Exponential Probability Distribution Function Research Articles

Reliability, availability, and condition monitoring of inverters of grid‐connected solar photovoltaic systems

AbstractReliability, Availability and Condition Monitoring (RACM) evaluation has become a critical area of interest for researchers as the output power quality of a Photo‐Voltaic (PV) system depend on the reliability of its components. In this paper, the RACM of grid‐connected PV systems is presented. For this, the Reliability Block Diagram (RBD) technique along with the exponential probability distribution function is used. The main objective of this work is to identify the weakest subsystem of a system in order to enhance system reliability. The condition monitoring system will be helpful in avoiding the sudden breakdown and unexpected maintenance of the system. An elaborate analysis is presented for PV system beginning from the sub‐assemblies to the subsystems and then to the overall system. In addition, the subsystems are ranked based on their impact on the overall availability of the system. This is decided based on the availability importance measures. It is observed that the inverter forms the weakest subsystem in the solar system. The novelty of the proposed RACM method is that one can monitor the health status or useful life of the system regularly which is not yet explored in the literature. Most of the papers have considered that the components of PV systems are non‐repairable but in this paper, the redundancy concept is explored which helps in increasing the reliability and availability of the system. When the proposed method and the results obtained are compared to existing methods, it is discovered that the proposed work outperforms them.

Driver propensity to fatigue and drowsiness: a probabilistic approach

This analysis is aimed at quantification, on the probabilistic basis, of the significance of driver fatigue and drowsiness (DD) in automated and manual driving conditions; the impact of driving time on the probability of an accident, because of the driver’s fatigue and possible drowsiness, and the observation that age groups of 20–25 and 65–70 are more prone to making a human fatigue and/or DD related error than the 26–64 old group. Our analyses are based on the application of the recently suggested double exponential probability distribution function (DEPDF), and on using entropy and adequate-trust based considerations. The general concepts are illustrated by numerical examples. It is concluded that analytical modeling technique employed in this study should complement, whenever possible, statistical analyses and computer simulations in challenging ergonomics tasks, including those of the type in question.

Actual Precipitation Index (API) for Drought Classification

The Standard Precipitation Index (SPI) is a widely used statistical technique for the characterization of droughts. It is based on a probabilistic standardization procedure, which converts a Gamma-type probability distribution function (PDF) into a normal (Gaussian) standard series with zero mean and unit standard deviation. Drought classification based on SPI indicates dry and wet spell characteristics, provided that the hydro-meteorological records abide by normal (Gaussian) PDF only, otherwise the results will be biased. Therefore, in this paper, the actual precipitation index (API) method is presented, which provides drought classification and information regardless of the underlying PDFs. The main purpose of this paper is to explain the main differences between SPI and API and to prove that the use of API is the more reliable solution for classification of droughts into five categories described as “Normal dry”, “Slightly dry”, “Medium dry”, “Very dry” and “Extremely dry”. The application of the methodology is presented for two sets of precipitation data; one with exponential PDF monthly precipitation records from Istanbul City, Turkey and one for New Jersey, USA with almost normal (Gaussian) PDF based on annual precipitation records. The comparisons indicate that API is applicable regardless of the underlying PDF of the hydro-meteorology data. It produces real drought classification from the original data without recourse to standard normal PDF conversion.

An EPQ inventory model considering an imperfect production system with probabilistic demand and collaborative approach

