Weibull Model Research Articles

Development of the Site Index Curves for <italic>Quercus acuta</italic> Stands

Background and objective: The purpose of this study is to develop a model for estimating the site index (SI), which is the criterion for determining the site productivity of the <i>Quercus acuta</i> stand as known as Evergreen broad-leaved tree (EBLT) species.Methods: The materials used in the analysis were data from 63 sample plots, and the sample plots data were collected from the National Forest Inventory (NFI) and other sites. Since the site index is determined by the height and stand age of the dominant trees, the Schumacher model, the Chapman-Richards model, and the Weibull model were applied to derive the optimal equation for estimating the dominant tree height.Results: The three models derived the parameters and went through a statistical test. Among the three models, the Chapman-Richards model was found to be optimal considering the fitness index, bias, and residuals. By transforming this model, site index estimation equations with the reference age of 30 years were created, and site index curves were derived. According to the analysis of the collected data, the site index of the <i>Quercus acuta</i> stand in Korea was found to be in the range of 10 to 16.Conclusion: As the growth distribution of <i>Quercus acuta</i> is expected to move north due to climate change, the derivation of the site index representing site productivity will be helpful in making policy and management decisions for this species.

Acanthus mollis Formulations for Transdermal Delivery: From Hydrogels to Emulsions.

Topical formulations of Acanthus mollis L. leaf and the optimization of the release of their active compounds and their topical bioavailability were investigated for the first time. In vitro, the release of active compounds from three formulations-an oil-in-water cream and two hydrogels (Carbopol 940 and Pluronic F-127)-was determined using Franz diffusion cells. Detection and quantification of the compounds was performed via high-performance liquid chromatography with a photodiode array (HPLC-PDA). DIBOA, a bioactive compound of this medicinal plant, exhibited release kinetics of the Weibull model for the Carbopol and Pluronic F-127 formulation, identifying it as a potential active agent to optimize the topical distribution of the formulations. The implications extend to applications in inflammation treatment and tyrosinase inhibition, suggesting that it can make a significant contribution to addressing skin conditions, including melanoma and various inflammatory diseases.

Cost-effectiveness of intravenous resuscitation fluids in sepsis patients: a patient-level data analysis in Jordan

Aim Albumin role as fluid resuscitation in sepsis remains understudied in low- and middle-income countries. This study aimed to evaluate the cost-effectiveness of intravenous (IV) Albumin compared to Crystalloids in sepsis patients using patient-level data in Jordan. Methods This was a retrospective cohort study of sepsis patients aged 18 or older admitted to intensive care units (ICU) at two major tertiary hospitals during the period 2018–2019. Patients information, type of IV fluid, and clinical outcomes were retrieved from medical records, and charges were retrieved from the billing system. A 90-day partitioned survival model with two health states (alive and dead) was constructed to estimate the survival of sepsis patients receiving either Albumin or Crystalloids as IV fluids for resuscitation. Overall survival was predicted by fitting a Weibull model on the patient-level data from the current study. To further validate the results, and to support the assessment of uncertainty, time-dependent transition probabilities of death at each cycle were estimated and used to construct a state-transition patient-level simulation model with 10,000 microsimulation trials. Adopting the healthcare system perspective, incremental cost-effectiveness ratios(ICERs) of Albumin versus Crystalloids were calculated in terms of the probability to be discharged alive from the ICU. Uncertainty was explored using probabilistic sensitivity analysis. Results In the partitioned survival model, Albumin was associated with an incremental cost of $1,007 per incremental1% in the probability of being discharged alive from the ICU. In the state-transition patient-level simulation model, ICER was $1,268 per incremental 1% in the probability of being discharged alive. Probabilistic sensitivity analysis showed that Albumin was favored at thresholds >$800 per incremental 1%in the probability of being discharged alive from the ICU. Conclusion IV Albumin use in sepsis patients might not be cost-effective from the healthcare perspective of Jordan. This has important implications for policymakers to readdress Albumin prescribing practice in sepsis patients.

