydrogen by means of electrolysis (carried out with solar, wind, and hydraulic renewable energies). The aforementioned green ammonia would be produced in Chile and it would be necessary to transport it to Japan. Sensitivity analysis of main parameters (plant operating hours, size of the ammonia synthesis plant - related to the capacity of the electrolysis plant size in MW-, electricity price, electrolyzer cost, Haber-Bosch cycle cost, and ammonia sales price) was performed to report what factors are primordial at the moment of carried out techno-economic analyses. An optimization process that minimize the NPV was run in order to settle the most convenient size of the electrolyser stack. A net present value (NPV) of base case is €77,414,525 and 7.62 years of pay-back period were calculated for this green ammonia production plant, which considered hydrogen production via electrolysis, Haber-Bosch processes, and trade values of different operational units. The sensitivity analysis has determined that the main variables affecting the NPV are the size of the ammonia synthesis plant and the electricity price. Furthermore, by considering triangular probability distribution of specific variables, it was observed that with a 95% of confidence, the NPV would be positive with a 76.1% of occurrence. The optimization process defined that a stack of 164.21 MW would be the most convenient electrolyser stack dimension, which was estimated by considering all different effects over the operational expenditure (OPEX), capital expenditure (CAPEX), and investments risk. Therefore, the hydrogen production in Chile and its transportation to Japan using ammonia as an energy carrier would be a technically viable and profitable solution, which also has environmental benefits.

A possibilistic programming approach to analyze a closed-loop polyethylene tanks supply chain based on decision tree and discounted cash flow

ABSTRACTAccording to environmental considerations, the traditional supply chain has replaced with a closed-loop supply chain. This study attempts to design the polyethylene tanks closed-loop supply chain network under uncertainty. The proposed network contains various levels such as suppliers, manufacturing plants, distribution warehouses, and retailers. A mixed integer linear programming model is developed with a single-objective, multiple products and multiple periods. Besides, after-sales service is considered that has economic and environmental effects on the supply chain and leads to customers’ satisfaction and loyalty. To deal with uncertainty, possibilistic programming is used. Therefore, some parameters of the model are considered as a fuzzy number with a triangular probability distribution. Also, a method based on decision tree and discounted cash flow is utilized to analyze the problem in multiple periods. Furthermore, to validate and show the applicability of the proposed model, a real case study is performed in the polyethylene tanks industry. Finally, the sensitivity analysis is used to check the robustness of the proposed model and framework. The results show that the net present value of the supply chain under new condition is increased by 0.8%. The results of this research can be useful for managers of the organizations.

Scenario uncertainties assessment within whole building LCA

Uncertainties evaluation is increasingly gaining traction within life cycle assessment (LCA), due to its key role as environmental decision support tool. When applied at whole-building scale, the large variety of materials, subjective choices and long lifespans introduce parameter, scenario and model uncertainties throughout the life cycle. Since normative choices are unavoidable within whole-building LCA (wbLCA), in this article we carried out a so-called ‘scenario’ uncertainty assessment for one illustrative case study. First, three uncertainty sources were selected, to include the two drivers most frequently cited in literature (reference service life and end of life management alternatives) and material wastage, a relevant issue to factor in variable construction optimization levels in contexts like Brazil. Cumulative energy demand (CED) and CML 2001 v.2.05 methods were used for calculating deterministic values of non-renewable embodied energy and global warming potential in SimaPro 7.3 The uncertainty assessment combined scenario analysis, stochastic modelling (Monte Carlo simulation of triangular probability distributions for the uncertainty drivers investigated) and global sensitivity analysis (GSA). The GSA confirmed the dominant contribution of the operational phase - strongly influenced by components replacement rate - to of life cycle non-renewable embodied energy and global warming potential result variance, whilst construction and end of life stages showed no correlation with life cycle results. Findings from this research also highlight the strategic importance of gathering service life information adherent to the assessed context. Building components replacement rates induced by the Brazilian standard are overestimated relatively to international figures used in LCAs worldwide.

