Preservation of stochastic orders for random minima and maxima,with applications

It is shown, in this note, that the right spread order and the increasing convex order are both preserved under the taking of random maxima, and the total time on test transform order and the increasing concave order are preserved under the taking of random minima. Some inequalities and preservation properties in reliability and economics are given as applications. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

由新比旧好元件组成的指数寿命系统的特性研究

文中研究了由独立的新比旧好元件组成的指数寿命系统,证明了:(i)对单调系统,它本质上是由指数寿命的元件串联而成;(ii)对系统的寿命是元件寿命的情形,除了一个元件是指数的外,其余元件的寿命分布均在零处退化。     

On the behavior and shape of mixture failure rates from a family of IFR Weibull distributions

Populations of many types of component are heterogeneous and often consist of a small number of different subpopulations. This is called a mixture and it arises in a number of situations. For example, a majority of products in industrial populations are mixtures of defective items with shorter lifetimes and standard items with longer lifetimes. It is a well‐known result that distributions with decreasing failure rates are closed under mixture. However, mixtures of distributions with increasing failure rates are not easily classifiable. If the subpopulations involved in the mixture have increasing failure rates, there might be some upward movement in the mixture and later a general downward pull towards the strongest component. Little work has been done in describing the shape of mixture failure rates when all subpopulations do not have decreasing failure rate. In this paper, we present general results that describe the shape and behavior of a failure rate of a mixture obtained from two Weibull subpopulations with strictly increasing failure rates. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Weak aging properties for coherent systems with statistically dependent component lifetimes

As a relevant topic in reliability theory, the preservation of aging properties under the formation of various coherent structures contributes to improving system performance through better structure design and more effective system maintenance. The classical research in this line usually focuses upon coherent systems with independent component lifetimes. Recently, some authors discussed the preservation of IFR, NBU, and DMRL in the setting of dependent component lifetimes. This paper further investigates sufficient conditions for coherent systems with dependent component lifetimes to preserve aging properties including NBUC, NBU (2), DMRL, and their dual versions. Some examples are presented to illustrate coherent structures and typical copula functions fulfilling the present sufficient conditions as well.     

Improving series and parallel systems through mixtures of duplicated dependent components

We discuss suitable conditions such that the lifetime of a series or of a parallel system formed by two components having nonindependent lifetimes may be stochastically improved by replacing the lifetimes of each of the components by an independent mixture of the individual components' lifetimes. We also characterize the classes of bivariate distributions where this phenomenon arises through a new weak dependence notion. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Optimal burn‐in procedure for periodically inspected systems

Burn‐in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, we study burn‐in procedure for a system that is maintained under periodic inspection and perfect repair policy. Assuming that the underlying lifetime distribution of a system has an initially decreasing and/or eventually increasing failure rate function, we derive upper and lower bounds for the optimal burn‐in time, which maximizes the system availability. Furthermore, adopting an age replacement policy, we derive upper and lower bounds for the optimal age parameter of the replacement policy for each fixed burn‐in time and a uniform upper bound for the optimal burn‐in time given the age replacement policy. These results can be used to reduce the numerical work for determining both optimal burn‐in time and optimal replacement policy. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Averaging frameworks for simulation optimization with applications to simulated annealing

We present two frameworks for designing random search methods for discrete simulation optimization. One of our frameworks is very broad (in that it includes many random search methods), whereas the other one considers a special class of random search methods called point‐based methods, that move iteratively between points within the feasible region. Our frameworks involve averaging, in that all decisions that require estimates of the objective function values at various feasible solutions are based on the averages of all observations collected at these solutions so far. Also, the methods are adaptive in that they can use information gathered in previous iterations to decide how simulation effort is expended in the current iteration. We show that the methods within our frameworks are almost surely globally convergent under mild conditions. Thus, the generality of our frameworks and associated convergence guarantees makes the frameworks useful to algorithm developers wishing to design efficient and rigorous procedures for simulation optimization. We also present two variants of the simulated annealing (SA) algorithm and provide their convergence analysis as example application of our point‐based framework. Finally, we provide numerical results that demonstrate the empirical effectiveness of averaging and adaptivity in the context of SA. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Inventory competition with yield reliability improvement

This article studies the inventory competition under yield uncertainty. Two firms with random yield compete for substitutable demand: If one firm suffers a stockout, which can be caused by yield failure, its unsatisfied customers may switch to its competitor. We first study the case in which two competing firms decide order quantities based on the exogenous reliability levels. The results from the traditional inventory competition are generalized to the case with yield uncertainty and we find that quantity and reliability can be complementary instruments in the competition. Furthermore, we allow the firms to endogenously improve their yield reliability before competing in quantity. We show that the reliability game is submodular under some assumptions. The results indicate that the competition in quantity can discourage the reliability improvement. With an extensive numerical study, we also demonstrate the robustness of our analytical results in more general settings. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 107–126, 2015     

