Shape Parameter Of Weibull Distribution Research Articles

Extremes and resource assessment of wind and waves in central Mediterranean Sea

This paper deals with extremes and resource assessment of wind and waves in central Mediterranean Sea. The extreme value analysis is performed following Equivalent Storm Models (ESMs) approach, commonly employed in the context of significant wave height return values estimation. In this work, it is extended to wind storm events thanks to some analogies between wave and wind processes at short and long-term scale. The Equivalent Exponential Storm (EES) Model is selected for this study because of its realistic description of actual events time evolution. Energy estimations are based on both real storm data and EES model. The input data used for this analysis comes from the re-analysis of atmospheric and wave conditions performed by MeteOcean group at DICCA of Genoa University and cover the period from January 1979 to December 2020. Sixteen points have been selected including the south and west coast of the Italian peninsula, the Sicily and Sardinia Islands. The study is focused on return values estimation and energy assessment, mainly related on the storm concept; it aims to elucidate analogies and/or differences of wind and wave at a given site as well as how the two resources are distributed along the examined locations, identifying the potential working time over the year and which are the storm events providing the prevalent energetic contribution to harvestable energy. Results show that the location characterized by the severest wind storm and wave storm events do not coincide and not always the location where the severest storm occur is also the most energetic site. Further, the variability of return values with different levels of return period for wind speeds is lower than for significant wave heights: this aspect is motivated by a shape parameter of Weibull distribution that is systematically higher for the wind speed with respect to the significant wave height. The extremes of significant wave height are more variable from one location to another than those of wind speed ones and the same behavior is exhibited by energy resources, elucidating that the wind resource in the investigated sites is more homogeneous.

Age-related changes in dynamic corneal backscatter observed in Scheimpflug imaging.

Corneal visualization Scheimpflug technology (Corvis ST) has the potential to indirectly provide information on corneal structure via the analysis of statistical properties of the backscatter. The aim of this work was to ascertain whether there are age-related changes in the dynamics of corneal backscatter during an air-puffed induced corneal deformation. Retrospective data from Corvis ST measurements of 151 young subjects (19-30 years) and 82 older subjects (50-87 years) were considered. Each measurement consisted of 140 frames (sampling frequency: 4330 fps). For every frame the cornea was first segmented, then regions of interest, encompassing temporal, central and nasal parts of cornea were selected, to which the parameters of Weibull distribution (scale and shape) were fitted, leading to time series of the estimated parameters. Apparent differences were found between the parameters of Weibull distribution between the two considered groups that manifest themselves mostly in the nasal region of the cornea. However, those differences cannot be attributed to the age alone. For this, a normalization method is proposed that leads to a much better separation between the groups in all considered regions. Clinical Relevance- The parameters of the corneal backscat-ter are widely used to asses corneal clarity (so-called corneal densitometry). Recently the parameters of Weibull distribution fitted to the corneal backscatter data have been used to support diagnosis of keratoconus. This work contributes to the assessment of corneal clarity by identifying the apparent age-related differences in those parameters when dynamic raw data is considered highlighting the need for such parameters to be appropriately normalized. Further it shown that the shape parameter of Weibull distribution unlike the scale parameter carries that information already for the raw non-normalized data.

NEONATAL DEATHS IN EMPOWERED ACTION GROUP STATES: MULTILEVEL MODELING TO STUDY THE WITHIN DISTRICT EDUCATION EFFECT ON NEONATAL SURVIVAL

Neonatal Deaths are deaths that occur during rst 28 days of life. It is still very high in demographically poor performing States in India termed as Empowered Action Group (EAG) States. Study using the National Family Health Survey-4 data suggests high neonatal death burden in EAG States including Odisha. Uttar Pradesh recorded the highest neonatal death at 51.6 deaths per 1000 live births and the lowest was recorded in Uttarakhand at 32.3 neonatal deaths per 1000 live births. Neonatal deaths in Chhattisgarh were recorded as 48.2 deaths per 1000 live births, followed by Odisha at 46.9, Madhya Pradesh at 44.9, Bihar at 41.9, Jharkhand at 39.2, Assam at 36.1 and Rajasthan at 34.4 per 1000 live births. The parametric Cox Hazard model was used to study the unobserved heterogeneity. The Weibull distribution shape parameter value greater than one suggests considerable unobserved heterogeneity in the data. Considering district as unit of analysis (group level variable), attempt was made to capture the between district individual variations in neonatal deaths with regard to women educated 12+grades within districts. The low levels of Intra Class Correlation are suggestive of individual level variations than group level differences in studying the variations in neonatal deaths.

