Search results for: Weibull bi-parameter probability function

Authors: O. D. Ohijeagbon, Oluseyi O. Ajayi, M. Ogbonnaya, Ahmeh Attabo

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This study analyzed the electricity generation potential from wind at seven sites spread across seven states of the North-Central region of Nigeria. Twenty-one years (1987 to 2007) wind speed data at a height of 10m were assessed from the Nigeria Meteorological Department, Oshodi. The data were subjected to different statistical tests and also compared with the two-parameter Weibull probability density function. The outcome shows that the monthly average wind speeds ranged between 2.2 m/s in November for Bida and 10.1 m/s in December for Jos. The yearly average ranged between 2.1m/s in 1987 for Bida and 11.8 m/s in 2002 for Jos. Also, the power density for each site was determined to range between 29.66 W/m2 for Bida and 864.96 W/m2 for Jos, Two parameters (k and c) of the Weibull distribution were found to range between 2.3 in Lokoja and 6.5 in Jos for k, while c ranged between 2.9 in Bida and 9.9m/s in Jos. These outcomes points to the fact that wind speeds at Jos, Minna, Ilorin, Makurdi and Abuja are compatible with the cut-in speeds of modern wind turbines and hence, may be economically feasible for wind-to-electricity at and above the height of 10 m. The study further assessed the potential and economic viability of standalone wind generation systems for off-grid rural communities located in each of the studied sites. A specific electric load profile was developed to suite hypothetic communities, each consisting of 200 homes, a school and a community health center. Assessment of the design that will optimally meet the daily load demand with a loss of load probability (LOLP) of 0.01 was performed, considering 2 stand-alone applications of wind and diesel. The diesel standalone system (DSS) was taken as the basis of comparison since the experimental locations have no connection to a distribution network. The HOMER® software optimizing tool was utilized to determine the optimal combination of system components that will yield the lowest life cycle cost. Sequel to the analysis for rural community utilization, a Distributed Generation (DG) analysis that considered the possibility of generating wind power in the MW range in order to take advantage of Nigeria’s tariff regime for embedded generation was carried out for each site. The DG design incorporated each community of 200 homes, freely catered for and offset from the excess electrical energy generated above the minimum requirement for sales to a nearby distribution grid. Wind DG systems were found suitable and viable in producing environmentally friendly energy in terms of life cycle cost and levelised value of producing energy at Jos ($0.14/kWh), Minna ($0.12/kWh), Ilorin ($0.09/kWh), Makurdi ($0.09/kWh), and Abuja ($0.04/kWh) at a particluar turbine hub height. These outputs reveal the value retrievable from the project after breakeven point as a function of energy consumed Based on the results, the study demonstrated that including renewable energy in the rural development plan will enhance fast upgrade of the rural communities.

Keywords: wind speed, wind power, distributed generation, cost per kilowatt-hour, clean energy, North-Central Nigeria

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Authors: Naoyuki Sugihashi, Toshiharu Kishi

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The probability of occurrence of thermal cracks in mass concrete in Japan is evaluated by the cracking probability diagram that represents the relationship between the thermal cracking index and the probability of occurrence of cracks in the actual structure. In this paper, we propose a method to directly calculate the cracking probability, following a probabilistic theory by modeling the variance of tensile stress and tensile strength. In this method, the relationship between the variance of tensile stress and tensile strength, the thermal cracking index, and the cracking probability are formulated and presented. In addition, standard deviation of tensile stress and tensile strength was identified, and the method of calculating cracking probability in a general construction controlled environment was also demonstrated.

Keywords: thermal crack control, mass concrete, thermal cracking probability, durability of concrete, calculating method of cracking probability

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Authors: Oscar Javier Herrera, Manuel Angel Camacho

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This paper addresses a cutting edge method of business demand forecasting, based on an empirical probability function when the historical behavior of the data is random. Additionally, it presents error determination based on the numerical method technique ‘propagation of errors’. The methodology was conducted characterization and process diagnostics demand planning as part of the production management, then new ways to predict its value through techniques of probability and to calculate their mistake investigated, it was tools used numerical methods. All this based on the behavior of the data. This analysis was determined considering the specific business circumstances of a company in the sector of communications, located in the city of Bogota, Colombia. In conclusion, using this application it was possible to obtain the adequate stock of the products required by the company to provide its services, helping the company reduce its service time, increase the client satisfaction rate, reduce stock which has not been in rotation for a long time, code its inventory, and plan reorder points for the replenishment of stock.

