A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type I extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.

Full threshold vs. Swedish interactive threshold algorithm (SITA) em pacientes glaucomatosos submetidos à perimetria computadorizada pela primeira vez

PURPOSE: To compare the Full Threshold (FT) and SITA Standard (SS) strategies in glaucomatous patients undergoing automated perimetry for the first time. METHODS: Thirty-one glaucomatous patients who had never undergone perimetry underwent automated perimetry (Humphrey, program 30-2) with both FT and SS on the same day, with an interval of at least 15 minutes. The order of the examination was randomized, and only one eye per patient was analyzed. Three analyses were performed: a) all the examinations, regardless of the order of application; b) only the first examinations; c) only the second examinations. In order to calculate the sensitivity of both strategies, the following criteria were used to define abnormality: glaucoma hemifield test (GHT) outside normal limits, pattern standard deviation (PSD) <5%, or a cluster of 3 adjacent points with p<5% at the pattern deviation probability plot. RESULTS: When the results of all examinations were analyzed regardless of the order in which they were performed, the number of depressed points with p<0.5% in the pattern deviation probability map was significantly greater with SS (p=0.037), and the sensitivities were 87.1% for SS and 77.4% for FT (p=0.506). When only the first examinations were compared, there were no statistically significant differences regarding the number of depressed points, but the sensitivity of SS (100%) was significantly greater than that obtained with FT (70.6%) (p=0.048). When only the second examinations were compared, there were no statistically significant differences regarding the number of depressed points, and the sensitivities of SS (76.5%) and FT (85.7%) (p=0.664). CONCLUSION: SS may have a higher sensitivity than FT in glaucomatous patients undergoing automated perimetry for the first time. However, this difference tends to disappear in subsequent examinations.

Low-temperature single-crystal Raman and neutron-diffraction study of the hydrogenous ammonium copper(II) tutton salt and the deuterated analogue in the metastable state

Low-temperature (15 K) single-crystal neutron-diffraction structures and Raman spectra of the salts (NX4)(2)[CU(OX2)(6)](SO4)(2), where X = H or D, are reported. This study is concerned with the origin of the structural phase change that is known to occur upon deuteration. Data for the deuterated salt were measured in the metastable state, achieved by application of 500 bar of hydrostatic pressure at similar to303 K followed by cooling to 281 K and the subsequent release of pressure. This allows for the direct comparison between the hydrogenous and deuterated salts, in the same modification, at ambient pressure and low temperature. The Raman spectra provide no intimation of any significant change in the intermolecular bonding. Furthermore, structural differences are few, the largest being for the long Cu-O bond, which is 2.2834(5) and 2.2802(4) Angstrom for the hydrogenous and the deuterated salts, respectively. Calorimetric data for the deuterated salt are also presented, providing an estimate of 0.17(2) kJ/mol for the enthalpy difference between the two structural forms at 295.8(5) K. The structural data suggest that substitution of hydrogen for deuterium gives rise to changes in the hydrogen-bonding interactions that result in a slightly reduced force field about the copper(II) center. The small structural differences suggest different relative stabilities for the hydrogenous and deuterated salts, which may be sufficient to stabilize the hydrogenous salt in the anomalous structural form.

A probabilistic methodology for distributed generation location in isolated electrical service area

Distributed generation unlike centralized electrical generation aims to generate electrical energy on small scale as near as possible to load centers, interchanging electric power with the network. This work presents a probabilistic methodology conceived to assist the electric system planning engineers in the selection of the distributed generation location, taking into account the hourly load changes or the daily load cycle. The hourly load centers, for each of the different hourly load scenarios, are calculated deterministically. These location points, properly weighted according to their load magnitude, are used to calculate the best fit probability distribution. This distribution is used to determine the maximum likelihood perimeter of the area where each source distributed generation point should preferably be located by the planning engineers. This takes into account, for example, the availability and the cost of the land lots, which are factors of special relevance in urban areas, as well as several obstacles important for the final selection of the candidates of the distributed generation points. The proposed methodology has been applied to a real case, assuming three different bivariate probability distributions: the Gaussian distribution, a bivariate version of Freund’s exponential distribution and the Weibull probability distribution. The methodology algorithm has been programmed in MATLAB. Results are presented and discussed for the application of the methodology to a realistic case and demonstrate the ability of the proposed methodology for efficiently handling the determination of the best location of the distributed generation and their corresponding distribution networks.

