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This paper presents a novel approach for analyzing bivariate positive data, taking into account a covariate vector and left-censored observations, by introducing a hierarchical Bayesian analysis. The proposed method assumes marginal Weibull distributions and employs either a usual Weibull likelihood or Weibull-Tobit likelihood approaches. A latent variable or frailty is included in the model to capture the possible correlation between the bivariate responses for the same sampling unit. The posterior summaries of interest are obtained through Markov Chain Monte Carlo methods. To demonstrate the effectiveness of the proposed methodology, we apply it to a bivariate data set from stellar astronomy that includes left-censored observations and covariates. Our results indicate that the new bivariate model approach, which incorporates the latent factor to capture the potential dependence between the two responses of interest, produces accurate inference results. We also compare the two models using the different likelihood approaches (Weibull or Weibull-Tobit likelihoods) in the application. Overall, our findings suggest that the proposed hierarchical Bayesian analysis is a promising approach for analyzing bivariate positive data with left-censored observations and covariate information.

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This paper aims to introduce a novel family of probability distributions by the well-known method of the T-X family of distributions. The proposed family is called a "Novel Generalized Exponent Power X Family" of distributions. A three-parameters special sub-model of the proposed method is derived and named a "Novel Generalized Exponent Power Weibull" distribution (NGEP-Wei for short). For the proposed family, some statistical properties are derived including the hazard rate function, moments, moment generating function, order statistics, residual life, and reverse residual life. The well-known method of estimation, the maximum likelihood estimation method is used for estimating the model parameters. Besides, a comprehensive Monte Carlo simulation study is conducted to assess the efficacy of this estimation method. Finally, the model selection criterion such as Akaike information criterion (AINC), the correct information criterion (CINC), the Bayesian information criterion (BINC), the Hannan-Quinn information criterion (HQINC), the Cramer-von-Misses (CRMI), and the ANDA (Anderson-Darling) are used for comparison purpose. The comparison of the NGEP-Wei with other rival distributions is made by Two COVID-19 data sets. In terms of performance, we show that the proposed method outperforms the other competing methods included in this study.

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This research analyzed, optimized and modeled the inactivation kinetics of pathogenic bacteria (PB1: Escherichia coli O157:H7 and PB2: Listeria monocytogenes) and determined the microbiological safety of tomato juice processed by UV-LED irradiation and heat treatment. UV-LED processing conditions were optimized using response surface methodology (RSM) and were 90% power intensity, 21 min and 273-275 nm (251 mJ/cm2) with R2 > 0.96. Using the optimal conditions, levels of PB1 and PB2 resulted a log reduction of 2.89 and 2.74 CFU/mL, respectively. The Weibull model was efficient for estimating the log inactivation of PB1 and PB2 (CFU/mL). The kinetic parameter δ showed that 465.2 mJ/cm2 is needed to achieve a 90% log (CFU/mL) reduction in PB1 and 511.3 mJ/cm2 for PB2. With respect to the scale parameter p > 1, there is a descending concave curve. UV-LED-treated tomato juice had an 11.4% lower Listeria monocytogenes count than heat-treated juice on day 28 (4.0 ± 0.82 °C). Therefore, UV-LED technology could be used to inactivate Escherichia coli O157:H7 and Listeria monocytogenes, preserving tomato juice for microbiological safety, but studies are required to further improve the inactivation of these pathogens and analyze other fruit and vegetable juices.