Keywords: demand forecasting, empirical distribution, propagation of error, Bogota

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Authors: Nkongho Ayuketang Arreyndip, Ebobenow Joseph

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In this paper, to model a real life wind turbine, a probabilistic approach is proposed to model the dynamics of the blade elements of a small axial wind turbine under extreme stochastic wind speeds conditions. It was found that the power and the torque probability density functions even though decreases at these extreme wind speeds but are not infinite. Moreover, we also found that it is possible to stabilize the power coefficient (stabilizing the output power) above rated wind speeds by turning some control parameters. This method helps to explain the effect of turbulence on the quality and quantity of the harness power and aerodynamic torque.

Keywords: probability, probability density function, stochastic, turbulence

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Authors: Al Omari Moahmmed Ahmed

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These papers describe the Bayesian Estimator using Markov Chain Monte Carlo and Lindley’s approximation and the maximum likelihood estimation of the Weibull distribution with Type-I censored data. The maximum likelihood method can’t estimate the shape parameter in closed forms, although it can be solved by numerical methods. Moreover, the Bayesian estimates of the parameters, the survival and hazard functions cannot be solved analytically. Hence Markov Chain Monte Carlo method and Lindley’s approximation are used, where the full conditional distribution for the parameters of Weibull distribution are obtained via Gibbs sampling and Metropolis-Hastings algorithm (HM) followed by estimate the survival and hazard functions. The methods are compared to Maximum Likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) and absolute bias to determine the better method in scale and shape parameters, the survival and hazard functions.

Keywords: weibull distribution, bayesian method, markov chain mote carlo, survival and hazard functions

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Authors: Mehran Naghizaderokni, Asscar Janalizadechobbasty

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This paper explores probabilistic method for assessing the liquefaction potential of sandy soils. The current simplified methods for assessing soil liquefaction potential use a deterministic safety factor in order to determine whether liquefaction will occur or not. However, these methods are unable to determine the liquefaction probability related to a safety factor. A solution to this problem can be found by reliability analysis.This paper presents a reliability analysis method based on the popular certain liquefaction analysis method. The proposed probabilistic method is formulated based on the results of reliability analyses of 190 field records and observations of soil performance against liquefaction. The results of the present study show that confidence coefficient greater and smaller than 1 does not mean safety and/or liquefaction in cadence for liquefaction, and for assuring liquefaction probability, reliability based method analysis should be used. This reliability method uses the empirical acceleration attenuation law in the Chalos area to derive the probability density distribution function and the statistics for the earthquake-induced cyclic shear stress ratio (CSR). The CSR and CRR statistics are used in continuity with the first order and second moment method to calculate the relation between the liquefaction probability, the safety factor and the reliability index. Based on the proposed method, the liquefaction probability related to a safety factor can be easily calculated. The influence of some of the soil parameters on the liquefaction probability can be quantitatively evaluated.

Keywords: liquefaction, reliability analysis, chalos area, civil and structural engineering

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Authors: Mustapha Kamel Mihoubi, Mohamed Essadik Kerkar

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Probabilistic risk analysis models are used to provide a better understanding of the reliability and structural failure of works, including when calculating the stability of large structures to a major risk in the event of an accident or breakdown. This work is interested in the study of the probability of failure of concrete dams through the application of reliability analysis methods including the methods used in engineering. It is in our case, the use of level 2 methods via the study limit state. Hence, the probability of product failures is estimated by analytical methods of the type first order risk method (FORM) and the second order risk method (SORM). By way of comparison, a level three method was used which generates a full analysis of the problem and involves an integration of the probability density function of random variables extended to the field of security using the Monte Carlo simulation method. Taking into account the change in stress following load combinations: normal, exceptional and extreme acting on the dam, calculation of the results obtained have provided acceptable failure probability values which largely corroborate the theory, in fact, the probability of failure tends to increase with increasing load intensities, thus causing a significant decrease in strength, shear forces then induce a shift that threatens the reliability of the structure by intolerable values of the probability of product failures. Especially, in case the increase of uplift in a hypothetical default of the drainage system.