Residual Control Chart Based on a Convolutional Neural Network and Support Vector Regression for Type-I Censored Data with the Weibull Model

Control charts with conditional expected value (CEV) can be used with novel statistical techniques to monitor the means of moderately and lowly censored data. In recent years, machine learning and deep learning have been successfully combined with quality technology to solve many process control problems. This paper proposes a residual control chart combining a convolutional neural network (CNN) and support vector regression (SVR) for type-I censored data with the Weibull model. The CEV and exponentially weighted moving average (EWMA) statistics are used to generate training data for the CNN and SVR. The average run length shows that the proposed chart approach outperforms the traditional EWMA CEV chart approach in various shift sizes and censored rates. The proposed chart approach is suitable to be used in detecting small shift size for highly censored data. An illustrative example presents the application of the proposed method in an electronics industry.

A Fractional‐Order Kinetics Approach for Modeling Enzymatic Starch Multiscale Digestion

AbstractThe characterization of the enzymatic hydrolysis of starch is a prerequisite for assessing the impact of starchy food in the gastrointestinal tract. The issue is relevant given the necessity of tailoring food products with a prescribed capacity of glucose production. Several empirical functions have been proposed for modeling starch digestograms. The first‐order exponential and the Weibull models are among the most used functions. Although tight numerical fitting of the experimental data may be obtained with such functions, a reliable interpretation of the underlying parameters is commonly a drawback. This work explores the use of fractional‐order kinetics for the modeling of starch digestograms. The aims are to show that: a) the fractional‐order framework offers a framework for capturing multiscale patterns observed, and b) the Weibull's and Peleg's models are particular cases of a more general function expressed as a generalized (Mittag‐Leffler) exponential function. The results showed that the Mittag–Leffler exponential function provided the best‐fitting results. However, the gain relative to Weibull's and fractional Peleg's functions may be small. It is concluded that Weibull's function approximates a more general function (the Mittag‐Leffler function), and as such its parameters find an easier interpretation in terms of the hydrolysis kinetics.

Measuring the Risk of Vulnerabilities Exploitation

Modeling the vulnerabilities lifecycle and exploitation frequency are at the core of security of networks evaluation. Pareto, Weibull, and log-normal models have been widely used to model the exploit and patch availability dates, the time to compromise a system, the time between compromises, and the exploitation volumes. Random samples (systematic and simple random sampling) of the time from publication to update of cybervulnerabilities disclosed in 2021 and in 2022 are analyzed to evaluate the goodness-of-fit of the traditional Pareto and log-normal laws. As censoring and thinning almost surely occur, other heavy-tailed distributions in the domain of attraction of extreme value or geo-extreme value laws are investigated as suitable alternatives. Goodness-of-fit tests, the Akaike information criterion (AIC), and the Vuong test, support the statistical choice of log-logistic, a geo-max stable law in the domain of attraction of the Fréchet model of maxima, with hyperexponential and general extreme value fittings as runners-up. Evidence that the data come from a mixture of differently stretched populations affects vulnerabilities scoring systems, specifically the common vulnerabilities scoring system (CVSS).

An In-Depth Review of the Weibull Model with a Focus on Various Parameterizations

The Weibull distribution is a versatile probability distribution widely applied in modeling the failure times of objects or systems. Its behavior is shaped by two essential parameters: the shape parameter and the scale parameter. By manipulating these parameters, the Weibull distribution adeptly captures diverse failure patterns observed in real-world scenarios. This flexibility and broad applicability make it an indispensable tool in reliability analysis and survival modeling. This manuscript explores five parameterizations of the Weibull distribution, each based on different moments, like mean, quantile, and mode. It meticulously characterizes each parameterization, introducing a novel one based on the model’s mode, along with its hazard and survival functions, shedding light on their unique properties. Additionally, it delves into the interpretation of regression coefficients when incorporating regression structures into these parameterizations. It is analytically established that all five parameterizations define the same log-likelihood function, underlining their equivalence. Through Monte Carlo simulation studies, the performances of these parameterizations are evaluated in terms of parameter estimations and residuals. The models are further applied to real-world data, illustrating their effectiveness in analyzing material fatigue life and survival data. In summary, this manuscript provides a comprehensive exploration of the Weibull distribution and its various parameterizations. It offers valuable insights into their applications and implications in modeling failure times, with potential contributions to diverse fields requiring reliability and survival analysis.