PurposeThe purpose of this paper is to propose an economic production quantity (EPQ) inventory model considering imperfect items and probabilistic demand for a two-echelon supply chain. The production process is imperfect and the imperfect quality items are removed from the lot size. The demand rate of the inventory system is random and follows an exponential probability density function and the demand of the retailers is depending on the initiatives of the sales team.Design/methodology/approachTwo approaches are examined. In the non-collaborative approach, any member of the supply chain can be the leader and takes decisions to optimize the profits, and in the collaborative system, all members make joint decisions about the production, supply, sales and inventory to optimize the profits of the supply chain members. The calculus approach is applied to find the maximum profit related to the members of the supply chain.FindingsA numerical example is presented to illustrate the performance of the EPQ model. The results show that collaborative approach generates greater profits to the supply chain and the market’s demand represents the variable behavior and uncertainty that is generated in the replenishment of a supply chain.Originality/valueThe new and major contributions of this research are: the inventory model considers demand for products is random variable which follows an exponential probability distribution function and it also depends on the initiatives of sales teams, the imperfect production system generates defective items, different cycle time are considered in manufacturer and retailers and collaborative and non-collaborative approaches are also studied.

Impact of subsystems on the overall system availability for the large scale grid-connected photovoltaic systems

This paper demonstrates the impact of subsystem availability on a large scale grid-connected photovoltaic (PV) systems’ performance. Subsystem denotes to the installation of some subassemblies, which can be very small or gigantic in size, that serve this subsystem and the overall system. The analysis is largely based on a huge worldwide dataset of failures and repairs of various subassemblies, derived from different large scale grid-connected solar-PV systems. Major subsystems, such as a photovoltaic inverters (PVI), are also included, which are shown to have a significant impact for improving on the overall system availability. An improved reliability block diagram (RBD) with an exponential probability distribution function is presented for estimating the reliability and availability performance of seven practical grid-connected solar-PV systems. In addition, availability importance measures are employed to rank various subsystems with regards to their impact on the overall system availability. Accordingly, it will be helping in identifying the subsystems that the planned maintenance should focus on in order to achieve the desired level of the availability. The secure operation of the system will be achieved by this approach. The implementation demonstrates the efficiency and the effectiveness of the proposed approach which may significantly contribute to enhancing the system availability.

Reliability Modeling of Microgrid System Using Hybrid Methods in Hot Standby Mode

The purpose of this paper is to accomplish the reliability assessment of hot standby microgrid system by using few hybrid methods. This paper has shown relative analysis on failure probability and reliability of microgrid system by means of Markov model, fault tree analysis (FTA) using reduced binary decision diagram (RBDD), and reduced sequential binary decision diagram (RSBDD) approaches. Hot standby mode is usually employed for the enrichment of reliability to prolong the system availability during any catastrophic situation. By analysis, microgrid which falls under the hot standby mode indicates that both the redundant as well as active components have similar failure rates. An inverter dominated photovoltaic system integrated to an IEEE 5-bus microgrid system is designed for which comparative overall system availability is calculated and analyzed in terms of failure probability and reliability by using hybrid approaches. Markov-based models mostly suffer from state-space explosion problems and it needs exponential probability distribution function only. Again, FTA-RBDD and FTA-RSBDD approaches have neither any constraint on time-to-failure distributions nor any computational burden issue. Moreover, FTA-RSBDD-based reliability assessment dealings are reusable with different time-to-failure rates.

An optimal ordering and replenishment policy for a vendor-buyer system under varying replenishment intervals and delayed payment

The replenishment intervals can be probabilistic when the system or the supplier has problem with manufacturing or shipping the goods. In this paper, an economic order quantity (EOQ) model with probabilistic replenishment intervals and permissible delay in payments with partial backordering is developed. This paper considers three different possible situations and suggests optimal inventory policy for each situation separately regarding the amount of expected order quantity and replenishment-up-to level that maximises the expected cyclic profit for the buyers. The model is analysed for the uniform and exponential probability distribution functions (PDF) for time of replenishment and a closed-form solution is achieved in all cases. Finally, a sensitivity analysis is performed to know the general functional behaviour and to clarify the applicability of the proposed model when the system behaviour is unstable. The results indicate that a customer can obtain the optimum replenishment-up-to level and order quantity when the replenishment intervals is probabilistic in three different possible situations. [Received: 17 August 2017; Revised: 10 January 2018; Revised: 23 August 2018; Accepted: 11 November 2018]

Short note - adequate trust, human-capacity-factor, probability-distribution-function of human non-failure and its entropy