Keywords: dam, failure, limit-state, monte-carlo, reliability, probability, simulation, sliding, taylor

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Authors: Kennedy Efosa Ehimwenma, Sujatha Krishnamoorthy, Safiya Al‑Sharji

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The probability computation of events is in the interval of [0, 1], which are values that are determined by the number of outcomes of events in a sample space S. The probability Pr(A) that an event A will never occur is 0. The probability Pr(B) that event B will certainly occur is 1. This makes both events A and B a certainty. Furthermore, the sum of probabilities Pr(E₁) + Pr(E₂) + … + Pr(Eₙ) of a finite set of events in a given sample space S equals 1. Conversely, the difference of the sum of two probabilities that will certainly occur is 0. This paper first discusses Bayes, the complement of probability, and the difference of probability for occurrences of learning-events before applying them in the prediction of learning objects in student learning. Given the sum of 1; to make a recommendation for student learning, this paper proposes that the difference of argMaxPr(S) and the probability of student-performance quantifies the weight of learning objects for students. Using a dataset of skill-set, the computational procedure demonstrates i) the probability of skill-set events that have occurred that would lead to higher-level learning; ii) the probability of the events that have not occurred that requires subject-matter relearning; iii) accuracy of the decision tree in the prediction of student performance into class labels and iv) information entropy about skill-set data and its implication on student cognitive performance and recommendation of learning.

Keywords: complement of probability, Bayes’ rule, prediction, pre-assessments, computational education, information theory

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Authors: Hamid Ahmadi, Amirreza Ghaffari

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Fatigue life of tubular joints in offshore structures is not only dependent on the value of hot-spot stress, but is also significantly influenced by the through-the-thickness stress distribution characterized by the degree of bending (DoB). The DoB exhibits considerable scatter calling for greater emphasis in accurate determination of its governing probability distribution which is a key input for the fatigue reliability analysis of a tubular joint. Although the tubular X-joints are commonly found in offshore jacket structures, as far as the authors are aware, no comprehensive research has been carried out on the probability distribution of the DoB in tubular X-joints. What has been used so far as the probability distribution of the DoB in reliability analyses is mainly based on assumptions and limited observations, especially in terms of distribution parameters. In the present paper, results of parametric equations available for the calculation of the DoB have been used to develop probability distribution models for the DoB in the chord member of tubular X-joints subjected to four types of bending loads. Based on a parametric study, a set of samples was prepared and density histograms were generated for these samples using Freedman-Diaconis method. Twelve different probability density functions (PDFs) were fitted to these histograms. The maximum likelihood method was utilized to determine the parameters of fitted distributions. In each case, Kolmogorov-Smirnov test was used to evaluate the goodness of fit. Finally, after substituting the values of estimated parameters for each distribution, a set of fully defined PDFs have been proposed for the DoB in tubular X-joints subjected to bending loads.

Keywords: tubular X-joint, degree of bending (DoB), probability density function (PDF), Kolmogorov-Smirnov goodness-of-fit test

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Authors: Ahmet Kaya

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Quantum mechanism is one of the most important approaches to calculating non-ruin probability. We apply standard Dirac notation to model given Hamiltonians. By using the traditional method and eigenvector basis, non-ruin probability is found for several examples. Also, non-ruin probability is calculated for two different Hamiltonian by using the tensor product. Finally, the path integral method is applied to the examples and comparison is made for stochastic simulations and path integral calculation.