Effects of spore purity on the wet heat resistance of Clostridium perfringens, Bacillus cereus and Bacillus subtilis spores

Heat resistance of spores of Clostridium perfringens 8238 (Hobbs Serotype 2), Bacillus cereus NCTC 11143 (4810/72), and Bacillus subtilis PS533, an isogenic derivative of strain PS832 (a 168 strain) was determined in ground beef at 95 °C. Spore purification was by centrifugation and washing with sterile distilled water (dH2O), followed by sonication and then Histodenz centrifugation for B. subtilis and C. perfringens, and centrifugation and washing with sterile dH2O followed by Histodenz centrifugation for B. cereus. Bags containing inoculated beef samples were submerged in a temperature-controlled water bath and held at 95 °C for predetermined lengths of time. Surviving spore populations were enumerated by plating on mannitol egg yolk polymyxin agar (MYP) agar plates for B. cereus and B. subtilis, and on tryptose-sulfite-cycloserine agar (TSC) agar plates for C. perfringens. Survivor curves were fitted to linear, linear with tail, and Weibull models using the USDA Integrated Pathogen Modeling Program (IPMP) 2013 software. The Weibull model provided a relatively better fit to the data since the root mean square error (RMSE), mean square error (MSE), sum of squared errors (SSE), and Akaike information criterion (AIC) values were lower than the values obtained using the linear or the linear with tail models. Additionally, the Weibull model accurately predicted the observed D-values at 95 °C for the three spore-formers since the accuracy factor (Af) values ranged from 1.03 to 1.08 and the bias factor (Bf) values were either 1.00 or 1.01. Times at 95 °C to achieve a 3-log reduction decreased from 206 min for C. perfringens spores purified with water washes alone to 191 min with water washes followed by sonication and Histodenz centrifugation, from 7.9 min for B. cereus spores purified with water washes alone to 1.4 min with water washes followed by Histodenz centrifugation, and from 20.6 min for B. subtilis spores purified with water washes alone to 6.7 min for water washes followed by sonication and Histodenz centrifugation. Thermal-death-time values reported in this study will assist food processors to design thermal processes to guard against bacterial spores in cooked foods. In addition, clearly spore purity is an additional factor in spore wet heat resistance, although the cause of this effect is not clear.

Co-encapsulation of curcumin and anthocyanins in bovine serum album-fucoidan nanocomplex with a two-steppH-driven method.

Curcumin (CUR) and anthocyanins (ACN) are recommended due to their bioactivities. However, their nutritional values and health benefits are limited by their low oral bioavailability. The incorporation of bioactive substances into polysaccharide-protein composite nanoparticles is an effective way to enhance their bioavailability. Accordingly, this study explored the fabrication of bovine serum albumin (BSA)-fucoidan (FUC) hybrid nanoparticles using a two-step pH-driven method for the delivery of CUR and ACN. Under a 1:1 weight ratio of BSA to FUC, the point of zero charge moved from pH ⁓ 4.7 for BSA to around 2.5 for FUC-coated BSA, and the formation of BSA-FUC nanocomplex was pH-dependent by showing the maximum CUR emission wavelength shifting from 546 nm (CUR-loaded BSA-FUC at pH 4.7) and 544 nm (CUR/ACN-loaded BSA-FUC nanoparticles at pH 4.7) to 540 nm (CUR-loaded BSA-FUC at pH 6.0) and 539 nm (CUR/ACN-loaded BSA-FUC nanoparticles at pH 6.0). Elevated concentrations of NaCl from 0 to 2.5 mol L-1 caused particle size increase from about 250 to about 800 nm, but showing no effect on the encapsulation efficiency of CUR. The CUR and ACN entrapped, respectively, in the inner and outer regions of the BSA-FUC nanocomplex were released at different rates. After incubation for 10 h, more than 80% of ACN was released, while less than 25% of CUR diffused into the receiving medium, which fitted well to Logistic and Weibull models. In summary, the BSA-FUC nanocomposites produced by a two-step pH-driven method could be used for the co-delivery of hydrophilic and hydrophobic nutraceuticals. © 2023 Society of Chemical Industry.

Supercritical Antisolvent Precipitation of Corticosteroids/β-Cyclodextrin Inclusion Complexes.