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OBJECTIVE: The objective of this study was to 1) compare the stress corrosion coefficient (n) of a Y-TZP obtained by two fatigue tests: cyclic and dynamic and 2) evaluate the effect of frequency in the characteristic lifetime and the existence of interaction between the cyclic fatigue and slow crack growth. METHODS: A total of 145 Y-TZP specimens were produced in accordance with the manufacturer's instructions. These specimens, measuring 4.0 × 3.0 × 25.0 mm, were used for dynamic (n = 70) and cyclic fatigue tests (n = 75). The specimens were obtained from CAD/CAM blocks, sectioned, and sintered in a furnace at 1530 °C with a heating rate of 25 °C/min. They were tested in their "as-sintered" form without any additional surface treatment. The fatigue tests were conducted using a four-point bending to obtain the slow crack growth parameters (n). The cyclic fatigue test was also conducted in two frequencies (2 and 10 Hz), using stress levels between 350 and 600 MPa. Data from these tests were analyzed using ASTM C 1368-00 formulas and Weibull statistics. Scanning electron microscope (SEM) was used for fracture surface analysis to identify the origin of the fracture. Critical defect size was measured and used, along with flexural strength values, to estimate fracture toughness. Dynamic fatigue test data were used to obtain subcritical crack growth (SCG) parameters and perform Weibull statistical analysis. The cyclic fatigue data were used in the General Log-linear Model equation using the ALTA PRO software. Data were analyzed using one-way ANOVA followed by Tukey post-hoc tests and Student's t-test at a significance level of p ≤ 0.05. RESULTS: In the dynamic fatigue test, the values obtained for σfo and n were 667 and 54, respectively. This parameter indicates how the strength of the material diminishes over time due to internal cracks. The Weibull parameters obtained from the same test results were m = 7.9, σ0 = 968, 9 and σ5% = 767, which indicates the reliability of the material. The Weibull parameters obtained by cyclic fatigue were statistically similar for the two frequencies used, the m* was 0.17 (2 Hz) and 0.21 (10 Hz); characteristic lifetimes (η) were 1.93 × 106 and 40,768, respectively. The n values obtained by cyclic fatigue were 48 and 40 at frequencies of 2 and 10 Hz, respectively. There was no effect of the frequency, the stress level or the interaction of the two in the Y-TZP lifetime, when analysed by General Log Linear Model. SIGNIFICANCE: the n values obtained by cyclic and dynamic fatigue tests showed no statistically significant difference and the effect of frequency in the characteristic lifetime and the existence of interaction between the cyclic fatigue and subcritical growth were not observed in the tested specimens.

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PURPOSE: To evaluate the reliability and failure modes of ultrathin (0.5 mm) lithium disilicate, translucent and ultra-translucent zirconia crowns for posterior teeth restorations. MATERIALS AND METHODS: Fifty-four mandibular first molar crowns of three ceramic materials: (1) Lithium disilicate (e.max CAD, Ivoclar Vivadent), (2) 3Y-TZP (Zirconn Translucent, Vipi), and (3) 5Y-PSZ (Cercon XT, Dentsply Sirona), with 0.5 mm of thickness were milled and cemented onto composite resin abutments. Eighteen samples of each group were tested under mouth-motion step-stress accelerated life testing in a humid environment using mild, moderate, and aggressive profiles. Data was subjected to Weibull statistics. Use level curves were plotted and reliability was calculated for a given mission of 100,000 cycles at 100, 200, and 300 N. Fractographic analyses of representative samples were performed in scanning electron microscope. RESULTS: Beta (ß) values suggest that failures were dictated by material's strength for lithium disilicate and by fatigue damage accumulation for both zirconias. No significant differences were detected in Weibull modulus and characteristic strength among groups. At a given mission of 100,000 cycles at 100 N, lithium disilicate presented higher reliability (98% CB: 95-99) regarding 3Y-TZP and 5Y-PSZ groups (84% CB: 65%-93% and 79% CB: 37&-94%, respectively). At 200 N, lithium disilicate reliability (82% CB: 66%-91%) was higher than 5Y-PSZ (20% CB: 4%-44%) and not significantly different from 3Y-TZP (54% CB: 32%-72%). Furthermore, at 300 N no significant differences in reliability were detected among groups, with a notable reduction in the reliability of all materials. Fractographic analyses showed that crack initiated at the interface between the composite core and the ceramic crowns due to tensile stress generated at the intaglio surface. CONCLUSIONS: Ultrathin lithium disilicate crowns demonstrated higher reliability relative to zirconia crowns at functional loads. Lithium disilicate and zirconia crown's reliability decreased significantly for missions at higher loads and similar failure modes were observed regardless of crown material. The indication of 0.5 mm thickness crowns in high-load bearing regions must be carefully evaluated. CLINICAL SIGNIFICANCE: Ultraconservative lithium disilicate and zirconia crowns of 0.5 mm thickness may be indicated in anterior restorations and pre-molars. Their clinical indication in high-load requirement regions must be carefully evaluated.