IGBT lifetime model considering composite failure modes

As a new generation of power devices, IGBT devices are widely used in fields such as aerospace, power transmission and transformation. Failures happen to the modules under different mechanisms and temperature conditions, but the current practice rarely considers the interaction of multiple failure mechanisms in the lifetime model, leading to an over optimistic lifetime prediction. With the analysis of the IGBT failure mechanism, this paper studies the IGBT's overall failure probability distribution assuming the failure of bonding wire and solder layer follows Weibull distribution. By exploring the impacts of the Weibull parameters, the relationship between the lifetime of each failed component and the IGBT's overall lifetime is quantified with the fitted coupling coefficients. The analyzing results show that when the bonding wire and the solder layer have similar lifetime, the IGBT's whole lifetime will be reduced, and the reduction degree is affected by the shape parameters of Weibull distribution, up to 30%. The IGBT lifetime model considering coupling effect is then established, which is verified by the experiments. The experimental results prove the existence of coupling effect, as well as the superiority of the model in lifetime prediction, whose error is reduced by 4.1% compared with that without coupling effect.

Offshore Wind Potential of West Central Taiwan: A Case Study

In this study, we present the wind distributions from a long-term offshore met mast and a novel approach based on the measure–correlate–predict (MCP) method from short-term onshore-wind-turbine data. The annual energy production (AEP) and capacity factors (CFs) of one onshore and four offshore wind-turbine generators (WTG) available on the market are evaluated on the basis of wind-distribution analysis from both the real met mast and the MCP method. Here, we also consider the power loss from a 4-month light detection and ranging (LiDAR) power-curve test on an onshore turbine to enhance the accuracy of further AEP and CF evaluations. The achieved Weibull distributions could efficiently represent the probability distribution of wind-speed variation, mean wind speed (MWS), and both the scale and shape parameters of Weibull distribution in Taiwan sites. The power-loss effect is also considered when calculating the AEPs and CFs of different WTGs. Successful offshore wind development requires (1) quick, accurate, and economical harnessing of a wind resource and (2) selection of the most suitable and efficient turbine for a specific offshore site.

Single-stage and two-stage total failure-based group-sampling plans for the Weibull distribution under neutrosophic statistics

If the sample or population has vague, inaccurate, unidentified, deficient, indecisive, or fuzzy data, then the available sampling plans could not be suitable to use for decision-making. In this article, an improved group-sampling plan based on time truncated life tests for Weibull distribution under neutrosophic statistics (NS) has been developed. We developed improved single and double group-sampling plans based on the NS. The proposed design neutrosophic plan parameters are obtained by satisfying both producer’s and consumer’s risks simultaneously under neutrosophic optimization solution. Tables are constructed for the selected shape parameter of Weibull distribution and various combinations of neutrosophic group size. The efficiency of the proposed group-sampling plan under the neutrosophic statistical interval method is also compared with the crisp method grouped sampling plan under classical statistics.