This note is an extension, a generalisation of and an attempt to quantify, on the probabilistic basis, the message of the recent Kaindl and Svetinovic (2019) publication Avoiding Undertrust and Overtrust. The author of the present analysis addresses some important aspects of the human-in-the-loop problem for safety-critical missions and situations, in which trust can be viewed as an essential part of the human-capacity-factor (HCF). This factor, as has been recently suggested, should be evaluated vs. mental workload (MWL), when there is a need to assure a successful and safe outcome of a particular human effort, such as, e.g., an aerospace mission or an extraordinary situation. The double exponential probability distribution function (DEPDF) for the random HCF is revisited. It is shown particularly that the entropy of this distribution, when applied to the trustee (a human, a technology, a methodology or a concept), can be viewed as an appropriate quantitative characteristic of the propensity of a decision maker to an under-trust or an over-trust judgment and, as a consequence of that, to the likelihood of making a mistake or an erroneous decision.

Human-in-the-loop: application of the double exponential probability distribution function enables one to quantify the role of the human factor

Human-in-the-loop: application of the double exponential probability distribution function enables one to quantify the role of the human factor

Human-in-the-loop: application of the double exponential probability distribution function enables one to quantify the role of the human factor

The probabilistic predictive modelling approach in human-in-the-loop related aerospace problems enables one to predict, quantify, assure and even specify the probability of the favourable outcome of an aerospace mission or a situation, when the performance of the never perfect human, never 100%-reliable instrumentation (equipment), never absolutely predictable response of the object of control (aero- or space-craft), uncertain and often harsh environment, as well as the interaction (interfaces) of the above uncertainties, contribute jointly to the likelihood of such an outcome. As to the human factor, it includes two major aspects: human performance (error) and his/her state of health. While the reliability of the navigation instrumentation (equipment) could be evaluated using suitable and more or less well established modelling means, the role of the human factor, when quantification of the human role is critical, could be considered by using the double-exponential-probability-distribution-function (DEPDF).

Exploring a semimechanistic episodic Langevin model for bed load transport: Emergence of normal and anomalous advection and diffusion regimes

AbstractBed load transport is a highly stochastic, multiscale process, where particle advection and diffusion regimes are governed by the dynamics of each sediment grain during its motion and resting states. Having a quantitative understanding of the macroscale behavior emerging from the microscale interactions is important for proper model selection in the absence of individual grain‐scale observations. Here we develop a semimechanistic sediment transport model based on individual particle dynamics, which incorporates the episodic movement (steps separated by rests) of sediment particles and study their macroscale behavior. By incorporating different types of probability distribution functions (PDFs) of particle resting times , under the assumption of thin‐tailed PDF of particle velocities, we study the emergent behavior of particle advection and diffusion regimes across a wide range of spatial and temporal scales. For exponential PDFs of resting times , we observe normal advection and diffusion at long time scales. For a power‐law PDF of resting times (i.e., ), the tail thickness parameter is observed to affect the advection regimes (both sub and normal advective), and the diffusion regimes (both subdiffusive and superdiffusive). By comparing our semimechanistic model with two random walk models in the literature, we further suggest that in order to reproduce accurately the emerging diffusive regimes, the resting time model has to be coupled with a particle motion model able to produce finite particle velocities during steps, as the episodic model discussed here.

Maximum Likelihood Estimation—A Reliable Statistical Method for Hydrate Nucleation Data Analysis

Analyses on hydrate nucleation and nucleation processes in general are assumed to require a large number of parallels due to the stochastic nature of the process. Stochastic processes are described by an exponential probability distribution. The present work adopts the Maximum Likelihood Estimation (MLE) with penalized estimators for data analysis in gas hydrate nucleation studies. Key parameters analyzed and discussed are nucleation rate and lag time during formation of critical size nuclei. The MLE technique is commonly used in analysis of other types of stochastic processes, but it has not, to our knowledge, previously been applied to hydrate nucleation. A total of six data sets, three on methane–propane hydrate nucleation from the present work, and three on general crystal nucleation extracted from the literature, were analyzed using the MLE. The MLE analysis was compared with a conventional method fitting the Experimental Probability Array to the exponential Probability Distribution Function (EPA-PDF...

