A Novel Modified Alpha Power Transformed Weibull Distribution and Its Engineering Applications

This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique.We refer to the new model as modified alpha power transformed Weibull distribution.The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions,which are quite familiar in environmental investigations.Its hazard rate function can be decreasing,increasing,bathtub and upside-down then bathtub shaped.Diverse structural properties of the proposed model are acquired including quantile function,moments,entropies,order statistics,residual life and reversed failure rate function.The parameters of the distribution were estimated using the maximum likelihood function.The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed.Via a simulation study,the performance of the point and interval estimates are compared using different criteria.Employing real lifetime data sets,we verify that the offered model furnishes a better fit than some other lifetime models including Weibull,gamma and alpha powerWeibull models.

A New Three-Parameter Inverse Weibull Distribution with Medical and Engineering Applications

The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of fields,including reliability,economics,engineering,biomedical science,biological research,environmental studies,and finance.For modeling real data,several expanded classes of distributions have been established.The modified alpha power transformed approach is used to implement the new model.The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models.It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters.Precise expressions for quantiles,moments,incomplete moments,moment generating function,characteristic generating function,and entropy expression are among the determined attributes of the new distribution.The point and interval estimates are studied using the maximum likelihood method.Simulation research is conducted to illustrate the correctness of the theoretical results.Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.

Neural stem cell-derived exosomes promote mitochondrial biogenesis and restore abnormal protein distribution in a mouse model of Alzheimer's disease

Mitochondrial dysfunction is a hallmark of Alzheimer’s disease.We previously showed that neural stem cell-derived extracellular vesicles improved mitochondrial function in the cortex of AP P/PS1 mice.Because Alzheimer’s disease affects the entire brain,further research is needed to elucidate alterations in mitochondrial metabolism in the brain as a whole.Here,we investigated the expression of several important mitochondrial biogenesis-related cytokines in multiple brain regions after treatment with neural stem cell-derived exosomes and used a combination of whole brain clearing,immunostaining,and lightsheet imaging to clarify their spatial distribution.Additionally,to clarify whether the sirtuin 1(SIRT1)-related pathway plays a regulatory role in neural stem cell-de rived exosomes interfering with mitochondrial functional changes,we generated a novel nervous system-SIRT1 conditional knoc kout AP P/PS1mouse model.Our findings demonstrate that neural stem cell-de rived exosomes significantly increase SIRT1 levels,enhance the production of mitochondrial biogenesis-related fa ctors,and inhibit astrocyte activation,but do not suppress amyloid-βproduction.Thus,neural stem cell-derived exosomes may be a useful therapeutic strategy for Alzheimer’s disease that activates the SIRT1-PGC1αsignaling pathway and increases NRF1 and COXIV synthesis to improve mitochondrial biogenesis.In addition,we showed that the spatial distribution of mitochondrial biogenesis-related factors is disrupted in Alzheimer’s disease,and that neural stem cell-derived exosome treatment can reverse this effect,indicating that neural stem cell-derived exosomes promote mitochondrial biogenesis.

Differential distribution of PINK1 and Parkin in the primate brain implies distinct roles

The vast majority of in vitro studies have demonstrated that PINK1 phosphorylates Parkin to work together in mitophagy to protect against neuronal degeneration.However,it remains largely unclear how PINK1 and Parkin are expressed in mammalian brains.This has been difficult to address because of the intrinsically low levels of PINK1 and undetectable levels of phosphorylated Parkin in small animals.Understanding this issue is critical for elucidating the in vivo roles of PINK1 and Parkin.Recently,we showed that the PINK1 kinase is selectively expressed as a truncated form(PINK1–55)in the primate brain.In the present study,we used multiple antibodies,including our recently developed monoclonal anti-PINK1,to validate the selective expression of PINK1 in the primate brain.We found that PINK1 was stably expressed in the monkey brain at postnatal and adulthood stages,which is consistent with the findings that depleting PINK1 can cause neuronal loss in developing and adult monkey brains.PINK1 was enriched in the membrane-bound fractionations,whereas Parkin was soluble with a distinguishable distribution.Immunofluorescent double staining experiments showed that PINK1 and Parkin did not colocalize under physiological conditions in cultured monkey astrocytes,though they did colocalize on mitochondria when the cells were exposed to mitochondrial stress.These findings suggest that PINK1 and Parkin may have distinct roles beyond their well-known function in mitophagy during mitochondrial damage.