Wind resource modelling in complex terrain using different mesoscale–microscale coupling techniques

Wind resource evaluation in two sites located in Portugal was performed using the mesoscale modelling system Weather Research and Forecasting (WRF) and the wind resource analysis tool commonly used within the wind power industry, the Wind Atlas Analysis and Application Program (WAsP) microscale model. Wind measurement campaigns were conducted in the selected sites, allowing for a comparison between in situ measurements and simulated wind, in terms of flow characteristics and energy yields estimates. Three different methodologies were tested, aiming to provide an overview of the benefits and limitations of these methodologies for wind resource estimation. In the first methodology the mesoscale model acts like “virtual” wind measuring stations, where wind data was computed by WRF for both sites and inserted directly as input in WAsP. In the second approach, the same procedure was followed but here the terrain influences induced by the mesoscale model low resolution terrain data were removed from the simulated wind data. In the third methodology, the simulated wind data is extracted at the top of the planetary boundary layer height for both sites, aiming to assess if the use of geostrophic winds (which, by definition, are not influenced by the local terrain) can bring any improvement in the models performance. The obtained results for the abovementioned methodologies were compared with those resulting from in situ measurements, in terms of mean wind speed, Weibull probability density function parameters and production estimates, considering the installation of one wind turbine in each site. Results showed that the second tested approach is the one that produces values closest to the measured ones, and fairly acceptable deviations were found using this coupling technique in terms of estimated annual production. However, mesoscale output should not be used directly in wind farm sitting projects, mainly due to the mesoscale model terrain data poor resolution. Instead, the use of mesoscale output in microscale models should be seen as a valid alternative to in situ data mainly for preliminary wind resource assessments, although the application of mesoscale and microscale coupling in areas with complex topography should be done with extreme caution.

Validation of three new measure-correlate-predict models for the long-term prospection of the wind resource

The estimation of the long-term wind resource at a prospective site based on a relatively short on-site measurement campaign is an indispensable task in the development of a commercial wind farm. The typical industry approach is based on the measure-correlate-predict �MCP� method where a relational model between the site wind velocity data and the data obtained from a suitable reference site is built from concurrent records. In a subsequent step, a long-term prediction for the prospective site is obtained from a combination of the relational model and the historic reference data. In the present paper, a systematic study is presented where three new MCP models, together with two published reference models �a simple linear regression and the variance ratio method�, have been evaluated based on concurrent synthetic wind speed time series for two sites, simulating the prospective and the reference site. The synthetic method has the advantage of generating time series with the desired statistical properties, including Weibull scale and shape factors, required to evaluate the five methods under all plausible conditions. In this work, first a systematic discussion of the statistical fundamentals behind MCP methods is provided and three new models, one based on a nonlinear regression and two �termed kernel methods� derived from the use of conditional probability density functions, are proposed. All models are evaluated by using five metrics under a wide range of values of the correlation coefficient, the Weibull scale, and the Weibull shape factor. Only one of all models, a kernel method based on bivariate Weibull probability functions, is capable of accurately predicting all performance metrics studied.

Influence of abutment-to-fixture design on reliability and failure mode of all-ceramic crown systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The generalized inverse Weibull distribution

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

The beta modified Weibull distribution

A five-parameter distribution so-called the beta modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments and examine the order statistics and their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.

A log-extended Weibull regression model

A bathtub-shaped failure rate function is very useful in survival analysis and reliability studies. The well-known lifetime distributions do not have this property. For the first time, we propose a location-scale regression model based on the logarithm of an extended Weibull distribution which has the ability to deal with bathtub-shaped failure rate functions. We use the method of maximum likelihood to estimate the model parameters and some inferential procedures are presented. We reanalyze a real data set under the new model and the log-modified Weibull regression model. We perform a model check based on martingale-type residuals and generated envelopes and the statistics AIC and BIC to select appropriate models. (C) 2009 Elsevier B.V. All rights reserved.

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution. (C) 2008 Elsevier B.V. All rights reserved.

Log-modified Weibull regression models with censored data: Sensitivity and residual analysis

This paper proposes a regression model considering the modified Weibull distribution. This distribution can be used to model bathtub-shaped failure rate functions. Assuming censored data, we consider maximum likelihood and Jackknife estimators for the parameters of the model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and we also present some ways to perform global influence. Besides, for different parameter settings, sample sizes and censoring percentages, various simulations are performed and the empirical distribution of the modified deviance residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for a martingale-type residual in log-modified Weibull regression models with censored data. Finally, we analyze a real data set under log-modified Weibull regression models. A diagnostic analysis and a model checking based on the modified deviance residual are performed to select appropriate models. (c) 2008 Elsevier B.V. All rights reserved.

General results for the beta-modified Weibull distribution

We study in detail the so-called beta-modified Weibull distribution, motivated by the wide use of the Weibull distribution in practice, and also for the fact that the generalization provides a continuous crossover towards cases with different shapes. The new distribution is important since it contains as special sub-models some widely-known distributions, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among several others. It also provides more flexibility to analyse complex real data. Various mathematical properties of this distribution are derived, including its moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are also derived for the chf, mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The estimation of parameters is approached by two methods: moments and maximum likelihood. We compare by simulation the performances of the estimates from these methods. We obtain the expected information matrix. Two applications are presented to illustrate the proposed distribution.

A Log-Linear Regression Model for the Beta-Weibull Distribution

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes, and censoring percentages, several simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.

Weibull model selection for reliability modelling

A large number of models have been derived from the two-parameter Weibull distribution and are referred to as Weibull models. They exhibit a wide range of shapes for the density and hazard functions, which makes them suitable for modelling complex failure data sets. The WPP and IWPP plot allows one to determine in a systematic manner if one or more of these models are suitable for modelling a given data set. This paper deals with this topic.