DISTRIBUTION OF INDIVIDUAL WAVE OVERTOPPING VOLUMES ON A SLOPING STRUCTURE WITH A PERMEABLE FORESHORE

Maximum wave overtopping volumes on sea defences are an indicator for identifying risks to people and properties from wave hazards. The probability distribution of individual overtopping volumes can generally be described by a two-parameter Weibull distribution function (shape and scale parameters). Therefore, the reliable prediction of maximum individual wave overtopping volumes at coastal structures relies on an accurate estimation of the shape factor in the Weibull distribution. This study contributes to an improved understanding of the distribution of individual wave overtopping volumes at sloping structures by analysing the wave-by-wave overtopping volumes obtained from physical model experiments on a 1V:2H sloped impermeable structure with a permeable shingle foreshore of slope 1V:20H. Measurements of the permeable shingle foreshore were benchmarked against those from an identical experimental set-up with a smooth impermeable foreshore (1V:20H) of the same geometry. Results from both experimental set-ups were compared to commonly used empirical formulations, underpinned by the assumption that an impermeable foreshore exists in front of the sea structure. The effect on the shape factor in the Weibull distribution of incident wave steepness, relative crest freeboard, probability of overtopping waves and discharge are examined to determine the variation of individual overtopping volumes with respect to these key parameters. A key finding from the study is that no major differences in Weibull distribution shape parameter were observed for the tested impermeable and permeable sloped foreshores. Existing empirical formulae were also shown to predict reasonably well the Weibull distribution shape parameter, b, at sloping structures with both impermeable and permeable slopes.

Quality Assessment and Identification of Fingerprints by Analysis of the Image’s Structural Properties

The paper addresses the problem of assessing the quality of fingerprint images using spatial analysis methods. The author proposes using the previously developed mathematical model to describe the set of magnitudes of the image gradient. The model is based on the two-parameter Weibull distribution. The author proposes two approaches to assess the quality of fingerprints. The first approach is implemented by the so-called “Full reference method”, which compares the Weibull distribution parameters’ values of statistical estimates. The results of identifying sweat pores using this method are presented. The second approach is called the “No-Reference method” and is used to assess fingerprints’ quality when analyzing and identifying the information content of their individual sections. It is proposed to use an image blur map as a quality characteristic and a statistical estimate of the Weibull distribution shape parameter as a measure of the blur. The shape parameter is estimated at each image point by the combination of magnitudes of the image gradient in the vicinity of the point; in this, the previously developed blur mapping technique is applied. The specific examples illustrate effectiveness of the proposed approaches.

Modelling for prediction of the spread and severity of COVID-19 and its association with socioeconomic factors and virus types

We report the development of a Weibull based Long-Short-Term-Memory approach (W-LSTM) for the prediction of COVID-19 disease. The W-LSTM model developed in this study, performs better in terms of MSE, R2 and MAPE, as compared to the previously published models, including ARIMA, LSTM and their variations. Using W-LSTM model, we have predicted the beginning and end of the current cycle of COVID-19 in several countries. Performance of the model was validated as satisfactory in 82% of the 50 test countries, while asking for prediction for 10 days beyond the period of training. Accuracy of the above prediction with days beyond training was assessed in comparison with the MAPE that the model gave with cumulative global data. The model was applied to study correlation between the growth of infection and deaths, and a number of effectors that may influence the epidemic. The model identified age groups, trade with China, air traffic, country temperature and CoV-2 virus types as the likely effectors of infection and virulence leading to deaths. The predictors likely to promote or suppress the epidemic were identified. Some of the predictors had significant effect on the shape parameters of Weibull distribution. The model has been deployed on cloud, taking inputs in real time to handle large data country wise, at low costs and make predictions dynamically. Such predictions are highly valuable in guiding policy makers, administration and health. Interactive prediction curves generated from the W-LSTM model deployed on cloud platform can be seen at http://collaboration.coraltele.com/covid2/ (updated daily).

Evaluation of wind resource potential using statistical analysis of probability density functions in New South Wales, Australia

ABSTRACT Wind energy is a vital part of Australia’s energy mix. The first step in a wind power project at a particular site is to assess the wind resource potential and feasibility for wind energy production. Research on wind potential and statistical analysis has been done throughout the world. Currently, recent potential wind studies are lacking, especially in New South Wales (NSW), Australia. This study highlighted the feasibility of wind potential at four sites in NSW, namely Ballina, Merriwa, Deniliquin, and the Bega region. The type of wind speed distribution function dramatically affects the output of the available wind energy and wind turbine performance at a particular site. Therefore, the accuracy of four probability density functions was evaluated, namely Rayleigh, Weibull, Gamma, and Lognormal distributions. The outcomes showed Weibull provided the most accurate distribution. The annual average scale and shape parameters of Weibull distribution varied between 2.935–5.042 m/s and 1.137–2.096, respectively. The maximum shape and scale factors were at Deniliquin, while the minimum shape and scale factors were at Bega area. Assessment of power density indicated that Deniliquin had a marginal wind speed resource, while Ballina, Bega, and Merriwa had poor wind resources.