NBBO: A new variant of biogeography-based optimization with a novel framework and a two-phase migration operator

Biogeography-based optimization (BBO) is a novel evolutionary algorithm, which is proposed with inspiration from the science of biogeography, to solve global optimization problems. To overcome the inability of BBO to make a good balance between its exploration and exploitation abilities, this paper introduces a new variant of BBO, which is called NBBO. The framework of NBBO considers two or more sub-iterations in an iteration of the algorithm to perform the evolution process. In each sub-iteration, a sample (sub-population) is selected from the input population of the iteration, based on a triangular probability distribution, to choose emigrating habitats (solutions) from. On the other hand, a novel two-phase migration operator is used in the framework of NBBO to make the algorithm effectively explore a search space. By making a good balance between its exploration and exploitation abilities, which is conducted by its new framework, NBBO can escape from local optima. Quantitative evaluations, based on extensive experiments on a set of 23 benchmark functions with diverse complexities, reveal that NBBO achieves favorable results which are quite superior to the results of other relevant state-of-the-art swarm intelligence-based and evolutionary algorithms.

Triple state reliability measurement for a complex autonomous robot system based on extended triangular distribution

Modern manufacturing systems should comply with high reliability and availability standards in order to guarantee efficient planning and optimization. Manufacturing systems including autonomous robots make the problem more challenging. By increasing the number of components in the autonomous manufacturing system and with respect to their intermittent interactions, a complex system is evolved. The reliability of such a system is significant due to high repair costs and failure downtime duration. Therefore, in this paper a reliability measurement framework is developed for a triple state autonomous robot system in an automated manufacturing environment. In this framework, an extension of the triangular probability distribution is proposed. In an implementation study, the effectiveness and computational efficiency of the proposed method is illustrated. In addition, an analysis on the failure rate using the maximum likelihood estimation is reported.

Systematic Sensitivity Analysis of the Full Economic Impacts of Sea Level Rise

The potential impacts of sea level rise (SLR) due to climate change have been widely studied in the literature. However, the uncertainty and robustness of these estimates has seldom been explored. Here we assess the model input uncertainty regarding the wide effects of SLR on marine navigation from a global economic perspective. We systematically assess the robustness of computable general equilibrium (CGE) estimates to model’s inputs uncertainty. Monte Carlo (MC) and Gaussian quadrature (GQ) methods are used for conducting a Systematic sensitivity analysis (SSA). This design allows to both explore the sensitivity of the CGE model and to compare the MC and GQ methods. Results show that, regardless whether triangular or piecewise linear Probability distributions are used, the welfare losses are higher in the MC SSA than in the original deterministic simulation. This indicates that the CGE economic literature has potentially underestimated the total economic effects of SLR, thus stressing the necessity of SSA when simulating the general equilibrium effects of SLR. The uncertainty decomposition shows that land losses have a smaller effect compared to capital and seaport productivity losses. Capital losses seem to affect the developed regions GDP more than the productivity losses do. Moreover, we show the uncertainty decomposition of the MC results and discuss the convergence of the MC results for a decomposed version of the CGE model. This paper aims to provide standardised guidelines for stochastic simulation in the context of CGE modelling that could be useful for researchers in similar settings.

Uma análise da situação financeira da indústria brasileira de aviação civil

ResumoA indústria brasileira de aviação civil tem voado baixo. O setor apresentou repetidos desempenhos financeiros negativos em 2011, 2012 e 2013, resultando em nível de endividamento médio muito acima do patrimônio líquido. Este estado de coisas não pode ser mantido, sob pena do setor ir à falência. A falência de companhias líderes do setor decerto trará graves consequências para a economia nacional. Este artigo estima a Demonstração do Resultado do Exercício de 2014 do setor. Há que ser dito que os demonstrativos financeiros de 2014 ainda não estão disponíveis. O método usado foi o de simulação de cenários, com o emprego de software específico de simulação Monte Carlo. A variável de risco foi a receita de passagens e a ela foi associada uma distribuição de probabilidade triangular. Os resultados simulados não são encorajadores. A probabilidade de o lucro líquido setorial ser negativo em 2014 é de aproximadamente 40%. Pode-se dizer que o setor balança no abismo da falência. Os resultados desta pesquisa servem de alerta para as autoridades responsáveis pelo controle e acompanhamento das atividades do setor de aviação civil do Brasil.

Estimating the Relative Role of Various Subcategories of Food, Water, and Animal Contact Transmission of 28 Enteric Diseases in Canada.

