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.

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.

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

In this research work we propose a mathematical model of an inventory system with time dependent three-parameter Weibull deterioration and price-dependent demand rate. The model incorporates shortages and deteriorating items are considered in which inventory is depleted not only by demand but also by decay, such as, direct spoilage as in fruits, vegetables and food products, or deterioration as in obsolete electronic components. Furthermore, the rate of deterioration is taken to be time-proportional, and a power law form of the price dependence of demand is considered. This price-dependence of the demand function is nonlinear, and is such that when price of a commodity increases, demand decreases and when price of a commodity decreases, demand increases. The objective of the model is to minimize the total inventory costs. From the numerical example presented to illustrate the solution procedure of the model, we obtain meaningful results. We then proceed to perform sensitivity analysis of our model. The sensitivity analysis illustrates the extent to which the optimal solution of the model is affected by slight changes or errors in its input parameter values.

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。

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.

基于Weibull混合分布的航空发动机零部件寿命建模

针对航空发动机在维修工作中存在重要零部件使用寿命及失效率难以估算的问题,搜集了发动机重要零部件燃油计量活门、整体驱动发电机、液压机械组件的使用寿命数据,并运用Weibull混合分布及单Weibull分布分别建立了上述重要零部件的寿命模型。在模型求解过程中采用了经典的三参数相关系数优化法,求出发动机重要零部件的可靠度、失效率及故障概率密度函数。通过计算得出Weibull混合分布模型的线性相关系数r_(g)比单Weibull分布模型的大;同时K-S假设检验结果显示,Weibull混合分布的统计量观测值D_(n)均小于临界值D_(30,0.1)。结果表明:相对于单Weibull分布,Weibull混合分布模型更精确地表征了发动机重要零部件的寿命数据,从而有效地提高寿命参数的估算精度;Weibull混合分布模型的可靠性有助于发动机管理工程师制定视情维修方案;并对航材备件的数量有指导意义,具有较高的推广应用价值。

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分布的缺口件多轴疲劳寿命建模

针对多轴缺口件,引入Weibull分布建立考虑应力梯度效应的疲劳寿命预测方法.首先,将最大应变能密度定义为损伤参量,并结合坐标变换确定能反映裂纹萌生和扩展的临界面位置;其次,利用有限元方法提取临界面特定路径的应力分布,并对其进行归一化处理得到多轴等效应力梯度因子,进而基于GSP应变能密度模型得出应变能密度与实验寿命的线性关系;最后,结合等效应力梯度因子、应变能密度模型和Weibull分布,基于Von-Mises准则提出了新的疲劳寿命预测方法,并利用该方法分别求出失效概率10%、50%和90%对应的疲劳寿命.为验证该方法,将计算结果与SWT模型、FS模型和Manson-Coffin方程的计算结果进行对比,结果表明该方法的预测精度较高.

基于混合双参数Weibull分布的冬夏两季香港地区某地的行人风环境舒适度分析

城市的密集建筑会影响周边区域风环境,甚至产生行人风环境问题。研究了香港地区气象条件,对比了双参数Weibull分布和混合双参数Weibull分布,结果表明混合双参数Weibull分布更加适合香港地区的气象数据;根据夏季以及冬季不同的情况,分析了夏季与冬季的行人风环境。在夏季,一号和二号建筑之间的空地有不舒适的区域,在冬季,行人风环境舒适度整体较好。

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.

结合改进Weibull时间函数的开采沉陷动态预测模型

煤炭开采引起的地表沉陷是一个多维动态变化过程,动态预测可以获取采空区上方任意位置、时刻的形变大小,对保护地面基础设施和人民生命安全具有重要意义。为实现地表沉陷的动态预测,针对Weibull时间函数模型结构复杂、参数较多等不足,基于开采沉陷相关理论,建立了仅含一个模型参数,且可以准确描述地表点下沉量、下沉速度、下沉加速度的改进Weibull时间函数模型。在此基础上,结合已有的地表沉陷盆地模型,建立了一种新的开采沉陷动态预测模型,详细阐述了模型参数的确定方法及其对沉陷盆地形态的影响,并结合某矿313工作面和3214工作面实测数据验证了模型的预测精度和适用性。结果表明:改进的Weibull时间函数模型最大均方根误差为52 mm,最大相对误差为2.1%,较改进前分别提高了60.3%和64.4%;开采沉陷动态预测模型预测的下沉曲线形态和实测下沉曲线形态一致,最大均方根误差为17 mm,最大相对误差为1.76%,表明该模型可以预测地表沉陷过程,具有较好的适用性和可靠性。该研究结果可为矿区地表沉陷动态预测提供参考。

