Weilbull Distribution Research Articles

Proposed Maintenance Plan for Maker Machinery with Reliability Centered Maintenance (RCM) Method and Maintenance Value Stream Mapping (MVSM) at PT. XYZ

PT XYZ is a company engaged in cigarette production, where most of the production process uses automatic machines. The problem faced by the company is damage that occurs at any time before the scheduled maintenance interval causes overhaul and replacement or corrective maintenance activities which causes downtime and stops the production process on production machines that have a high average downtime compared to other machines. With these problems, calculations are carried out to obtain maintenance scheduling time intervals. The index of fit is used to measure how well the Weilbull distribution is based on the time to repair data. The fit index value (r) for the Hoper component downtime data is 0.92 or 92%, which means that the Hoper component downtime data can be completed using the Weilbull distribution. Calculation of the time to failure and time to repair parameters uses the Weilbull distribution by finding the intercept (a), gradient (b), shape parameter (α) and scale parameter (β). Calculation of the mean time to failure and mean time to repair using the results of parameter calculations using the Weilbull distribution based on the gamma table results in a mean time to failure of 1054.67 hours and a mean time to repair of 218.18 minutes. Calculation of the inspection time interval on the Hope component for 250 hours or 10 days per month. Analysis of maintenance efficiency using the maintenance value stream mapping approach obtained a maintenance efficiency percentage of 77.5%. Activities that provide added value have a longer time, namely 218.18 minutes. While activities that do not have added value is 63.2 minutes.

Fractional creep model of temperature-stress-time coupled damage for deep coal based on temperature-equivalent stress

The effective stress concept of temperature equivalent stress and actual stress acting together is established from the point of view that stress and temperature cause the same strain. The yield failure of coal and rock mass arises from the effective stress formed by the combination of temperature equivalent stress and actual stress. A temperature-stress coupled damage variable is established according to the hypothesis that the strength of coal and rock microunits obeys Weilbull distribution law and meet Drucker-Prager (D-P) yield failure criterion. A temperature-stress-time coupled damage variable is established by introducing a negative exponential function related to temperature and actual stress duration. The temperature-stress coupled damage variable of coal and rock mass is independent of the action time of temperature and time, but only related to the yield function F. The time damage variable is associated with the action time after the effective stress reaches the yield, which is mainly manifested in the viscoplastic deformation. Uniaxial and triaxial fractional creep models considering temperature-stress-time coupled damage are established by using Caputo fractional derivative definition. The parameters of temperature-stress-time coupled damage creep model are obtained by fitting the laboratory test data of deep coal body. The sensitivity of fitting parameters to the model and the goodness of fit analysis show that temperature-stress-time coupled damage model can well demonstrate the creep curves under different temperatures and stresses and the fitting accuracy is high.

Sample size calculation for randomized selection trials with a time-to-event endpoint and a margin of practical equivalence.

Selection trials are used to compare potentially active experimental treatments without a control arm. While sample size calculation methods exist for binary endpoints, no such methods are available for time‐to‐event endpoints, even though these are ubiquitous in clinical trials. Recent selection trials have begun using progression‐free survival as their primary endpoint, but have dichotomized it at a specific time point for sample size calculation and analysis. This changes the clinical question and may reduce power to detect a difference between the arms. In this article, we develop the theory for sample size calculation in selection trials where the time‐to‐event endpoint is assumed to follow an exponential or Weilbull distribution. We provide a free web application for sample size calculation, as well as an R package, that researchers can use in the design of their studies.

Investigation of concrete box girder positive temperature gradient patterns considering different climatic regions

Due to the inevitable exposure of bridges to complex ambient environment, the effects of temperature variation on the structure itself should be considered. Accurate evaluation of the cross-sectional temperature distribution is a significant concern in the bridge design phase. Temperature gradient patterns have been provided by current bridges codes with the consideration of the thermal effects on the structures. However, the current codes are insufficient to describe the temperature gradients of different climatic regions in China. This paper aims to develop a more efficient positive temperature gradient pattern considering different climatic regions within a 100-year return period. Long-term numerical simulations of two-year continuous thermal actions regarding seven different regions have been conducted to investigate the thermal effects on concrete box girders. Then, the comparison of the simulated results and current bridge design specifications illustrates the deficiencies of the current specifications. Furthermore, a 2-step method with curve fitting and extreme values analysis (EVA) has been utilized to determine the temperature gradient patterns. The curve fitting shows that the temperature gradient patterns of different regions can be described by a piecewise function with parabola. And, EVA shows that all the temperature gradients fit well with the Weilbull distribution. The representative values of different regions have also been obtained through the EVA. Finally, a positive temperature gradient pattern with the consideration of both the locations and design period has been proposed in this paper. The proposed temperature gradient pattern shows a better applicability in different regions comparing with the current Chinese codes. It hopes that the present study could contribute to further application of bridge temperature gradients and the investigation of other infrastructural areas in respect of the temperature gradients.