Keywords: quantum physics, Hamiltonian system, path integral, tensor product, ruin probability

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Authors: Rafik Ouared

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The purpose of this paper is to invalidate decisions made by the Islamic conference led at Istanbul in 2016, which had defined two basic criteria to determine the start of the lunar month: (1)they are all based on the sighting of the crescent, be it observed or computed with modern methods, and (2) they've strongly recommended the adoption of the principle of 'unification of sighting', by which any occurrence of sighting anywhere would be applicable everywhere. To demonstrate the invalidation of those statements, a survey of 101 years of data, from 1938 to 2038, have been analyzed to compare the probability density function (PDF) of time difference between different types of fajr and new moon. Two groups of fajr have been considered: the 'natural fajr', which is the very first fajr following new moon, and the 'biased fajr', which is defined by human being inclusively of all chosen definitions. The parametric and non-parametric statistical comparisons between the different groups have shown the all the biased PDFs are significantly different from the unbiased (natural) PDF with probability value (p-value) less than 0.001. The significance level was fixed to 0.05. Conclusion: the on-going reference to sighting of crescent is inducing an significant bias in defining lunar calendar. Therefore, 'natural' calendar would be more applicable requiring a more contextualized revision of issue in fiqh.

Keywords: biased fajr, lunar calendar, natural fajr, probability density function, sighting of crescent, time difference between fajr and new moon

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Authors: M. R. Ghasemi, R. Ghiasi, H. Varaee

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Surrogate model has received increasing attention for use in detecting damage of structures based on vibration modal parameters. However, uncertainties existing in the measured vibration data may lead to false or unreliable output result from such model. In this study, an efficient approach based on Monte Carlo simulation is proposed to take into account the effect of uncertainties in developing a surrogate model. The probability of damage existence (PDE) is calculated based on the probability density function of the existence of undamaged and damaged states. The kriging technique allows one to genuinely quantify the surrogate error, therefore it is chosen as metamodeling technique. Enhanced version of ideal gas molecular movement (EIGMM) algorithm is used as main algorithm for model updating. The developed approach is applied to detect simulated damage in numerical models of 72-bar space truss and 120-bar dome truss. The simulation results show the proposed method can perform well in probability-based damage detection of structures with less computational effort compared to direct finite element model.

Keywords: probability-based damage detection (PBDD), Kriging, surrogate modeling, uncertainty quantification, artificial intelligence, enhanced ideal gas molecular movement (EIGMM)

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Authors: Toby Li, Julian Zhu

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In this paper, a model based on a simplified geometry is introduced to give a very conservative collision probability prediction for the Starlink satellite in its most densely clustered region. Under the model in this paper, the probability of collision for Starlink satellite where it clustered most densely is found to be 8.484 ∗ 10^−4. It is found that the predicted collision probability increased nonlinearly with the increased safety distance set. This simple model provides evidence that the continuous development of maneuver avoidance systems is necessary for the future of the orbital safety of satellites under the harsher Lower Earth Orbit environment.

Keywords: Starlink, collision probability, debris, geometry model

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Authors: Chang He, Hiroshi Tamura, Hiroshi Katsuchi, Jiaqi Wang

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In this study, the aim is to infer the slip limit (static friction limit) of contact interfaces in bolt friction joints by analyzing other bolt friction joints with the same contact surface but in a different shape. By using the Weibull distribution to deal with microelements on the contact surface statistically, the slip limit of a certain type of bolt joint was predicted from other types of bolt joint with the same contact surface. As a result, this research succeeded in predicting the slip limit of bolt joins with different numbers of contact surfaces and with different numbers of bolt rows.

Keywords: bolt joints, slip coefficient, finite element method, Weibull distribution

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Authors: Elzbieta Babula, Juhyun Park

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Tversky and Kahneman’s cumulative prospect theory assumes symmetric probability cumulation with regard to the reference point within decision weights. Theoretically, this model should be invariant under the change of the direction of probability cumulation. In the present study, this phenomenon is being investigated by creating a reference model that allows verifying the parameter interactions in the cumulative prospect theory specifications. The simultaneous parametric fitting of utility and weighting functions is applied to binary choice data from the experiment. The results show that the flexibility of the probability weighting function is a crucial characteristic allowing to prevent parameter interactions while estimating cumulative prospect theory.