Integrating inventory planning, pricing and maintenance for perishable products in a two-component parallel manufacturing system with common cause failures

Since inventory level is a function of two factors of production and demand rates, and on the other side, demand rate is a function of price and shortage time, and production rate is a function of maintenance policy applied on machine, in this study, inventory planning, pricing and maintenance are integrated for perishable products in a parallel system including two components, although they are analyzed separately in the literature. On the other hand, it is a known fact that the failure of a component affects the other component performance, however, in the majority of researches, in an effort to simplify, failures are assumed to be independent from one another. In order to show the effectiveness of the proposed model three comparative studies are carried out. The first comparative study confirms the effect of maintenance activities on increasing profit and reduction of product price, whereas, the second study shows the effect of assuming perishability of products with different lifetimes, and the last comparison shows the effect of assuming interdependence of failures on reduction of corrective maintenance costs. With the aim of examining the effect of the parameters on the profit per time unit, sensitivity analysis is done on three parameters (1) the shape parameter of Weibull distribution; (2) the repairing costs of each component; (3) sensitivity coefficient of price.

Inferences on the performance index of Weibull distribution based on k-record values

Process capability indices are used to measure the performance of a process in the manufacturing industry. This paper derives inferences for the lifetime performance index using k-record values when the lifetime of products has a Weibull distribution. The UMVUE, an exact test and a classical confidence interval are proposed for this index when the shape parameter of Weibull distribution is known. With unknown shape parameter, a generalized confidence interval and two Bayesian confidence intervals are given. Also, it is estimated by the maximum likelihood and Bayesian estimators as well as a generalized approach. Based on the concept of generalized test variable, a generalized p-value is derived for testing the lifetime performance index. The behaviour of the proposed approaches are evaluated using Monte Carlo simulation. An illustration is given to demonstrate the proposed approaches. We also explain that the results can be utilized when the lifetime of products has an extreme value distribution.

The influence of TiB2 content on high temperature flexural strength and reliability of the developed titanium carbonitride based ceramic tool material

n this study, the influence of TiB2 content on flexural strength and reliability of the developed Titanium carbonitride based ceramic tool materials at high temperature was investigated. It was found that the flexural strength of Titanium carbonitride based ceramic tool materials (TB30TW) with 30 wt% TiB2 content was 1.49 times that of Titanium carbonitride based ceramic tool materials (TB20TW) with 20 wt% TiB2 content at room temperature. However, when the temperature exceeded 800 °C, the flexural strength of the two composites tended to be similar. The flexural strength of the TB30TW with higher TiB2 content dropped greatly at high temperature ascribed the oxidation behavior of TiB2. The distribution of measured high temperature flexural strength for TB30TW at 800 °C could well obey a Weibull distribution function, which was consistent with TB20TW. The Weibull distribution shape parameter of the flexural strength of TB30TW was higher than that of TB20TW at 800 °C, then the distribution of the high temperature flexural strength of TB30TW was less discrete than that of TB20TW. The results can serve as reference in the design composite ceramic tool materials and help to evaluate cutting reliability of ceramic cutting tools.

No-Reference Quality Assessment of an Image Resizing Algorithms

In this paper, a No-Reference method is proposed for quality assessment of an image resizing methods based on interpolation algorithms. Quality refers to the image blur. To this end, it is proposed to use a previously developed measure based on a statistical assessment of the Weibull distribution shape parameter, adopted as a model for gradient magnitude of an image. The results of numerical experiments are presented that allow us to evaluate and compare the quality of various image resizing algorithms.