On the behavior of the high order stop-loss transform for convolutions with some applications

High order stop-loss transforms provide a risk measure that enables some flexibility on the weight given to high or low values of the risk. We interpret stop-loss transforms as iterated distributions and prove a recursive representation for risks expressed as convolutions. We apply this to the case of gamma distributions with integer shape parameter, the Erlang distributions, proving that high order stop-loss transforms are equivalent to the tails of the exponential distribution. The latter result is also extended to general gamma distributions. Furthermore, we prove that this equivalence to exponential tails does not hold in general, by proving that the stop-loss transform for a Weilbull distribution degenerates, unless, of course, in the exponential case.

Estimating the Modified Weibull Parameters in Presence of Constant-Stress Partially Accelerated Life Testing

Accelerated life testing is very important in life testing experiments because it saves time and cost. In this paper, assuming that the lifetime of items under use condition follows the modified Weilbull distribution, partially accelerated life tests based on progressive Type-II censored samples are considered. The likelihood equations are to be solved numerically to obtain the maximum likelihood estimates. Based on normal approximation to the asymptotic distribution of maximum likelihood estimates, the approximate confidence intervals for the parameters are derived. Two bootstrap confidence intervals called bootstrap-p and bootstrap-t are also discussed. It is difficult to get explicit form for Bayes estimates, so we use Markov chain Monte Carlo method to solve this problem, which gives us flexibility to construct the credible intervals for parameters. Finally, a simulation study is performed to compare between MLEs and Bayes estimates.

Dependence structure analysis with copula GARCH method and for data set suitable copula selection

Objective: Multivariate GARCH (MGARCH) models are forecasted under normality. In this study, for non-elliptically distributed the data set which are generated Weilbull distribution. Copula-based GARCH (Copula-GARCH) was used. The aim of the paper is to model GARCH for non-normal distributions using copulas. Material and Methods: A two-step Copula-GARCH model to analyze the dependence structure of data sets was used. In the first step, we show data using univariate GARCH model to get standard residuals and construct marginal distributions. In this section GARCH (p,q) and GARCH (1,1) method are introduced. GARCH (1,1) method for data set was used for first step. In the second step, for dependence structures of the data sets were calculated Kendall Tau and Spearman Rho values which are nonparametric. Based on this method, parameters of copula are obtained. Results: A clear advantage of the copula-based model is that it allows for maximum-likelihood estimation using all available data. Conclusion: The aim of the method is basic to find the parameters that make the likelihood functions get its maximum value. With the help of the maximum-likelihood estimation method, for copula families obtain likelihood values. This values, Akaike information criteria (AIC) and Schwartz information criteria (SIC) are used to determine which copula supplies to suitability to the data set.

Comparison of Wind Potential of Ormara and Jiwani (Balochistan), Pakistan

This paper presents comparison of wind potential of Ormara and Jiwani and evaluation of Weilbull distribution function for two coastal areas of Balochistan. Ten years data (1998-2007) of wind speed have been obtained from Pakistan Meteorological | department (PMD) of Karachi, Pakistan. The analysis of wind data is carried out and fitted by Weibull function. The two parameters of the distribution are also evaluated. Monthly mean wind speed of two coastal locations (Ormara and Jiwan) was also predicted.

A pore network model reconstruction method via genetic algorithm

A pore network model could represent the porous medium space to predict rocks' various flow properties. This paper proposes a new method via genetic algorithm (GA) to reconstruct the pore network model with irregular distribution and topologically equivalent based on the real porous medium. Firstly, the properties of pore and throat are based on the Weilbull distribution function. A random pore network model is built by some assumptions and Weilbell parameters. In order to obtain the reliable parameters of pore and throat, the Avizo Fire analysis software is used to analysis the sample's micro-computed tomography (micro-CT) images. The theory of pore network simulation also is introduced simply in this section. Second, two objective functions for GA are given. We build up an objective function to reduce the discrepancy of slices of numerical model with the real micro-CT images, which is controlled by the core porosity. The second objective function makes model much more agreed with the experiment value. Thirdly, according to the characteristics of control parameters, we choose three steps alternating optimization to construct the model via GA. It demonstrates that this method has a quick convergence speed than before experiments. We adopt two kinds of complex geological porous medium to test the validity of our proposed method. One is a rock with high porosity (Sample One). The other is the dense sandstone (Sample Two). After the optimization, two appropriate pore network models are performed excellent of the prediction displacement in primary oil flooding of the target porous medium.

English

Storage life of ‘green’ locust beans condiment is less than 72 h due to inherent high moisture content (>55%) and vulnerability to peroxidation due to high fat content (> 37%). Therefore, elimination or significant reduction of moisture and fat should lead to increase in storage life hence studied. ‘Green’ locust beans condiment was dried and delipidated using three solvents. Assessment of some physiochemical, biochemical, sensory characteristics and shelf-life preliminary study on the preparation were conducted. Moisture content (<10%) of samples was at the level that samples are stable to spoilage microorganism. Lipids were extracted using three solvents in the order of diethylether > hexane > methanol with concomitant increase in proportion of protein in the delipidated sample in comparison to non-delipidated sample. Analysis of sensory scores (p = 0.05) showed that diethylether extracted sample was the most preferred and methanol extracted sample the least preferred. Using off-odour perception as accelerated storage instrument, shelf-life model insight (scale factor = 28 days, shape factor 3.8) was obtained using Weilbull distribution.   Key words: Locust beans condiment, poor storability, processing, biochemical characteristics, shelf-life model insight.