Keywords: binary choice experiment, cumulative prospect theory, decision weights, parameter interactions

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Authors: Saleem Z. Ramadan

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This paper discusses the effects of using progressive Type-I right censoring on the design of the Simple Step Accelerated Life testing using Bayesian approach for Weibull life products under the assumption of cumulative exposure model. The optimization criterion used in this paper is to minimize the expected pre-posterior variance of the PTH percentile time of failures. The model variables are the stress changing time and the stress value for the first step. A comparison between the conventional and the progressive Type-I right censoring is provided. The results have shown that the progressive Type-I right censoring reduces the cost of testing on the expense of the test precision when the sample size is small. Moreover, the results have shown that using strong priors or large sample size reduces the sensitivity of the test precision to the censoring proportion. Hence, the progressive Type-I right censoring is recommended in these cases as progressive Type-I right censoring reduces the cost of the test and doesn't affect the precision of the test a lot. Moreover, the results have shown that using direct or indirect priors affects the precision of the test.

Keywords: reliability, accelerated life testing, cumulative exposure model, Bayesian estimation, progressive type-I censoring, Weibull distribution

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Authors: Avan Al-Saffar, Eun-Jin Kim

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Both the logistic growth model and the gompertz growth model are used to describe growth processes. Both models driven by perturbations in different cases are investigated using information theory as a useful measure of sustainability and the variability. Specifically, we study the effect of different oscillatory modulations in the system's parameters on the evolution of the system and Probability Density Function (PDF). We show the maintenance of the initial conditions for a long time. We offer Fisher information analysis in positive and/or negative feedback and explain its implications for the sustainability of population dynamics. We also display a finite amplitude solution due to the purely fluctuating growth rate whereas the periodic fluctuations in negative feedback can lead to break down the system's self-regulation with an exponentially growing solution. In the cases tested, the gompertz and logistic systems show similar behaviour in terms of information and sustainability although they develop differently in time.

Keywords: dynamical systems, fisher information, probability density function (pdf), sustainability

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Authors: Yuan-Lin Chen

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This paper presents an approaching forward collision probability index (AFCPI) for alerting and assisting driver in keeping safety distance to avoid the forward collision accident in highway driving. The time to collision (TTC) and time headway (TH) are used to evaluate the TTC forward collision probability index (TFCPI) and the TH forward collision probability index (HFCPI), respectively. The Mamdani fuzzy inference algorithm is presented combining TFCPI and HFCPI to calculate the approaching collision probability index of the vehicle. The AFCPI is easier to understand for the driver who did not even have any professional knowledge in vehicle professional field. At the same time, the driver’s behavior is taken into account for suiting each driver. For the approaching index, the value 0 is indicating the 0% probability of forward collision, and the values 0.5 and 1 are indicating the 50% and 100% probabilities of forward collision, respectively. The AFCPI is useful and easy-to-understand for alerting driver to avoid the forward collision accidents when driving in highway.

Keywords: approaching index, forward collision probability, time to collision, time headway

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Authors: Oh Hyeon Jeon, WooYoung Jung

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In this study, seepage analysis was performed by the level difference between upstream and downstream of weir structure for safety evaluation of weir structure against flooding. Monte Carlo Simulation method was employed by considering the probability distribution of the adjacent ground parameter, i.e., permeability coefficient of weir structure. Moreover, by using a commercially available finite element program (ABAQUS), modeling of the weir structure is carried out. Based on this model, the characteristic of water seepage during flooding was determined at each water level with consideration of the uncertainty of their corresponding permeability coefficient. Subsequently, fragility function could be constructed based on this response from numerical analysis; this fragility function results could be used to determine the weakness of weir structure subjected to flooding disaster. They can also be used as a reference data that can comprehensively predict the probability of failur,e and the degree of damage of a weir structure.

Keywords: weir structure, seepage, flood disaster fragility, probabilistic risk assessment, Monte-Carlo simulation, permeability coefficient

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Authors: P. K. Singhal, R. Naresh, V. Sharma