Predicting compressive stress‒strain curves of structural adobe cubes based on Acoustic Emission (AE) hits and Weibull distribution

Purpose The purpose of this paper is to provide a method to predict the situation of a loaded element in the compressive stress curve to prevent failure of crucial elements in load-bearing masonry walls and to propose a material model to simulate a compressive element successfully in Abaqus software to study the structural safety by using non-linear finite element analysis. Design/methodology/approach A Weibull distribution function was rewritten to relate between failure probability function and axial strain during uniaxial compressive loading. Weibull distribution parameters (shape and scale parameters) were defined by detected acoustic emission (AE) events with a linear regression. It was shown that the shape parameter of Weibull distribution was able to illustrate the effects of the added fibers on increasing or decreasing the specimens’ brittleness. Since both Weibull function and compressive stress are functions of compressive strain, a relation between compressive stress and normalized cumulative AE hits was calculated when the compressive strain was available. By suggested procedures, it was possible to monitor pretested plain or random distributed short fibers reinforced adobe elements (with AE sensor and strain detector) in a masonry building under uniaxial compression loading to predict the situation of element in the compressive stress‒strain curve, hence predicting the time to element collapse by an AE sensor and a strain detector. In the predicted compressive stress‒strain curve, the peak stress and its corresponding strain, the stress and strain point with maximum elastic modulus and the maximum elastic modulus were predicted successfully. With a proposed material model, it was illustrated that the needed parameters for simulating a specimen in Abaqus software with concrete damage plasticity were peak stress and its corresponding strain, the stress and strain point with maximum elastic modulus and the maximum elastic modulus. Findings The AE cumulative hits versus strain plots corresponding to the stress‒strain curves can be divided into four stages: inactivity period, discontinuous growth period, continuous growth period and constant period, which can predict the densifying, linear, non-linear and residual stress part of the stress‒strain relationship. By supposing that the relation between cumulative AE hits and compressive strain complies with a Weibull distribution function, a linear analysis was conducted to calibrate the parameters of Weibull distribution by AE cumulative hits for predicting the failure probability as a function of compressive strain. Parameters of m and θ were able to predict the brittleness of the plain and tire fibers reinforced adobe elements successfully. The calibrated failure probability function showed sufficient representation of the cumulative AE hit curve. A mathematical model for the stress–strain relationship prediction of the specimens after detecting the first AE hit was developed by the relationship between compressive stress versus the Weibull failure probability function, which was validated against the experimental data and gave good predictions for both plain and short fibers reinforced adobe specimens. Then, the authors were able to monitor and predict the situation of an element in the compressive stress‒strain curve, hence predicting the time to its collapse for pretested plain or random distributed short fibers reinforced adobe (with AE sensor and strain detector) in a masonry building under uniaxial compression loading by an AE sensor and a strain detector. The proposed model was successfully able to predict the main mechanical properties of different adobe specimens which are necessary for material modeling with concrete damage plasticity in Abaqus. These properties include peak compressive strength and its corresponding axial strain, the compressive strength and its corresponding axial strain at the point with maximum compressive Young’s modulus and the maximum compressive Young’s modulus. Research limitations/implications The authors were not able to decide about the effects of the specimens’ shape, as only cubic specimens were chosen; by testing different shape and different size specimens, the authors would be able to generalize the results. Practical implications The paper includes implications for monitoring techniques and predicting the time to the collapse of pretested elements (with AE sensor and strain detector) in a masonry structure. Originality/value This paper proposes a new method to monitor and predict the situation of a loaded element in the compressive stress‒strain curve, hence predicting the time to its collapse for pretested plain or random distributed short fibers reinforced adobe (with AE sensor and strain detector) in a masonry building under uniaxial compression load by an AE sensor and a strain detector.

Study of local assessments of contrast for digital images

The article study notion of the digital image contrast. Various quantitative estimates of the contrast of digital images are investigated. Comparative experimental studies of different contrast estimates were performed on two standard image databases. It is shown that the evaluation of contrast by calculating the arithmetic average or MSE values of a set of local estimates does not always coincide with the visual contrast assessment. Experimental results showed that the Weibull distribution shape parameter is a more accurate estimate of the set of local contrast estimates calculated by the BEGH, GORD, LOEN functions and correlates well with the visual contrast estimates.

