An Optimal Policy with Quadratic Demand, Three-Parameter Weibull Distribution Deterioration Rate, Shortages and Salvage Value

The present paper focuses an optimal policy of an inventory model for deteriorating items with generalized demand rate and deterioration rate. Shortages are allowed and partially backlogged. The salvage value is included into deteriorated units. The main objective of the model is to minimize the total cost by optimizing the value of the shortage point, cycle length and order quantity. A numerical example is carried out to illustrate the model and sensitivity analyses of major parameters are discussed.

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.

Hypothesis testing for reliability with a three-parameter Weibull distribution using minimum weighted relative entropy norm and bootstrap

With the help of relative entropy theory,norm theory,and bootstrap methodology,a new hypothesis testing method is proposed to verify reliability with a three-parameter Weibull distribution.Based on the relative difference information of the experimental value vector to the theoretical value vector of reliability,six criteria of the minimum weighted relative entropy norm are established to extract the optimal information vector of the Weibull parameters in the reliability experiment of product lifetime.The rejection region used in the hypothesis testing is deduced via the area of intersection set of the estimated truth-value function and its confidence interval function of the three-parameter Weibull distribution.The case studies of simulation lifetime,helicopter component failure,and ceramic material failure indicate that the proposed method is able to reflect the practical situation of the reliability experiment.

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.

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。

基于Weibull分布的非均质隧洞围岩破裂碎胀FDEM数值模拟研究

岩石材料具有非均质特征,矿物颗粒和胶结材料强度在统计学上服从Weibull分布。基于有限元-离散元耦合数值模拟方法(FDEM)提出了三角形单元弹性模量和四边形节理单元强度服从Weibull分布的参数赋值流程,随后研究了非均质岩样在单轴压缩、三轴压缩和巴西劈裂下的力学特征和破坏行为,最后对非均质隧洞围岩在高应力下的破裂碎胀大变形机制进行了模拟研究。结果表明:提出的随机参数赋值方法可建立不同弹性模量三角形单元数目服从Weibull分布、且空间分布具有随机性的FDEM数值模型;非均质岩样单轴抗压强度、三轴抗压强度、巴西劈裂抗拉强度、等效粘聚力和等效内摩擦角随着非均质度m的增大,均呈指数增大,并向均质材料逼近;高应力非均质隧洞围岩随着m的增大,裂隙网络形态变化不大,均以共轭剪切破裂为主,并伴随少量拉伸裂隙,但围岩破坏程度和裂隙扩展范围呈指数降低。

由Chvátal定理引出的关于Weibull分布和Pareto分布的研究

受Chvátal定理的启发,本文研究了随机变量不超过其期望的概率的下确界问题.利用分析的方法,我们得到了当随机变量的分布为Weibull分布或Pareto分布时该随机变量不超过其期望的概率的下确界.

区间删失数据下Weibull 比例优势模型的参数估计

基于区间删失数据建模是当前复杂数据分析的热点之一。本研究在两类区间删失数据下建立Weibull比例优势模型,基于极大似然估计给出了模型参数,进一步讨论了估计量的渐近性质。数值模拟验证了模型参数的估计效果,并将提出的模型及方法应用到艾滋病临床试验数据和肺肿瘤试验数据中,给出了感兴趣事件的生存函数曲线,通过与生存函数的非参数极大似然估计比较,表明所提方法具有较好的拟合效果。

Weibull分布模型改性再生混凝土微观损伤机理分析

为研究再生骨料改性对再生混凝土微观损伤机理的影响,该文用5%硅酸钠溶液(Na_(2)O·nSiO_(2)溶液)和10%聚乙烯醇溶液(PVA溶液)对不同级配再生骨料预浸泡进行改性。通过再生混凝土微小单元强度服从Weibull统计分布对抗压强度进行损伤演化分析和扫描电子显微镜(SEM)对骨料和混凝土微观形貌和机理分析。结果表明:经过5%硅酸钠溶液(Na_(2)O·nSiO_(2)溶液)和10%聚乙烯醇溶液(PVA溶液)改性后的再生混凝土均能显著提升内部微小单元损伤抗性和微观结构的密实性,且5%硅酸钠溶液(Na_(2)O·nSiO_(2)溶液)浸泡改性再生骨料对再生混凝土的提升效果劣于10%聚乙烯醇溶液(PVA溶液)。采用连续级配5~31.5 mm的再生混凝土损伤抗性显著高于单一级配10~16 mm和16~25 mm的再生混凝土损伤抗性。