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This paper presents the three optimization models, namely New Binary Artificial Bee Colony (NBABC) algorithm, NBABC with Local Search (NBABC-LS), and NBABC with Genetic Crossover (NBABC-GC) for solving the Wind-Thermal Unit Commitment (WTUC) problem. The uncertain nature of the wind power is incorporated using the Weibull probability density function, which is used to calculate the overestimation and underestimation costs associated with the wind power fluctuation. The NBABC algorithm utilizes a mechanism based on the dissimilarity measure between binary strings for generating the binary solutions in WTUC problem. In NBABC algorithm, an intelligent scout bee phase is proposed that replaces the abandoned solution with the global best solution. The local search operator exploits the neighboring region of the current solutions, whereas the integration of genetic crossover with the NBABC algorithm increases the diversity in the search space and thus avoids the problem of local trappings encountered with the NBABC algorithm. These models are then used to decide the units on/off status, whereas the lambda iteration method is used to dispatch the hourly load demand among the committed units. The effectiveness of the proposed models is validated on an IEEE 10-unit thermal system combined with a wind farm over the planning period of 24 hours.

Keywords: artificial bee colony algorithm, economic dispatch, unit commitment, wind power

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Authors: Muhammad Noor Ul Ane, Dong-Soon Kim, Myron P. Zalucki

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Models can be useful to help understand population dynamics of insects under diverse environmental conditions and in developing strategies to manage pest species better. Adult longevity and fecundity of Helicoverpa armigera (Hübner) were evaluated against a wide range of constant temperatures (15, 20, 25, 30, 35 and 37.5ᵒC). The modified Sharpe and DeMichele model described adult aging rate and was used to estimate adult physiological age. Maximum fecundity of H. armigera was 973 egg/female at 25ᵒC decreasing to 72 eggs/female at 37.5ᵒC. The relationship between adult fecundity and temperature was well described by an extreme value function. Age-specific cumulative oviposition rate and age-specific survival rate were well described by a two-parameter Weibull function and sigmoid function, respectively. An oviposition model was developed using three temperature-dependent components: total fecundity, age-specific oviposition rate, and age-specific survival rate. The oviposition model was validated against independent field data and described the field occurrence pattern of egg population of H. armigera very well. Our model should be a useful component for population modeling of H. armigera and can be independently used for the timing of sprays in management programs of this key pest species.

Keywords: cotton bollworm, life table, temperature-dependent adult development, temperature-dependent fecundity

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi

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This study was designed to find the best-fit probability distribution of annual rainfall based on 50 years sample (1966-2015) in the Karkheh river basin at Iran using six probability distributions: Normal, 2-Parameter Log Normal, 3-Parameter Log Normal, Pearson Type 3, Log Pearson Type 3 and Gumbel distribution. The best fit probability distribution was selected using Stormwater Management and Design Aid (SMADA) software and based on the Residual Sum of Squares (R.S.S) between observed and estimated values Based on the R.S.S values of fit tests, the Log Pearson Type 3 and then Pearson Type 3 distributions were found to be the best-fit probability distribution at the Jelogir Majin and Pole Zal rainfall gauging station. The annual values of expected rainfall were calculated using the best fit probability distributions and can be used by hydrologists and design engineers in future research at studied region and other region in the world.

Keywords: Log Pearson Type 3, SMADA, rainfall, Karkheh River

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Authors: Komeil Valipourian

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Urban advances and the growing need for developing infrastructures has increased the importance of deep excavations. In this study, after the introducing probability analysis as an important issue, an attempt has been made to apply it for the deep excavation project of Bangkok’s Metro as a case study. For this, the numerical probability model has been developed based on the Finite Difference Method and Monte Carlo sampling approach. The results indicate that disregarding the issue of probability in this project will result in an inappropriate design of the retaining structure. Therefore, probabilistic redesign of the support is proposed and carried out as one of the applications of probability analysis. A 50% reduction in the flexural strength of the structure increases the failure probability just by 8% in the allowable range and helps improve economic conditions, while maintaining mechanical efficiency. With regard to the lack of efficient design in most deep excavations, by considering geometrical and geotechnical variability, an attempt was made to develop an optimum practical design standard for deep excavations based on failure probability. On this basis, a practical relationship is presented for estimating the maximum allowable horizontal displacement, which can help improve design conditions without developing the probability analysis.