A simulation study of the Bayes estimator for parameters in Weibull distribution

The Weibull distribution is one of the most popular distributions in analyzing the lifetime data . In this study, we consider the Bayes estimators of the scale and shape parameters of Weibull distribution under the assumptions of gamma priors and squared error loss function. While computing the Bayes estimates for a Weibull distribution, the continuous conjugate joint prior distribution of the shape and scale parameters does not exist and the closed form expressions of the Bayes estimators cannot be obtained. In this study first we will consider the Bayesian inference of the scale parameter under the assumption that the shape parameter is known. We will assume that the scale parameter has a gamma prior. Under these assumptions Bayes estimate can be obtained in explicit form. When both the parameters are unknown, the Bayes estimates cannot be obtained in closed form. In this case, we will assume that the scale parameter has the gamma prior, and the shape parameter also has the gamma prior and they are independently distributed. We will use the Lindley approximation to obtain the approximate Bayes estimators. Under these assumptions, we will compute approximate Bayes estimators and compare with the maximum likelihood estimators by Monte Carlo simulations.

Statistical Analysis of Partial Discharge, Lightning Impulse and BDV Characteristics of Nano SiO2-Corn Oil for HV Insulation Applications

Recent concern towards environmental and fire safety of transformer operation has led to the development of natural ester based liquid insulation for power transformers. Recent advancements in nano technology confirm that the nano modified liquid insulation provides superior dielectric and thermal properties. Statistical analysis of the dielectric properties of nano modified liquid dielectrics is very important to qualify them for high voltage insulation applications. In this work, experimental works are carried out to understand the partial discharge (PD), lightning impulse (LI) and breakdown voltage (BDV) characteristics of corn oil filled with SiO2 nano fillers at different wt% concentration such as 0.01%, 0.05% and 0.1%. Needle/plane and rod/plane electrode geometry was used for creation of PD source. PD inception voltage, time domain and frequency domain characteristics of PD signals are evaluated. Weibull parameters of Phase Resolved PD pattern are evaluated. LI tests are performed at needle/plane and needle/sphere electrode geometry with standard 1.2/50 µs waveform at both positive and negative polarity. Weibull distribution analysis of LI breakdown voltage values are evaluated at different experimental conditions. BDV tests are carried out at different electrode gap distances such as 1, 2.5, 4 and 5 mm. Scale parameter and shape parameter of Weibull distribution of BDV values are computed. It is mostly observed that addition of nano SiO2 filler at lower wt% concentration in the range of 0.01–0.05% has substantial effect in enhancing the PD, LI and BDV characteristics of corn oil. Improvement in PD, LI and BDV characteristics gives confident that nano modified corn oil may be considered for outdoor transformer applications.

On convergence of iterative method for determination of weibull parameters by maximum likelihood method

The Weibull distribution is frequently used for the assessment of wind energy potential and modeling of wind speed data. The parameters of Weibull distribution are determined by a number of methods; Maximum Likelihood Methods is one of them. The values of scale and shape parameters of Weibull distribution are found by the help of Maximum Likelihood function. Two different techniques are used to find the parameters. One is known as iterative method, in which a start value of ‘k’ is set and iterations are terminated when given criterion is reached. The second method is Newton Raphson method of finding roots. We report here a problem of non-convergence of iterative method. We suggest the Newton Raphson method as the best choice for finding the value of ‘k’ through Maximum Likelihood Method.

A Method for Predicting the Effects of Specimen Geometry and Loading Condition on Fatigue Strength

Specimen geometry and loading condition usually have a great influence on the fatigue strength of metallic materials, which is an important issue in evaluating the reliability of component parts. In this paper, a rotating bending fatigue test is performed at first on an hourglass specimen and a notch specimen of a high strength titanium alloy. Experimental results indicate that, in terms of local stress, the notch specimen endures higher fatigue strength in comparison with the hourglass specimen due to its relatively smaller control volume. Then, a probabilistic control volume method is proposed for correlating the effects of specimen geometry and loading condition on the fatigue strength based on Weibull distribution and the concept of control volume. A simple formula is obtained for the fatigue strength in relation to control volumes, in which the parameter is the shape parameter of Weibull distribution of fatigue strength. The predicted results are in good agreement with the present experimental data for high strength titanium alloy and the data for the high strength steel and the full scale EA4T axle in the literature.