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Ignoring the presence of dependent censoring in data analysis can lead to biased estimates, for example, not considering the effect of abandonment of the tuberculosis treatment may influence inferences about the cure probability. In order to assess the relationship between cure and abandonment outcomes, we propose a copula Bayesian approach. Therefore, the main objective of this work is to introduce a Bayesian survival regression model, capable of taking into account the dependent censoring in the adjustment. So, this proposed approach is based on Clayton's copula, to provide the relation between survival and dependent censoring times. In addition, the Weibull and the piecewise exponential marginal distributions are considered in order to fit the times. A simulation study is carried out to perform comparisons between different scenarios of dependence, different specifications of prior distributions, and comparisons with the maximum likelihood inference. Finally, we apply the proposed approach to a tuberculosis treatment adherence dataset of an HIV cohort from Alvorada-RS, Brazil. Results show that cure and abandonment outcomes are negatively correlated, that is, as long as the chance of abandoning the treatment increases, the chance of tuberculosis cure decreases.

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This paper develops an extension of spatiotemporal models that handle count data using nonhomogeneous Poisson processes. In this new proposal, we incorporate a seasonal cycle component in the definition of the intensity function to control possible effects produced by the occurrence of the event of interest in regular periods. The seasonal cycle can cause problems in estimating the shape parameter of the Weibull and generalized Goel intensity functions. This shape parameter serves to confront the research hypothesis that seeks to identify a trend in the occurrence rate of an event of interest. In the case of the Weibull intensity function, a value significantly equal to one of the shape parameters indicates a constant rate of occurrence, less than one indicates a decreasing rate, and greater than one indicates an increasing rate. In the case of the Goel intensity function, parameter values less than or equal to one indicate a decreasing occurrence rate, and values greater than one indicate the presence of a change point. We also built a spatial model using the Musa-Okumoto intensity function as an alternative to approximate counting processes for which there is a decreasing trend in the occurrence rate of the event of interest. We estimated the parameters of the proposed method from a Bayesian perspective. Finally, we fitted the proposed model and compared it with other approximations to analyze the frequency of extreme rainfall in the northern region of the states of Maranhão and Piauí in northeastern Brazil over ten years. Among the main results, we found that (1) the proposed method has proven superior in terms of fit and prediction performance than the other models, and (2) unlike other approximations, the proposed model does not detect changes in the rate of extreme rainfall occurrences.

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High hydrostatic pressure (HHP) is a non-thermal process widely used in the food industry to reduce microbial populations. However, rarely its effect has been assessed in products with high oil content. This study evaluated the efficacy of HHP (200, 250, and 300 MPa) at different temperatures (25, 35, and 45 °C) by cycles (1, 2, or 3) of 10 min in the inactivation of Aspergillus niger spores in a lipid emulsion. After treatments at 300 MPa for 1 cycle at 35 or 45 °C, no surviving spores were recovered. All treatments were modeled by the linear and Weibull models. The presence of shoulders and tails in the treatments at 300 MPa at 35 or 45 °C resulted in sigmoidal curves which cannot be described by the linear model, hence the Weibull + Tail, Shoulder + Log-lin + Tail, and double Weibull models were evaluated to elucidate the inactivation kinetics. The tailing formation could be related to the presence of resistance subpopulations. The double Weibull model showed better goodness of fit (RMSE <0.2) to describe the inactivation kinetics of the treatments with the higher spore reductions. HHP at 200-300 MPa and 25 °C did not reduce the Aspergillus niger spores. The combined HHP and mild temperatures (35-45 °C) favored fungal spore inactivation. Spore inactivation in lipid emulsions by HHP did not follow a linear inactivation. HHP at mild temperatures is an alternative to the thermal process in lipid emulsions.