Keywords: numerical probability modeling, deep excavation, allowable maximum displacement, finite difference method (FDM)

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Authors: Yun-Pang Flötteröd, Jakob Erdmann

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The human behaviors during evacuations are quite complex. One of the critical behaviors which affect the efficiency of evacuation is route choice. Therefore, the respective simulation modeling work needs to function properly. In this paper, Simulation of Urban Mobility’s (SUMO) current dynamic route modeling during evacuation, i.e. the rerouting functions, is examined with a real case study. The result consistency of the simulation and the reality is checked as well. Four influence factors (1) time to get information, (2) probability to cancel a trip, (3) probability to use navigation equipment, and (4) rerouting and information updating period are considered to analyze possible traffic impacts during the evacuation and to examine the rerouting functions in SUMO. Furthermore, some behavioral characters of the case study are analyzed with use of the corresponding detector data and applied in the simulation. The experiment results show that the dynamic route modeling in SUMO can deal with the proposed scenarios properly. Some issues and function needs related to route choice are discussed and further improvements are suggested.

Keywords: evacuation, microscopic traffic simulation, rerouting, SUMO

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Authors: Seon Soon Choi

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Magnesium alloy has been widely used in structure such as an automobile. It is necessary to consider probabilistic characteristics of a structural material because a fatigue behavior of a structure has a randomness and uncertainty. The purpose of this study is to find the characteristics of the cumulative distribution function (CDF) of the grown crack size at a specified fatigue crack propagation life and to investigate a statistical crack propagation in magnesium alloys. The statistical fatigue data of the grown crack size are obtained through the fatigue crack propagation (FCP) tests under different maximum fatigue load conditions conducted on the replicated specimens of magnesium alloys. The 3-parameter Weibull distribution is used to find the CDF of grown crack size. The CDF of grown crack size in case of larger maximum fatigue load has longer tail in below 10 percent and above 90 percent. The fatigue failure occurs easily as the tail of CDF of grown crack size becomes long. The fatigue behavior under the larger maximum fatigue load condition shows more rapid propagation and failure mode.

Keywords: cumulative distribution function, fatigue crack propagation, grown crack size, magnesium alloys, maximum fatigue load

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Authors: Khandoker Akib Mohammad

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While analyzing time-to-event data, it is possible that a certain fraction of subjects will never experience the event of interest, and they are said to be cured. When this feature of survival models is taken into account, the models are commonly referred to as cure models. In the presence of covariates, the conditional survival function of the population can be modelled by using the cure model, which depends on the probability of being uncured (incidence) and the conditional survival function of the uncured subjects (latency), and a combination of logistic regression and Cox proportional hazards (PH) regression is used to model the incidence and latency respectively. In this paper, we have shown the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the variance estimator with an implicit function in the profile likelihood. We have also shown the efficient score function based on projection theory and the profile likelihood score function are equal. Our contribution in this paper is that we have expressed the efficient information matrix as the variance of the profile likelihood score function. A simulation study suggests that the estimated standard errors from bootstrap samples (SMCURE package) and the profile likelihood score function (our approach) are providing similar and comparable results. The numerical result of our proposed method is also shown by using the melanoma data from SMCURE R-package, and we compare the results with the output obtained from the SMCURE package.

Keywords: Cox PH model, cure model, efficient score function, EM algorithm, implicit function, profile likelihood

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Authors: Rouhallah Bagheri, Morteza Mahmoudi, Hadi Moheb-Alizadeh

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This paper aims at developing a multi-objective model for supplier selection and order allocation problem in stochastic environment, where purchasing cost, percentage of delivered items with delay and percentage of rejected items provided by each supplier are supposed to be stochastic parameters following any arbitrary probability distribution. In this regard, dependent chance programming is used which maximizes probability of the event that total purchasing cost, total delivered items with delay and total rejected items are less than or equal to pre-determined values given by decision maker. The abovementioned stochastic multi-objective programming problem is then transformed into a stochastic single objective programming problem using minimum deviation method. In the next step, the further problem is solved applying a genetic algorithm, which performs a simulation process in order to calculate the stochastic objective function as its fitness function. Finally, the impact of stochastic parameters on the given solution is examined via a sensitivity analysis exploiting coefficient of variation. The results show that whatever stochastic parameters have greater coefficients of variation, the value of the objective function in the stochastic single objective programming problem is deteriorated.