Reliability assessment for components of large scale photovoltaic systems

Photovoltaic (PV) systems have significantly shifted from independent power generation systems to a large-scale grid-connected generation systems in recent years. The power output of PV systems is affected by the reliability of various components in the system. This study proposes an analytical approach to evaluate the reliability of large-scale, grid-connected PV systems.The fault tree method with an exponential probability distribution function is used to analyze the components of large-scale PV systems. The system is considered in the various sequential and parallel fault combinations in order to find all realistic ways in which the top or undesired events can occur. Additionally, it can identify areas that the planned maintenance should focus on. By monitoring the critical components of a PV system, it is possible not only to improve the reliability of the system, but also to optimize the maintenance costs. The latter is achieved by informing the operators about the system component's status. This approach can be used to ensure secure operation of the system by its flexibility in monitoring system applications. The implementation demonstrates that the proposed method is effective and efficient and can conveniently incorporate more system maintenance plans and diagnostic strategies.

Mechanism of Debris Flows in Mountain Streams

This paper suggests the mechanism of occurrence of debris flow in mountain streams. It is found that the sliding of the undermined stream banks follows the exponential probability distribution function. This indicates that the major amount of debris is from an intensive sliding in the initial stage of flood flow development. This can be otherwise proved by the viscous flow boundary layer theory such as the shear stresses on the wall are initially very large. Through a relative dimensional analysis, a special dimensionless parameter K is grouped which has a very important effect on the occurrence of the acceleration of the heavy debris by the flow. It interprets, during the flood flow development, the amount of debris on the stream bed can only be accelerated when the kinetic energy of the flow is greater than the apparent work of the debris against the flow. Of course, as a transient behavior, once it starts, the sudden acceleration of a huge amount of debris flow bore will usually cause an unpredictable downstream disaster.

'Miracle-on-the-Hudson': quantitative aftermath

Application of the quantitative probabilistic risk management (PRM) concept should complement in various human-in-the-loop (HITL) situations, whenever feasible and possible, the existing vehicular psychology practices, which are typically qualitative a-posteriori statistical assessments. A PRM approach based on the double exponential probability distribution function of the extreme value distribution type is suggested as a suitable quantitative technique for assessing the probability of the human non-failure in an off-normal flight situation. The famous 2009 US Airways ‘miracle-on-the-Hudson’ successful landing (ditching) and the infamous 1998 Swiss Air ‘UN-shuttle’ disaster are chosen to illustrate the usefulness and fruitfulness of the approach. It is concluded that the developed formalisms, after trustworthy input data are obtained (using, e.g., flight simulators or Delphi method) might be applicable even beyond the vehicular domain in various HITL situations, when a short term high human performance is imperative and the ability to quantify it is highly desirable.

An investigation into application of jointly distributed random variables method in reliability assessment of rock slope stability

Analysis of stability of rock slopes is a branch of rock engineering that is highly amenable to probabilistic treatment. Probabilistic analysis of rock slope stability has been used as an effective tool to evaluate uncertainty so prevalent in variables and has received considerable attention in the literature. In this research the application of the Jointly Distributed Random Variables (JDRVs) method for probabilistic analysis and reliability assessment of rock slop stability with plane sliding is investigated. The selected probabilistic parameters are friction angle of sliding surface and apparent cohesion which are modeled using a truncated normal probability distribution function and the depth of water in tension cracks and earthquake acceleration ratio which are considered to have truncated exponential probability distribution function. The parameters related to geometry and unit weight are regarded as deterministic parameters. The results are compared with the Monte Carlo (MC) simulation. Comparison of the results indicates that the results of the JDRV method include a degree of error, primarily due to the interdependency of some of the variables in the formulation. It is also shown that due to this interdependency of the variables, the application of JDRV method in reliability assessment of rock slope stability will result in errors and hence, the MC method will be the preferable method. The results of sensitivity analysis using Monte Carlo simulation show that the friction angle of sliding surface is the most effective parameter in rock slope stability with plane sliding.