基于响应面法和Weibull分布的不锈钢纤维再生混凝土抗冻性能研究

【目的】在我国严寒地区,冻融损伤会使再生混凝土(RAC)结构提前达到耐久性极限甚至导致构件失效,为了延长再生混凝土(RAC)结构在严寒地区的使用寿命,【方法】对再生混凝土(RAC)、天然混凝土(NC)、普通钢纤维再生混凝土(PFRAC)和不锈钢纤维再生混凝土(SFRAC)进行冻融循环试验。经过冻融循环后,测得RAC、NC、PFRAC、SFRAC的质量损失及相对动弹性模量,分析冻融循环过程中混凝土内部的损伤机理及劣化规律。以相对动弹性模量为损伤变量,基于响应面模型(RSM)和Weibull分布建立了钢纤维再生混凝土冻融损伤模型,研究冻融循环次数、PF和SF的掺量对再生混凝土抗冻性的影响。【结果】结果表明,SF的掺入能有效延缓RAC质量的损失和相对动弹性模量的降低。冻融循环150次时,掺量为2%的SFRAC质量损失和相对动弹性模量分别下降3.01%和19.57%。SFRAC与RAC相比,质量损失率降低了0.4%,相对动弹性模量提高了14.17%。【结论】Weibull分布和响应面模型(RSM)的预测结果 基本一致,但RSM预测值的相对误差要低于Weibull分布的预测值。两种模型的相关系数R2均在0.94以上,预测结果较为准确,可为钢纤维再生混凝土在寒冷地区的使用提供理论参考。

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。

基于Weibull分布的高温高围压岩石统计损伤本构模型

深部岩石通常处于高温及高围压环境中,深入研究深部岩石的本构关系对于深地矿产资源的开采、地热的高效利用以及岩体的稳定性分析等具有重要的理论和现实意义。为研究岩石在不同温度和围压作用下的静态三轴压缩破坏全过程本构关系,基于宏观唯象损伤力学的概念,从岩石的弹性模量随着温度变化的角度出发,得到了岩石在温度作用下的损伤表达式;又基于Weibull分布和修正的Mohr-Coulomb强度准则,将岩石细观均匀化,并结合统计损伤理论,得到了岩石在轴向压力作用下的统计损伤表达式;然后根据推广的应变等价性原理将两部分损伤耦合,得到了岩石在高温及轴压力作用下的岩石耦合损伤表达式。将所得的耦合损伤表达式结合考虑岩石残余应力的Lemaitre应变等价性假说以及有效应力原理,同时考虑岩石内部裂纹起裂阈值的影响,将本构模型分为阈值应变之前和阈值应变之后两部分,得到了一种分段函数形式的可反映高温及高围压影响的岩石统计损伤本构模型。为验证模型的适用性和准确性,分别将岩石在温度为25、200、400、600、800、1000℃和围压为0、10、20、30、40 MPa情况下的模型本构曲线与试验本构曲线进行了对比验证,对比结果较好,可以反映出岩石存在临界温度。在围压一定时,随着温度的升高,岩石的强度先增大后减小;在温度一定时,随着围压的升高,岩石的延性逐渐增强。

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。

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.

Analysis of an Inventory System for Items with Stochastic Demand and Time Dependent Three-Parameter Weibull Deterioration Function

In recent times, mathematical models have been developed to describe various scenarios obtainable in the management of inventories. These models usually have as objective the minimizing of inventory costs. In this research work we propose a mathematical model of an inventory system with time-dependent three-parameter Weibull deterioration and a stochastic type demand in the form of a negative exponential distribution. Explicit expressions for the optimal values of the decision variables are obtained. Numerical examples are provided to illustrate the theoretical development.

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.