Objective: Enteric illness represents a significant burden of illness in Canada and internationally. Building on previous research, an expert elicitation was undertaken to explore the routes of transmission for 28 pathogens involved in enteric illness in Canada. This article considers the subcategories of foodborne, waterborne, and animal contact transmission.Methods: As part of an expert elicitation, 31 experts were asked to provide estimates of source attribution for subcategories of foodborne (n = 15), waterborne (n = 10), and animal contact (n = 3) transmission. The results from an online survey were combined using triangular probability distributions, and median and 90% credible intervals were produced. The total proportion and estimated number of cases of enteric illness attributable to each type of food commodity, water source, and animal exposure route were calculated using results from the larger elicitation survey and from a recent Canadian foodborne burden of illness study (Thomas et al., 2013).Results: Thirty experts provided foodborne subcategory estimates for 15/28 pathogens, waterborne subcategory estimates for 14/28 pathogens and animal contact subcategory estimates for 5/28. The elicitation identified raw produce, recreational water, and farm animal contact as important risk factors for enteric illness. These results also highlighted the complexity of transmission, with greater uncertainty for certain pathogens and routes of transmission.Conclusions: This study is the first of its kind to explore subcategories of foodborne, waterborne, and animal contact transmission across such a range of enteric pathogens. Despite inherent uncertainty, these estimates present an important quantitative synthesis of the roles of foodborne commodities, water sources, and pathways of animal contact in the transmission of enteric illness in Canada.

Use of UAV or remotely piloted aircraft and forward-looking infrared in forest, rural and wildland fire management: evaluation using simple economic analysis

Investment in emerging technologies may contribute to a reduction in the suppression costs of wildfires, and is thus worth careful consideration and trialling by researchers and managers. This investigation looked at the potential incorporation of a newly emerging remote sensing technology, remotely piloted aircraft and forward-looking infrared investigated using a cost-benefit analysis approach. An online survey-based approach targeting subject matter experts in wildland fire management and unmanned aircraft was used to evaluate the percentage change in the effectiveness of five different management scenarios using remotely piloted aircraft and forward-looking infrared. The most commonly accepted economic model in wildland fire management was adapted to determine the net value change between the five scenarios. The benefits of incorporated unmanned aerial vehicles (UAV) or remotely piloted aircraft and forward-looking infrared were measured as the reduction in cost-opportunity of helicopter use, and were estimated as an average of $548 per fire (where the average cost of fires was $1767) or a 31 % cost saving on total suppression costs. The return on investment of such technology was estimated at 24 fires, whereas the return of investment of the existing thermal camera/helicopter use occurred after 160 fires. The incorporation of remotely piloted aircraft and forward-looking infrared if implemented and managed appropriately, could well improve the cost effectiveness of the current forest, rural and wildland fire fighting efforts. The inherent uncertainty on such unevaluated technology (the combination of remotely piloted aircraft and forward-looking infrared) was addressed by adding stochastic variability and a triangular probability distribution approximation. Key management issues and recommendations are identified such as; greater use of current thermal camera equipment where possible, taking a project management based approach for further testing of remotely piloted aircraft and other emerging technologies, and the improved financial recording and reporting of fire management efforts.

The effects of stage recovery uncertainty in the performance of concentration circuits

This paper analyzes the effect of uncertainty in the recovery of each concentration stage on the global recovery and concentrate grade. The uncertainties are represented by normal, uniform and triangular probability distribution functions (PDFs). The case studies include the uncertainty in the recovery of each stage separately and simultaneously across all of the stages with different standard deviation levels. A total of 2880 cases were studied, which corresponded with twelve circuits, three distribution functions and 84 different combinations with standard deviations in the stage recoveries. For each case, 2000 simulations were performed, with an overall simulation total of 5.76 million. Among the conclusions obtained in this work are the following: 1) The shape of the distribution function in the output variables is dependent on the input distribution function, the concentration circuit and the uncertainty level; 2) when the recovery of a single stage is represented by a PDF, the other stage recoveries are assigned a deterministic value then the type of the PDF obtained for the global recovery is similar to the input distribution; 3) when considering uncertainty in several stages simultaneously, the resulting PDF type usually is not the same PDF type observed for the input variables; and 4) the circuit structure affects more than the stage recoveries in the analysis of the global recovery and concentrate grade.