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Mathematical models are used to characterize and optimize drug release in drug delivery systems (DDS). One of the most widely used DDS is the poly(lactic-co-glycolic acid) (PLGA)-based polymeric matrix owing to its biodegradability, biocompatibility, and easy manipulation of its properties through the manipulation of synthesis processes. Over the years, the Korsmeyer-Peppas model has been the most widely used model for characterizing the release profiles of PLGA DDS. However, owing to the limitations of the Korsmeyer-Peppas model, the Weibull model has emerged as an alternative for the characterization of the release profiles of PLGA polymeric matrices. The purpose of this study was to establish a correlation between the n and ß parameters of the Korsmeyer-Peppas and Weibull models and to use the Weibull model to discern the drug release mechanism. A total of 451 datasets describing the overtime drug release of PLGA-based formulations from 173 scientific articles were fitted to both models. The Korsmeyer-Peppas model had a mean Akaike Information Criteria (AIC) value of 54.52 and an n value of 0.42, while the Weibull model had a mean AIC of 51.99 and a ß value of 0.55, and by using reduced major axis regression values, a high correlation was found between the n and ß values. These results demonstrate the ability of the Weibull model to characterize the release profiles of PLGA-based matrices and the usefulness of the ß parameter for determining the drug release mechanism.

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This study set out to develop a thermally compatible glass to be infiltrated into zirconia partially stabilized by yttrium oxide (5Y-PSZ), to characterize it, and to evaluate its structural reliability and mechanical behavior. 5Y-PSZ zirconia discs (N = 90), dimensions 1.5 mm × 15 mm were produced, polished with #600 alumina oxide and #1200 silicon carbide sandpaper in a polisher. Three groups of 5Y-PSZ discs were assigned (n = 30): Zctrl: as sintered zirconia, Zinf-comp: glass-infiltrated zirconia on the occlusal surface, and sintered, and Zinf-tens: glass-infiltrated zirconia on the cementing surface and sintered; for biaxial flexural strength testing (ISO 6872:2015). A gel was synthesized via the sol-gel method and applied to the ceramic surface. Mechanical assay data (MPa) were evaluated via Weibull analysis (α = 5%) and specimens via X-Ray Diffractometry (XRD), Scanning Electron Microscopy (SEM), and fractographic analysis. The Zinf-tens group showed a characteristic strength of 824 MPa and m = 9.9; Zinf-comp 613 MPa and m = 10.2; Zctrl 534 MPa and m = 8; all groups differed statistically (σ0). However, they were similar in structural homogeneity (m). XRD showed 20-50 µm of infiltration, which means dissolution of part of the yttrium and reduction in the size of the cubic grains. In addition, the Zinf-tens group presented a failure origin from inside the material. The developed glass infiltrated into zirconia partially stabilized by yttrium oxide, increasing its characteristic strength and structural homogeneity by reducing surface defects and changing the failure mode.

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In this article, we propose a comparative study between two models that can be used by researchers for the analysis of survival data: (i) the Weibull regression model and (ii) the random survival forest (RSF) model. The models are compared considering the error rate, the performance of the model through the Harrell C-index, and the identification of the relevant variables for survival prediction. A statistical analysis of a data set from the Heart Institute of the University of São Paulo, Brazil, has been carried out. In the study, the length of stay of patients undergoing cardiac surgery, within the operating room, was used as the response variable. The obtained results show that the RSF model has less error rate for the training and testing data sets, at 23.55% and 20.31%, respectively, than the Weibull model, which has an error rate of 23.82%. Regarding the Harrell C-index, we obtain the values 0.76, 0.79, and 0.76, for the RSF and Weibull models, respectively. After the selection procedure, the Weibull model contains variables associated with the type of protocol and type of patient being statistically significant at 5%. The RSF model chooses age, type of patient, and type of protocol as relevant variables for prediction. We employ the randomForestSRC package of the R software to perform our data analysis and computational experiments. The proposal that we present has many applications in biology and medicine, which are discussed in the conclusions of this work.