Estudo da precipitação mensal durante a estação chuvosa em Diamantina, Minas Gerais

O objetivo deste trabalho foi estudar o comportamento da precipitação pluvial no período da estação chuvosa na região de Diamantina, MG. Dados de precipitação pluviométrica mensal, da série histórica de 1977 a 2006, foram utilizados e averiguada a probabilidade para várias classes de precipitação, através da função de frequência acumulada, usando-se a metodologia da distribuição Weibull com averiguação de aderência pelo teste Kolmogorov-Smirnov com nível de significância de 5%; de classes definidas em função de percentis predeterminados. Os resultados mostram que a estação chuvosa, compreendida entre outubro e março, representa 88% do total precipitado anual. Os meses de janeiro e dezembro apontam as maiores probabilidades de ocorrência de precipitação com 220,1 mm e 167,8 mm, respectivamente, a nível de 25% de probabilidade de ocorrência. O modelo de distribuição Weibull apresentou bom ajuste da série climatológica para estudos probabilísticos mostrando os parâmetros dentro dos limites estatísticos preestabelecidos.

Deformations of the Tracy-Widom distribution

In random matrix theory, the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists of removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristic of extreme values of an uncorrelated sequence, is obtained.

Color Constancy Based on Effective Regions

None of the existing color constancy algorithms can be considered universal. Furthermore, they use all the image pixels, although actually not all of the pixels are effective in illumination estimation. Consequently, how to select a proper color constancy algorithm from existing algorithms and how to select effective(or useful) pixels from an image are two most important problems for natural images color constancy. In this paper, a novel Color Constancy method using Effective Regions (CCER) is proposed, which consists of the proper algorithm selection and effective regions selection. For a given image, the most proper algorithm is selected according to its Weilbull distribution while its effective regions are chosen based on image similarity. The experiments show promising results compared with the state-of-the-art methods.

A stratified model for the assessment of meteorologically adjusted trends of surface ozone

We consider the problem of assessing long-term trends of ozone concentrations measured on a single site located in an urban area. Among the many methods proposed in the literature to eliminate the confounding effect of changing weather conditions, we employ a stratification of daily maxima based on regression trees. Within each stratum conditional independence and Weilbull distribution are assumed for maxima. Long-term trend is defined non-parametrically by the sequence of yearly medians. Models are estimated following the Bayesian approach. The alternative assumptions of common and stratum specific trends are compared and a model with common trend for all strata is selected for the analyzed real dataset. The conditional independence assumption is checked by the comparison with a model including an autoregressive component.

Destruction of living cells by pulsed high-voltage application

Destruction of living cells in liquid has been formed by pulsed high-voltage application to the liquid. S. cerevsaie (yeast cell) or Bacillus natto, dispersed in deionized water and one- and three-percent NaCl solution, were used in this experiment. Four different electrodes (plate-plate, needle-plate wire-cylinder, and rod-rod electrode) were tested. The survival rate of cells was measured against peak electric field E/sub p/ pulsewidth T/sub W/, and pulse application number N. The experimental results indicate that the survivability roughly follows Weilbull distribution. Yeast cells dispersed in deionized water could be almost completely destroyed when the wire-cylinder electrode was used with E/sub p/=20 kV/cm, T/sub W/=100 mu s, and N=200. The energy input to a unit volume of the liquid to complete the cell destruction, however, differed significantly with the electrode type. The wire-cylinder electrode required above 10-30 cal/cm/sup 3/ to destroy the yeast cell in deionized water to 10/sup -6/ survivability. This value was less than that required more than 70 cal/cm/sup 3/. Using the rod-rod electrode contained in a pressure vessel, an arc discharge was generated to produce an intensive shock wave, which also destroyed the cells by its mechanical force. In this case, 5-10 cal/cm/sup 3/ of energy was required to decrease the survivability of yeast cells in deionized water to 10/sup -6/. Though further studies are necessary, this results indicate a possibility of the cell destruction by pulsed high voltage to be used as an energy-efficient sterilization process.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In situ rock strength from triaxial testing

An empirical approach is presented to obtain the mean and standard deviation of the in-situ rock strength. The strength estimate is calculated from the compressive strength of both sound and jointed (fractured) samples of drill core and is valid for the drilling direction only. Two hundred and seventy-seven triaxial compression tests and 71 Braxilian disc tests were carried out on samples of siderite with diameters ranging between 2.2 cm (0.88 in.) and 24.1 cm (5.5 in.). All the samples were obtained in the same drilling direction and the interpolated uniaxial compressive strengths for jointed and sound samples show a convergence with size. The convergence is used to calculate the in-situ rock strength. This approach yields more realistic values than that obtained by extrapolation of a strength/size relationship with the aid of Weilbull's distribution.