基于改进Weibull模型的高强缝合锚钉缝线强度预测

为消除缝合锚钉缝线在使用过程中存在断裂的风险,以8.3 tex超高分子量聚乙烯纤维为原材料,采用编织工艺制备了单层编织缝线和轴向衬纱双层编织缝线。为了研究其力学性能,选择8、16、24、32、40、48 mm隔距对单纤维的断裂强力进行测试,选择50、200 mm隔距对8.3 tex复丝的断裂强力进行测试,选择200 mm隔距对单层编织缝线和轴向衬纱双层编织缝线的断裂强力进行测试。对纤维的直径和缝线中纤维与轴向夹角的角度进行测量。采用两参数Weibull模型和改进Weibull模型对单纤维、8.3 tex复丝和单层编织缝线的断裂强度进行预测。结果表明:单层编织缝线的断裂强力为299.8 N,轴向衬纱双层编织缝线的断裂强力高达393.0 N。对8.3 tex复丝和单层编织缝线的断裂强度进行预测,改进Weibull模型的预测值准确度高。高强骨锚钉缝线的强力比同类型医用缝线更高,改进Weibull模型可对高强缝合锚钉缝线的强力进行精准预测,实现了从单纤维到复丝再到纱线的断裂强度预测,可为医用缝线结构设计和力学性能分析提供理论依据。

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。

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.

Lithium-ion cell inconsistency analysis based on three-parameter Weibull probability model

The inconsistency of lithium-ion cells degrades battery performance,lifetime and even safety.The complexity of the cell reaction mechanism causes an irregular asymmetrical distribution of various cell parameters,such as capacity and internal resistance,among others.In this study,the Newman electrochemical model was used to simulate the 1 C discharge curves of 100 LiMn2 O4 pouch cells with parameter variations typically produced in manufacturing processes,and the three-parameter Weibull probability model was used to analyze the dispersion and symmetry of the resulting discharge voltage distributions.The results showed that the dispersion of the voltage distribution was related to the rate of decrease in the discharge voltage,and the symmetry was related to the change in the rate of voltage decrease.The effect of the cells’capacity dominated the voltage distribution thermodynamically during discharge,and the phase transformation process significantly skewed the voltage distribution.The effects of the ohmic drop and polarization voltage on the voltage distribution were primarily kinetic.The presence of current returned the right-skewed voltage distribution caused by phase transformation to a more symmetrical distribution.Thus,the Weibull parameters elucidated the electrochemical behavior during the discharge process,and this method can guide the prediction and control of cell inconsistency,as well as detection and control strategies for cell management systems.

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。

开采沉陷动态预测时间函数参数变化规律研究——以Weibull为例

针对开采沉陷动态预测模型中时间函数参数主要以最大下沉点的下沉时间序列为基础反演获取,在工作面上方空间位置变化规律研究不足的问题;依据工作面推进过程中覆岩受力、垮落情况,在平面方向上将采空区分为竖向整体受压区、中间区、动态完全区3个区间;以Weibull时间函数为例,分析了动态预测m、k 2个参数的含义、空间分布规律及特点,并构建2个参数的分区数学模型及选取准则;分别以实测最终值、概率积分法预测值为基准,通过实例验证了其正确性,丰富了开采沉陷动态预测参数研究。

基于Weibull分布和MOV脉冲电流特性的智能SPD脉冲电流寿命评估方法

浪涌保护器(SPD)是低压电力线路中用于限制过电压,泄放电涌电流的重要电气装置。随着物联网的发展,传统的SPD逐步发展成为具有在线监测工作状态、故障诊断、寿命预测等功能的智能SPD。由于SPD的寿命与其核心元件金属氧化物压敏电阻(MOV)的寿命密切相关,文中基于Weibull分布并结合MOV的脉冲电流寿命特性,通过试验得到了MOV在不同冲击下的特性方程。根据建立的脉冲电流寿命特性方程和运行中SPD的脉冲电流监测数据,提出了一种SPD剩余寿命评估方法,为智能SPD的不断发展提供了理论支持。

基于Weibull时间函数的采煤沉陷区地表动态沉陷预测模型

煤矿地表开采沉陷是一个复杂的时空过程,是矿山开采沉陷重点解决的问题。本文将时间参数引入到地表移动变形的动态预计中,分析了Weibull模型及其描述地表动态沉陷规律的适用性,并进行了参数分析,建立了地表动态沉陷预测模型。进行了实例分析。研究结果表明,参数n和k是该函数模型的重要参数,对描述地表动态移动变形量较为敏感;通过运用本文提出的地表动态移动变形预计模型,计算得到的地表下沉值相对误差均在7.0%以内,预计结果与实测结果较为吻合,预测模型可靠,预测结果可为相关减损措施的制定提供参考。

排序集抽样下Weibull分布的产品可靠度估计

排序集抽样方法用于样本单元排序容易但测量困难的情形。产品可靠度是描述产品可靠性的重要度量指标,Weibull分布在可靠性试验中占有非常重要的地位。为了提高Weibull分布产品可靠度的估计效率,本文采用排序集抽样方法,研究了产品可靠度的极大似然估计,计算了Weibull分布形状参数和尺度参数的Fisher信息阵,证明了极大似然估计量的渐近正态性,并给出了新估计量的渐近方差。渐近相对效率和模拟相对效率的计算结果表明:排序集抽样下极大似然估计量的估计效率一致高于简单随机抽样下极大似然估计量。最后,单碳纤维强度数据的实际分析结果验证了排序集抽样方法的高效率性。