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Relay-assisted wireless communications, where both the relay and the final destiny employ diversity-combining techniques, represent a compelling strategy for improving the signal-to-noise ratio (SNR) for mobile terminals, mainly at millimeter-wave (mmWave) frequency bands. In this sense, this work considers a wireless network that employs a dual-hop decode-and-forward (DF) relaying protocol, in which the receivers at the relay and at the base station (BS) use an antenna array. Moreover, it is considered that the received signals are combined at reception using equal-gain-combining (EGC). Recent works have enthusiastically employed the Weibull distribution so as to emulate the small-scale fading behavior in mmWave frequencies, which also motivates its use in the present work. For this scenario, exact and asymptotic expressions for the system's outage probability (OP) and average bit error probability (ABEP) are derived in closed form. Useful insights are gained from these expressions. More precisely, they illustrate how the system and fading parameters affect the performance of the DF-EGC system. Monte Carlo simulations corroborate the accuracy and validity of the derived expressions. Furthermore, the mean achievable rate of the considered system is also evaluated via simulations. Useful insights regarding the system performance are obtained from these numerical results.

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OBJECTIVES: Photo- and dual-polymerized resin-based luting agent was evaluated for elastic moduli effects on ultra-thin lithium disilicate (LD) glass-ceramic strengthening, structural reliability, and stress distribution. MATERIALS AND METHODS: One hundred-sixty LD discs (IPS e.max CAD, Ivoclar/Vivadent) were produced in ultra-thin thicknesses (half with 0.3 mm and the other half with 0.5 mm). The ultra-thin ceramic disks were coated with two different cement types (Variolink Veneer - V and Panavia F 2.0 - P). Two positive control groups were tested following hydrofluoric (HF) acid etching (LDt3, LDt5) and two negative control groups were tested for untreated ceramic (LD 3, LD 5). Biaxial flexural strength (BFS), characteristic strength (σ0) and Weibull modulus (m) were the response variables (n = 20) at the ceramic/resin cement interface (z = 0). Finite element analysis (FEA) was used to calculate maximum principal stress. Data were analyzed using two-way ANOVA, and Tukey's test. Scanning electron microscopy (SEM) was used to analyze the failed specimens using fractography and surface morphology. RESULTS: The BFS of LD at either thickness was not affected by cement types, as also demonstrated by FEA. Structural reliability significantly improved in the positive control group (LDt5). CONCLUSION: The cementation of ultra-thin LD with a resin-cement of varying elastic moduli did not influence BFS. LD surface modification by HF acid-etching increased the reliability. CLINICAL RELEVANCE: Ultra-thin anterior veneer designs made from lithium disilicate have been widely proposed and the apparent success of LD ultra-thin veneers was not influenced by the cement choice in the current studies albeit the elastic moduli luting agents used were of similar values.

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Over the last decades, the challenges in survival models have been changing considerably and full probabilistic modeling is crucial in many medical applications. Motivated from a new biological interpretation of cancer metastasis, we introduce a general method for obtaining more flexible cure rate models. The proposal model extended the promotion time cure rate model. Furthermore, it includes several well-known models as special cases and defines many new special models. We derive several properties of the hazard function for the proposed model and establish mathematical relationships with the promotion time cure rate model. We consider a frequentist approach to perform inferences, and the maximum likelihood method is employed to estimate the model parameters. Simulation studies are conducted to evaluate its performance with a discussion of the obtained results. A real dataset from population-based study of incident cases of melanoma diagnosed in the state of São Paulo, Brazil, is discussed in detail.

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Circadian systems are composed of multiple oscillatory elements that contain both circadian and ultradian oscillations. The relationships between these components maintain a stable temporal function in organisms. They provide a suitable phase to recurrent environmental changes and ensure a suitable temporal sequence of their own functions. Therefore, it is necessary to identify these interactions. Because a circadian rhythm of activity can be recorded in each crayfish cheliped, this paired organ system was used to address the possibility that two quasi-autonomous oscillators exhibiting both circadian and ultradian oscillations underlie these rhythms. The presence of both oscillations was found, both under entrainment and under freerunning. The following features of interactions between these circadian and ultradian oscillations were also observed: (a) circadian modal periods could be a feature of circadian oscillations under entrainment and freerunning; (b) the average period of the rhythm is a function of the proportions between the circadian and ultradian oscillations; (c) the release of both populations of oscillations of Zeitgeber effect results in the maintenance or an increase in their number and frequency under freerunning conditions. These circadian rhythms of activity can be described as mixed probability distributions containing circadian oscillations, individual ultradian oscillations, and ultradian oscillations of Gaussian components. Relationships among these elements can be structured in one of the following six probability distributions: Inverse Gaussian, gamma, Birnbaum-Saunders, Weibull, smallest extreme value, or Laplace. It should be noted that at one end of this order, the inverse Gaussian distribution most often fits the freerunning rhythm segments and at the other end, the Laplace distribution fits only the segments under entrainment. The possible relationships between the circadian and ultradian oscillations of crayfish motor activity rhythms and between the probability distributions of their periodograms are discussed. Also listed are some oscillators that could interact with cheliped rhythms.