In this study, corticosteroid-β-cyclodextrin (β-CD) inclusion complexes were prepared by using supercritical antisolvent (SAS) precipitation to enhance the dissolution rate of dexamethasone (DEX) and prednisolone (PRED), which are poorly water soluble drugs. The processing of the active principles in the absence of a carrier led to their almost complete extraction (the small amount of obtained material precipitates in the form of crystals). The coprecipitation of the ingredients in the presence of β-CD was investigated at different concentrations, pressures, and molar ratios. For both the corticosteroids, the optimized operating conditions were 40 °C, 120 bar, an equimolar ratio, and a concentration in DMSO of 20 mg/mL; these conditions led to the attainment of microparticles with mean diameters equal to 0.197 ± 0.180 μm and 0.131 ± 0.070 μm in the case of DEX and PRED, respectively. Job's method confirmed the formation of inclusion complexes with a 1/1 mol/mol ratio. Compared to the pure ingredients, the obtained powders have an improved release rate, which is about three times faster in both cases. The release curves obtained under the best operating conditions were fitted using different models. The best fitting was obtained using the Weibull model, whose parameters are compatible with a combined release mechanism involving Fickian diffusion and controlled release.

Study of convective air turbulence based on the probability distribution function of angle of arrival fluctuations

This study investigates the probability density function (PDF) of angle of arrival (AoA) fluctuations of a laser beam propagating through convective air turbulence in two settings: indoor turbulence and atmospheric surface layer. The indoor turbulence is generated by an electric heater with a 50 cm × 100 cm surface area placed horizontally on the bottom. The atmospheric turbulence experiments are conducted over a level at 60 cm height from an asphalted area using a slightly divergent laser beam that propagates along 350 m. Image motion monitoring of four sub-apertures installed in front of the receiving telescope aperture is used to record the AoA fluctuations and their PDFs over the entrance pupil at the sub-aperture locations for both types of turbulence. The observations are made in two perpendicular directions to the propagation of the laser beam. The experimental PDFs of the AoA fluctuations are fitted with Gaussian, Lognormal, Weibull, and Gamma distribution functions. The results show that the Weibull and Gamma models are more consistent with the experimental data for the indoor convective air and atmospheric turbulence respectively. For the indoor convective turbulence, the full width at half maximum and the peak location of the measured PDFs increase with the heater temperature, as well as the goodness of fit, which saturates at high temperatures.

Clinical evaluation of liposome-based gel formulation containing glycolic acid for the treatment of photodamaged skin

Background: Long contact of UV causes skin damage. Glycolic acid (GA) as an alpha hydroxy acid is used to treat photodamaged skin. However, GA leads to side effects including; burning, erythema and peeling. Purpose: The aim of this study was to develop a controlled delivery systems loading GA in order to increasing its efficacy and lowering its side effects. Methods: Liposomes were evaluated for encapsulation efficiency, size and morphology. Optimized formulation was dispersed in HPMC gel bases and drug release kinetics were also studied. Clinical efficacy and safety of GA-loaded liposomal gel and GA gel formulation were evaluated in patients with photodamaged skin. Results: The EE% and average particle size of liposomes were 64 ±2.1 % and 317±3.6 nm, respectively. SEM image showed that liposomes were spherical in shape. In vitro release kinetics of GA from both formulations followed Weibull model. Clinical evaluation revealed that GA-loaded liposomal gel was more effective than GA gel formulation. Treatment with GA-loaded liposomal gel resulted in a statistically significant reduction in the scores of hyperpigmentation, fine wrinkling and lentigines. Moreover, liposomal gel formulation was able to minimize side effects of GA. Conclusion: According to the obtained results, the liposome-based gel formulation can be used as potential drug delivery system to enhance permeation of GA through skin layers and also reduce its side effects.

Effects of rapeseed protein addition on soybean protein-based textured protein produced by low-moisture extrusion: Changes in physicochemical attributes, structural properties and barrel flow behaviors