基于Arrhenius-Weibull模型的ECU步进应力加速试验设计

文章基于Arrhenius-Weibull模型对ECU的加速寿命试验方法展开研究,基于加速模型试验原理选择步进应力施加方式。为满足产品的可靠度指标,通过分析Weibull分布情况计算最小试验样件数量。通过最大似然估计的方法确定产品的Arrhenius-Weibull模型参数,以便完成各个应力阶段的等效转换。通过对步进加速试验设计过程示例,提供一种满足产品寿命参数指标的判断依据,为后续从业者进行相关的加速试验设计提供依据。

三参数Weibulldistribution场合下定数截尾矩估计

本文讨论了在定数截尾样本下三参数威布尔分布的矩估计问题,并改进了文[4]的结果。

基于Weibull分布的石砌体单轴受压损伤本构模型

石砌体的本构模型是石砌体力学计算和有限元数值模拟的重要基础和前提条件。为了深入研究石砌体单轴受压下的本构关系,基于损伤力学理论,应用双参数Weibull分布函数反映损伤变量,根据石砌体单轴受压应力-应变全过程曲线的特征条件确定其参数,推导并建立了石砌体单轴受压损伤本构模型,将已有试验数据验证本构模型的正确性,并将本构模型与典型的砌体本构模型进行对比分析,最后应用本构模型对已有石砌体拱桥试验进行有限元分析以验证本构模型的适用性。结果表明:所建模型与已有石砌体单轴受压试验结果吻合良好;所建模型验证了石砌体损伤演化的一般规律,符合典型的砌体本构模型的一般趋势;所建模型可应用于石砌体结构有限元分析计算,适用性良好。

基于Weibull分布的煤矸石对混凝土断裂损伤特性的影响

为探索煤矸石质量取代率、粉煤灰质量取代率、水灰比对I型裂缝煤矸石混凝土荷载-裂缝张开位移、荷载-跨中挠度曲线、断裂韧性、断裂能的影响规律,对I型裂缝煤矸石混凝土进行三点弯曲试验,将所得结果结合损伤力学及Weibull分布函数建立煤矸石混凝土的断裂损伤本构模型。结果表明:煤矸石质量取代率对预制I型裂缝的煤矸石混凝土断裂性能影响最大,粉煤灰质量取代率对其断裂韧度影响较大,水灰比对其断裂能影响较大;提升煤矸石混凝土断裂时断裂韧度及断裂能的最佳组合的煤矸石质量取代率为25%、粉煤灰质量取代率为10%、水灰比为0.5;经对比可知,所得损伤本构模型对应的应力-应变曲线与试验曲线高度吻合。研究成果为煤矸石混凝土的制备及工程实际应用研究提供了参考。

Parameter Estimations for Some Modifications of the Weibull Distribution

Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibility, some modifications of the Weibull distribution have been made from several researches in order to best adjust the non-monotonic shapes. This paper gives a study on the performance of two specific modifications of the Weibull distribution which are the exponentiated Weibull distribution and the additive Weibull distribution.

Comparison of the Bayesian Methods on Interval-Censored Data for Weibull Distribution

This study considers the estimation of Maximum Likelihood Estimator and the Bayesian Estimator of the Weibull distribution with interval-censored data. The Bayesian estimation can’t be used to solve the parameters analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the scale and shape parameters are obtained via Metropolis-Hastings algorithm. Also Lindley’s approximation is used. The two methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the mean square error (MSE) to determine the best for estimating of the scale and shape parameters.