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This work presents an extension of the slash Lindley-Weibull distribution, of which it can be considered a modification. The new family is obtained by using the quotient of two independent random variables: a two-parameter Lindley-Weibull distribution divided by a power of the exponential distribution with parameter equal to 2. We present the pdf and cdf of the new distribution, analyzing their risk functions. Some statistical properties are studied and the moments and coefficients of asymmetry and kurtosis are shown. The parameter estimation problem is carried out by the maximum likelihood method. The method is assessed by a Monte Carlo simulation study. We use nutrition data, which are characterized by high kurtosis, to illustrate the usefulness of the proposed model.

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Bimodal data sets are very common in different areas of knowledge. The crude birth rates data, fish length data, egg diameter data, the eruption and interruption times of the Old Faithful geyser, are examples of this type of data. In this paper, a new class of symmetric density functions for modeling bimodal data as described above are presented. From density functions with support on [ 0 , + ∞ ) , the symmetry is getting by reflecting the density function in the negative semi-axis with their respective normalization. In this way, if the primitive density function is unimodal, then the resulting density will be bimodal. We introduce asymmetry parameters and study their behavior, in particular the values of their modes and some other statistical values of interest. The cases for densities generated by Gamma, Weibull, Log-normal, and Birnbaum-Saunders densities, among others are studied. Statistical inference is performed from a classical perspective. A small simulation study to evaluate the benefits and limitations of the new proposal. In addition, an application to a data set related to the fetal weight in grams obtained through ultrasound in a sample of 500 units is also presented; the results show the great usefulness of the model in practical situations.

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This paper aims to discuss the Bayesian estimation approach for the zero-inflated cure class of models, which extends the standard cure model by accommodating zero-inflated data in the survival analysis context. A comprehensive simulation study is carried out to assess the performance of the estimation procedure. A new estimation methodology is illustrated using a real dataset related to women diagnosed with invasive cervical cancer in Brazil.

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Modelling is challenging topic and using parametric models is important stage to reach flexible function for modelling. Weibull distribution has shape and scale parameters which play the main role for modelling. Bimodality parameter is added and so bimodal Weibull distribution can capture real data set with bimodality which can be actually combination of two populations. The properties of the proposed distribution and estimation method are examined extensively to show its usability in modelling accurately and safely for practitioners. After examination as first stage in modelling issue, it is appropriate to use bimodal Weibull for modelling bimodality in real data sets if it exists. Two estimation methods including objective functions are used to estimate the parameters of shape, scale and bimodality parameters of function. The second stage in modelling is overcome by using heuristic algorithms for optimization of function according to parameters due to the fact that converging to global point of objective function is performed by heuristic algorithms from stochastic optimization. Real data sets are provided to show the modelling competence of objective functions from bimodal forms of Weibull and Gamma distributions having well defined shape, scale and bimodality parameters and potentially less parameters when compared with the existing distributions.

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It is very important to study the occurrence of high levels of particulate matter due to the potential harm to people's health and to the environment. In the present work we use a non-homogeneous Poisson model to analyse the rate of exceedances of particulate matter with diameter smaller that 2.5 microns (PM 2.5 ). Models with and without change-points are considered and they are applied to data from Bogota, Colombia, and Mexico City, Mexico. Results show that whereas in Bogota larger particles pose a more serious problem, in Mexico City, even though nowadays levels are more controlled, in the recent past PM 2.5 were the ones causing serious problems.