This study investigated the potential of rapeseed protein as a novel alternative protein source in meat analogs produced by extrusion cooking technology. To study the substitutability of rapeseed protein to soybean protein, the addition ratios of rapeseed protein to soybean protein in the extrusion experiment were 0:50, 10:40, 20:30, 30:20, 40:10 and 50:0 (w/w), respectively. The results showed that adding 0–20% rapeseed protein not only decreased the specific mechanical energy and mass flow rate of the mixture during extrusion, but also enhanced the hardness and chewiness of the extrudates while reducing their elasticity and resilience. In addition, increasing the amount of rapeseed protein may lead to decreased expansion characteristics, internal pore structure, and water absorption rate of the extrudates, as well as a decrease in brightness and an increase in redness on the surface. Weibull model could well describe the rehydration behavior for dynamic fitting of the extrusion rehydration process. Moreover, with the increase of rapeseed protein substitution, the content of disulfide bonds, and the proportion of relatively ordered protein secondary structures with high stability increased, and the degree of protein denaturation decreased. Besides, the degree of starch gelatinization reduced and the thermal stability of extrudates improved. Interaction analysis indicated that disulfide bonds are the primary force maintaining protein-mediated interactions in the extrudates. The incorporation of rapeseed protein shortened the mean residence time of molten feedstock and shifted the flow state to plug flow. Overall, our investigation suggests that within low levels of addition (≤20%, w/w), rapeseed protein has the potential to partially substitute for the soybean protein-based textured proteins. High substitution levels or complete substitution are not feasible due to the relatively low expansion and rehydration rates.

Evaluation of pulsed vacuum drying efficiency and quality of garlic sprout based on infrared radiation heating and electronic panel conduction heating

In view of the problems of short storage periods, high cost, and high energy consumption in low-temperature storage and controlled atmospheric storage of garlic sprouts, pulsed vacuum drying (PVD) technology was applied in this study for improving the commodity value and reducing the storage cost of garlic sprouts. The drying characteristics and quality attributes of garlic sprouts at different temperatures (65, 70, and 75 °C) and pulsing ratios (2:4, 3:4, 4:4, 3:2, and 3:6) based on the different heating techniques of infrared radiation (FIR-PVD) and electronic panel conduction (EPC-PVD) were investigated. The results showed that EPC-PVD shortened drying time by 11.45–24.94% compared with FIR-PVD, while FIR-PVD achieved better quality in terms of color and allicin retention as compared with EPC-PVD. Prolonging the vacuum duration and reducing the atmospheric pressure duration were helpful in the formation of porous structures, thus obtaining a faster drying rate and better product quality. The Weibull model could precisely describe the drying kinetics of garlic sprouts. FIR-PVD at 75 °C and 3:4 was recommended as the most suitable drying condition due to the highest comprehensive score (0.7856) considering drying time and product quality. The findings provide a new idea for low carbon high-quality storage of garlic sprouts.

Impact of plasma activated water (PAW) at different temperatures on Alicyclobacillus acidoterrestris spores

This study aimed to determine the impact of plasma activated water (PAW) combined with heating on the Alicyclobacillus acidoterrestris spores’ inactivation. For this, viable spore counts were determined after contact with PAW at 20–90 °C/5–150 min and inactivation kinetic parameters were determined at 90 °C by fitting Bigelow and Weibull models. Results showed that A. acidoterrestris spores were resistant to PAW at room temperature (reduction <0.8 log CFU/mL after 2h of exposure), while PAW at 80 and 90 °C for 30 min inactivated 2.8 and 3.6 log CFU/mL, respectively, showing a synergistic effect (p < 0.05). Moreover, Weibull model fitted the data better (R2 ≥ 0.95) than Bigelow (R2 ≥ 0.90), due to the tail behavior observed. Although PAW sanitation is insufficient to guarantee high levels of inactivation of A. acidoterrestris spores, its association with mild temperatures reduces 1–2 log CFU/mL, potentially improving the shelf life of fruit products.

Repairable System Analysis Using the Discrete Weibull Distribution

In many practical circumstances, a repair can be performed when a system fails to restore to a condition before a failure. This type of repair is known as minimal repair and one of the most used models is the power law process (PLP). It is common to consider equipment failure time as a continuous variable in this model, assuming a high degree of accuracy in the measurement tool. However, in practical situations, failures are usually observed and recorded as integer numbers of time units, such as the number of days and hours, indicating a discrete process. In this study, we used a discrete Weibull distribution instead of a continuous Weibull distribution. Since both Weibull models have similar complexities, some benefits are observed in the usage of the discrete model, such as a lower standard deviation of the parameter related to the system deterioration and also a lower Akaike's information criterion. For illustrative purposes, the use of a discrete Weibull distribution was applied to a dataset related to the failures of concrete mixer trucks. Moreover, an approach using a Markov chain with discrete states to obtain the average number of failures and the respective optimum maintenance policy was included. Additionally, six cases (found in the literature) fitted by the PLP model were reanalyzed and compared under the discrete model perspective.