Keywords: supplier selection, order allocation, dependent chance programming, genetic algorithm

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Authors: Mohadeseh Shojaei Shahrokhabadi, Ding-Geng (Din) Chen

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Positive continuous outcomes with a substantial number of zero values and incomplete longitudinal follow-up are quite common in medical cost data. To jointly model semi-continuous longitudinal cost data and survival data and to provide marginalized covariate effect estimates, a marginalized two-part joint model (MTJM) has been developed for outcome variables with lognormal distributions. In this paper, we propose MTJM models for outcome variables from a generalized gamma (GG) family of distributions. The GG distribution constitutes a general family that includes approximately all of the most frequently used distributions like the Gamma, Exponential, Weibull, and Log Normal. In the proposed MTJM-GG model, the conditional mean from a conventional two-part model with a three-parameter GG distribution is parameterized to provide the marginal interpretation for regression coefficients. In addition, MTJM-gamma and MTJM-Weibull are developed as special cases of MTJM-GG. To illustrate the applicability of the MTJM-GG, we applied the model to a set of real electronic health record data recently collected in Iran, and we provided SAS code for application. The simulation results showed that when the outcome distribution is unknown or misspecified, which is usually the case in real data sets, the MTJM-GG consistently outperforms other models. The GG family of distribution facilitates estimating a model with improved fit over the MTJM-gamma, standard Weibull, or Log-Normal distributions.

Keywords: marginalized two-part model, zero-inflated, right-skewed, semi-continuous, generalized gamma

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Authors: Quznetsov Gunn

Abstract:

In the study of the logical foundations of probability theory, it was found that the terms and equations of the fundamental theoretical physics represent terms and theorems of the classical probability theory, more precisely, of that part of this theory, which considers the probability of dot events in the 3 + 1 space-time. In particular, the masses, moments, energies, spins, etc. turn out of parameters of probability distributions such events. The terms and the equations of the electroweak and of the quark-gluon theories turn out the theoretical-probabilistic terms and theorems. Here the relation of a neutrino to his lepton becomes clear, the W and Z bosons masses turn out dynamic ones, the cause of the asymmetry between particles and antiparticles is the impossibility of the birth of single antiparticles. In addition, phenomena such as confinement and asymptotic freedom receive their probabilistic explanation. And here we have the logical foundations of the gravity theory with phenomena dark energy and dark matter.

Keywords: classical theory of probability, logical foundation of fundamental theoretical physics, masses, moments, energies, spins

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Authors: Mustapha Kamel Mihoubi, Essadik Kerkar, Abdelhamid Hebbouche

Abstract:

According to the randomness of most of the factors affecting the stability of a gravity dam, probability theory is generally used to TESTING the risk of failure and there is a confusing logical transition from the state of stability failed state, so the stability failure process is considered as a probable event. The control of risk of product failures is of capital importance for the control from a cross analysis of the gravity of the consequences and effects of the probability of occurrence of identified major accidents and can incur a significant risk to the concrete dam structures. Probabilistic risk analysis models are used to provide a better understanding the reliability and structural failure of the works, including when calculating stability of large structures to a major risk in the event of an accident or breakdown. This work is interested in the study of the probability of failure of concrete dams through the application of the reliability analysis methods including the methods used in engineering. It is in our case of the use of level II methods via the study limit state. Hence, the probability of product failures is estimated by analytical methods of the type FORM (First Order Reliability Method), SORM (Second Order Reliability Method). By way of comparison, a second level III method was used which generates a full analysis of the problem and involving an integration of the probability density function of, random variables are extended to the field of security by using of the method of Mont-Carlo simulations. Taking into account the change in stress following load combinations: normal, exceptional and extreme the acting on the dam, calculation results obtained have provided acceptable failure probability values which largely corroborate the theory, in fact, the probability of failure tends to increase with increasing load intensities thus causing a significant decrease in strength, especially in the presence of combinations of unique and extreme loads. Shear forces then induce a shift threatens the reliability of the structure by intolerable values of the probability of product failures. Especially, in case THE increase of uplift in a hypothetical default of the drainage system.

Keywords: dam, failure, limit state, monte-carlo, reliability, probability, sliding, Taylor

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