Interval Estimation in a Two Parameter Weibull Distribution Based on Type-2 Censored Data

In this paper, we consider the construction of the approximate profile- likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.

A New Study on Combustion Behavior of Pine Sawdust Characterized by the Weibull Distribution

An isothermal operation is implemented by employing a thermogravimetric analyzer (TGA) for simulating the thermal decomposition behavior of 58μm pine sawdust in air atmosphere.An independent parallel reaction model is adopted in this study to describe the thermal decomposition mechanism.The Weibull distribution function is used to record and analyze the weight loss during isothermal decomposition at different temperatures(500,600,700,and 800°C).The total weight loss of the pine sawdust is assumed as a linear combination of individual weight loss from three components,including the char and two volatile matters.The plot of the thermal decomposition rate curve leads to kinetic parameters such as the reaction rate constants and the reaction order.The results show that the Weibull distribution function successfully represents decomposition curves of three components,and fits the experimental data very well.Therefore,this study provides a simple way to evaluate the decomposition rate of biomass combustion in a real combustor.

Application of the Weibull Distribution to Estimate the Volume of Water Pumping by a Windmill

Given the steady increase in use of alternative energy sources to supply part of the energy demand of the world, and considering that Mexico has enough wind resources to produce all the electricity required by the country, in this work, it is carried out the development of a system of wind resource assessment to determine the volume of water that a windmill pumping system can provide in a specific area. To this end, it has developed a computer program for wind resource assessment by measurements of wind speed, direction, temperature, barometric pressure and relative humidity. Measuring equipments were mounted in a wind measurement tower of 10 m high, within the premises of the University of Quintana Roo which is located along the coast. Until this day, there are records over a period of five months of the variables of wind speed, wind direction, temperature, relative humidity and atmospheric pressure. These variables were used for statistical calculations using the Weibull distributions. To give a better use of the calculated data, they were applied to the evaluation of a Pumping System.

Performance of Weibull function as a diameter distribution model for Pinus thunbergii stands in the eastern coast of South Korea

This study was carried out to determine the performance of percentile-based Weibull diameter distribution model for Pinus thunbergii stands thriving along the eastern coast of South Korea.The parameter recovery technique was used to estimate the three parameters of the Weibull model.The analysis demonstrated satisfactory results based on the following test statistics for the principal percentile models:fit index(FI) range from 0.501(minimum diameter) to 0.932(50th diameter percentiles) and root mean square error(RMSE) range from 0.112(quadratic mean diameter) to 3.572(minimum diameter).The developed model was further evaluated by determining the mean bias(ē) in trees per ha(TPH) for each diameter class,and the results showed highest over-prediction in the 20 cm,andunder-prediction in the 16 cm and 24 cm diameter classes.The goodness of fit tested by KolmogorovSmirnov(KS) test showed no significant differences(p>0.05) between the observed and predicted diameter distributions for almost all plots.Using site index and aboveground biomass(AGB) models developed for P.thunbergii in South Korea,a model to predict the AGB per ha for each diameter class and subsequently the total AGB of the stand was created.An application guide was also created,which will serve as a decision-support tool for forest managers in quantifying the future total AGB in P.thunbergii stands located in the eastern coast of South Korea and,subsequently,the quantification of potential carbon stocks aside from being a vital input in designing efficient management and protection strategies for these stands.

The Marshall-Olkin Right Truncated Fréchet-Inverted Weibull Distribution: Its Properties and Applications

In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are derived. The method of maximum likelihood is used to estimate the model parameters. The graphs of the reliability function and hazard rate function are plotted by taken some values of the parameters. Three real life applications are introduced to compare the behaviour of the new distribution with other distributions.