Reliability assessment of liquefaction potential using the jointly distributed random variables method

Prediction of liquefaction potential is a complex engineering problem due to heterogeneous nature of soils and participation of a large number of factors involved. The inherent uncertainties of the parameters which affect liquefaction potential dictate that problem is of a probabilistic nature rather than being deterministic. Probabilistic analysis of liquefaction potential has received considerable attention in the literature and has been used as an effective tool to evaluate uncertainty so prevalent in variables. In this research the jointly distributed random variables method is used for probabilistic analysis and reliability assessment of liquefaction potential based on triaxial test results. The selected stochastic parameters are relative density which is modeled using a truncated normal probability distribution function and the earthquake acceleration ratio and earthquake magnitude which are considered to have exponential probability distribution function. The depth is regarded as a constant parameter. The results are compared with the Monte Carlo simulation. Comparison of the results indicates very good performance of the proposed approach for assessment of reliability. The results of sensitivity analysis show that relative density is the most effective parameter in factor of safety against liquefaction.

Probability distribution function for self-organization of shear flows

The first prediction of the probability distribution function (PDF) of self-organized shear flows is presented in a nonlinear diffusion model where shear flows are generated by a stochastic forcing while diffused by a nonlinear eddy diffusivity. A novel nonperturbative method based on a coherent structure is utilized for the prediction of the strongly intermittent exponential PDF tails of the gradient of shear flows. Numerical simulations using Gaussian forcing not only confirm these predictions but also reveal the significant contribution from the PDF tails with a large population of supercritical gradients. The validity of the nonlinear diffusion model is then examined using a threshold model where eddy diffusivity is given by discontinuous values, elucidating an important role of relative time scales of relaxation and disturbance in the determination of the PDFs.

Funções de distribuição de probabilidade decendial e mensal para a deficiência hídrica no solo

A determinação das probabilidades de ocorrência de certos níveis de deficiência hídrica do solo (DHS) é fundamental para o planejamento agropecuário e a gestão ambiental. O objetivo deste trabalho foi determinar as funções de distribuição de probabilidades (fdp) que melhor caracterizam a distribuição dos valores de deficiência hídrica no solo. As DHSs decendiais e mensais foram determinadas por meio de balanço hídrico diário do solo para as diferentes capacidades de armazenamento de água disponível dos solos da região de abrangência da estação meteorológica de Santa Maria. Verificou-se que os valores mensais e decendiais de DHS se ajustam às funções de distribuição de probabilidades lognormal, gama, exponencial e Weibull. Utilizando-se as fdp selecionadas para cada período do ano, é possível determinar a probabilidade de ocorrência de qualquer valor de DHS para os solos da região de abrangência da estação meteorológica de Santa Maria.

A statistical approach for sedimentation inside a microphysical precipitation scheme

A statistical approach for the sedimentation of prognostic precipitating species inside a microphysical scheme is proposed. The unique fall speed of precipitation used by a typical advective scheme is replaced by three probabilities of transfer associated with the following three types of precipitation: (i) precipitation present in the layer at the beginning of the time step; (ii) precipitation coming from the layer above which crosses the layer under consideration and (iii) precipitation locally produced (or destroyed) during the time step. The use of a decreasing exponential Probability Distribution Function (PDF) as basis for these probabilities ensures that the normalized probabilities do not depend on the origin of the precipitation. The main advantage of this characteristic is that the sedimentation process can now be computed in a single vertical loop. Other functions can also be used as basis for the probabilities and the case with a step function is discussed. The performance of the proposed PDF-based sedimentation scheme is validated in an academic single column model and in a full 3-D framework.