On the identifiability and statistical features of a new distributional approach with reliability applications

Probability distributions have prominent applications in different sectors. Among these sectors, probability models are mostly used to analyze datasets in engineering. Among the existing probability distributions, the two-parameter Weibull model plays an important role in providing the best fit for engineering and other related datasets. This paper introduces a new method called a novel updated-W (denoted by “NU-W”) family of distributions that is used to develop a new updated form of the Weibull distribution. The proposed updated extension of the Weibull model is referred to as a novel updated Weibull (denoted as NU-Weibull) distribution. Distributional properties such as identifiability, heavy-tailed characteristic, and rth moment of the NU-W family are derived. The residual life analysis of the NU-Weibull distribution is provided. Finally, two physical applications from civil engineering and reliability sectors are analyzed to demonstrate the application and effectiveness of the NU-Weibull distribution. The data fitting results show that the NU-Weibull distribution is a more suitable and best fit for engineering datasets.

Group Maintenance for Numerical Control Machine Tools: A Case Study

The high-reliability requirement of numerical control (NC) machine tools emphasizes the effectiveness of preventive maintenance (PM). However, most existing PM decisions are made by treating them as single-component systems, resulting in the problems of “excessive maintenance” or “insufficient maintenance.” Moreover, real failure data has rarely been utilized for maintenance decision-making, which leads to idealized policies far from practice. This article presents a framework to derive the optimal group maintenance (GM) policy from real failure histories for an NC machine tool comprised of heterogeneous components. Criticality analysis is first conducted to identify high-risk and low-risk components. The lifetime of each high-risk component is characterized by a two-parameter Weibull model or by a Weibull competing-risk model according to whether its failures are independent of the other components. High-risk components with strictly increasing or bathtub-shaped failure rates are selected for PM decision-making. This article introduces a multilevel PM decision-making approach: 1) a repair-replacement model is developed at the component level to derive the optimal PM interval and the maximum number of PM actions; and 2) at the system level, a GM procedure is presented to obtain the optimal PM interval of the system. The failure histories of an NC machine tool with 13 components are used to illustrate the effectiveness of the proposed approach. A maintenance plan is finally made based on optimization results to guide maintenance implementation.

Effects of Temperature, Moisture, and Ultraviolet Light on Germination, Infection, and Survival of Gymnosporangium yamadae Teliospores and Basidiospores.

Apple rust caused by Gymnosporangium yamadae is a significant disease in China's main apple production areas. We evaluated the effects of temperature, moisture, and ultraviolet (UV) light on the germination, infection, and survival of teliospore horns and basidiospores under artificially controlled environmental conditions. The temperature required for the germination and infection of teliospores and basidiospores of G. yamadae ranged from 5 to 25°C, with an optimum temperature of approximately 17°C. The teliospore horns germinated after soaking in distilled water for 5 min and required at least 2.3 h of development to produce basidiospores under the most favorable conditions. The basidiospores germinated only in free water and produced germ tubes 0.8 h after being placed in the water. The half-life of the basidiospore was 72.5 h in the dark and only 9.5 h when exposed to intense UV light. The basidiospores inoculated on the host leaves required at least 2.3 h of water exposure to cause rust lesions. A revised Weibull model could describe the relationships between the germination and infection of teliospore horns and basidiospores with temperature and wetness duration. Collectively, these results can serve as a valuable guide for developing a model to predict future apple rust epidemics and establish a method for effective control strategies.

Method for estimating the future annual mass of decommissioned wind turbine blade material in Denmark

AbstractA model of the evolution of the onshore wind turbine blade mass installed in Denmark is proposed described by a Weibull distribution, and the age of the blades is estimated from decommissioning data to = 29 years when half of the blade mass of an installation year has been decommissioned. This is considerably longer than the 20 year design lifetime of onshore turbines, which is often assumed to be an estimate of the End‐of‐Life of turbine blades. Thus, blade waste predictions using the simple assumption may predict that installed blade masses are entering recycling processes about 9 years sooner that what is observed in Denmark. The blade mass for decommissioning in Denmark is estimated to peak at 2000 and 5000 ton/year in 2028 and 2045 using the Weibull model.