A New Approach for Parameter Estimation of Mixed Weibull Distribution:A Case Study in Spindle

In order to improve the accuracy and efficiency of graphical method and maximum likelihood estimation( MLE) in Mixed Weibull distribution parameters estimation,Graphical-GA combines the advantage of graphical method and genetic algorithm( GA) is proposed.Firstly,with the analysis of Weibull probability paper( WPP),mixed Weibull is identified to data fitting.Secondly,the observed value of shape and scale parameters are obtained by graphical method with least square,then optimizing the parameters of mixed Weibull with GA.Thirdly,with the comparative analysis on graphical method,piecewise Weibull and two-Weibull,it shows graphical-GA mixed Weibull is the best.Finally,the spindle MTBF point estimation and interval estimation are got based on mixed Weibull distribution.The results indicate that graphical-GA are improved effectively and the evaluation of spindle can provide the basis for design and reliability growth.

Fracture Statistics Dominated by Hot-Cutting Defect and Deviation from Weibull Distribution

This paper characterizes the rarely noticeable hot-cutting defect and statistically models the fracture governed by this new type defect. The morphology of the defect on fired ceramic is examined and quantitatively featured through comparing the fracture strength governed by intrinsic defect and hot-cutting defect. Weibull distribution is utilized to fit the observed strength data and chi-square goodness-of-fit test is conducted to analyze the deviation. Kernel density estimation is introduced to explore the underlying strength distribution dominated by hot-cutting defect. Based on the shape information from kernel density estimating,gamma and lognormal distribution are compared and the hot-cutting defect governing fracture statistics is finally confirmed by chisquare test. Results show that the newly-defined hot-cutting defect is more dangerous than the intrinsic defect and the priori Weibull distribution fails to describe the fracture statistic governed by the edge defect while the lognormal with a slightly right skewed shape fits it very well.

Evaluation of the location parameter in Weibull distribution of CTOD testing results of high strength steel weldments

In this paper, the location parameter δ_(a) in Weibull distribution i.e. the lower limiting CTOD toughness of high strength steel weldments is evaluated from Gleeble simulated coarse grained specimens. The Charpy-V transition temperature obtained from these specimens is transformed to a fracture toughness K_(IC) value at a given temperature using Sanz' relation. Then, the location parameter a is δ_(a) evaluated. The predicted location parameter arrives at agreement with the lowest CTOD value as obtained from thick multilayer weldments. The improvement of the fracture toughness of multilayer weldments needs the increase of the lowering limiting CTOD.toughness i.e. the toughness of the coarse grained zone.

Parameter Estimation of Mixed Weibull Distributions Using Cuckoo Search

The lifetime data of products with multiple failure modes which are collected from life testing are often fitted by the mixed Weibull distributions. Since the mixed Weibull distributions contain no less than five parameters,the parameter estimation is difficult and inaccurate. In order to enhance the accuracy,a new method of parameter estimation based on Cuckoo search( CS) is proposed. An optimization model for the mixed Weibull distribution is formulated by minimizing the residual sum of squares. The optimal parameters are searched via CS algorithm. In the case study,the lifetime data come from the life testing of diesel injectors and are fitted by the twocomponent Weibull mixture. Regarding the maximum absolute error and the accumulative absolute error between estimated and observed values as the accuracy index of parameter estimation,the results of four parameter estimation methods that the graphic estimation method,the nonlinear least square method,the optimization method based on particle swarm optimization( PSO) and the proposed method are compared. The result shows that the proposed method is more efficient and more accurate than the other three methods.

Investigations into Some Simple Expressions of the Gamma Function in Wind Power Theoretical Estimate by the Weibull Distribution

The Weibull distribution is a probability density function (PDF) which is widely used in the study of meteorological data. The statistical analysis of the wind speed v by using the Weibull distribution leads to the estimate of the mean wind speed , the variance of v around and the mean power density in the wind. The gamma function Γ is involved in those calculations, particularly Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k). The paper reports the use of the Weibull PDF f(v) to estimate the gamma function. The study was performed by looking for the wind speeds related to the maximum values of f(v), v2 f(v) and v3 f(v). As a result, some approximate relationships were obtained for Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k), that use some fitting polynomial functions. Very good agreements were found between the exact and the estimated values of Γ (1+n/k) that can be used for the estimation of the mean wind speed , the variance σ2 of the wind speed v;around the mean speed and the average wind power density.