定应变作用下NEPE推进剂老化特性及寿命预估研究

为考察定应变作用下NEPE推进剂的老化特性,研究了20%定应变作用下NEPE推进剂贮存老化过程中力学性能、凝胶性能和界面性能的变化.研究结果表明:定应变作用下NEPE推进剂在贮存老化过程中最大抗拉强度降低,最大延伸率变化较小,其老化失效主要表现为强度的失效;定应变下NEPE推进剂的凝胶百分数和粘附功随老化时间的延长而降低,NEPE推进剂粘合剂基体的降解断裂和界面的"脱湿"是其主要的老化机理;定应变下NEPE推进剂的力学性能与细观性能的相关性研究表明,最大抗拉强度与凝胶百分数和粘附功存在相关关系,计算了其关系式,建立了由细观性能评估推进剂宏观力学性能的方法;选择最大抗拉强度下降30%时失效,20%定应变下NEPE推进剂的贮存寿命为8.3年.     

模糊随机变量的模糊概率特征的性质

应用模糊数理论 ,给出了模糊随机变量的数学期望和模糊随机变量的方差的定义 ,并研究讨论了模糊随机变量的数学期望和模糊随机变量的方差的性质。研究结果进一步丰富和完善了模糊随机变量理论。     

Optimal redesign decisions through failure rate estimates

To reduce the time-to-market of newly developed systems, manufacturers increasingly adopt strategies where systems are brought to market while system field reliability is still uncertain. These systems are typically sold under performance-based contracts, which incentivizes potential customers to invest in them despite reliability uncertainty. Such contracts make the manufacturer (partly) responsible for the availability of the system. Subsequently, when field reliability is lower than anticipated, the manufacturer may choose to redesign the system to avoid high contract penalties. Redesign is a costly effort which may substantially increase field reliability. Deciding when to redesign is challenging, especially because the initial failure rate estimate by the system's engineers is refined over time as failure data accrues. We propose a model that endogenizes the failure rate updating to analyze this tactical redesign decision. We study additive and multiplicative redesigns and show that the optimal policy has a control limit structure. We benchmark our optimal policy against a static counterpart numerically, and conclude that basing redesign decisions on the updated estimate of the failure rate can substantially reduce costs.     

Numerical investigation of the failure mechanism of cubic concrete specimens in SHPB tests

Cylindrical specimens are commonly used in Split Hopkinson pressure bar (SHPB) tests to study the uniaxial dynamic properties of concrete-like materials.In recent years,true tri-axial SHPB equipment has also been developed or is under development to investigate the material dynamic properties under tri-axial impact loads.For such tests,cubic specimens are needed.It is well understood that static material strength obtained from cylinder and cube specimens are different.Conversion factors are obtained and adopted in some guidelines to convert the material strength obtained from the two types of specimens.Previous uniaxial impact tests have also demonstrated that the failure mode and the strain rate effect of cubic specimens are very different from that of cylindrical ones.However,the mechanical background of these findings is unclear.As an extension of the previous laboratory study,this study performs numerical SHPB tests of cubic and cylindrical concrete specimens subjected to uniaxial impact load with the validated numerical model.The stress states of cubic specimens in relation to its failure mode under different strain rates is analyzed and compared with cylindrical specimens.The detailed analyses of the numerical simulation results show that the lateral inertial confinement of the cylindrical specimen is higher than that of the cubic specimen under the same strain rates.For cubic specimen,the corners are more severely damaged because of the lower lateral confinement and the occurrence of the tensile radial stress which is not observed in cylindrical specimens.These results explain why the dynamic material strengths obtained from the two types of specimens are different and are strain rate dependent.Based on the simulation results,an empirical formula of conversion factor as a function of strain rate is proposed,which supplements the traditional conversion factor for quasi-static material strength.It can be used for transforming the dynamic compressive strength from cylinders to cubes obtained from impact tests at different strain rates.     

考虑多轴应力与共振影响的随机振动疲劳寿命预测

目前工程上计算结构随机疲劳寿命时,仍经常采用基于单轴拉-压疲劳寿命(Stress-Number of cycles,S-N)曲线的应力寿命方法。虽然使用简单方便,但这种方法不仅忽视了单轴S-N曲线且不能准确反映结构在多轴应力状态下的疲劳,还忽略了随机振动中共振对结构疲劳寿命的影响,因此该方法在预测结构在随机振动下的疲劳寿命时与实际寿命往往有较大误差。对此引入三轴因子来反映结构在随机振动下的多轴应力状态,同时推广得到其在频域上的表达式,并在此基础上引入非线性函数,提出了一个新的随机振动疲劳损伤参量——多轴振动因子。新的损伤参量不仅同时考虑了结构随机振动下的多轴应力状态与共振对疲劳寿命的影响,而且该损伤参量形式简单,便于工程应用。利用新的随机振动疲劳损伤参量,得到了适用于随机振动下的多轴S-N曲线,从而建立了一种新的随机振动疲劳寿命预测方法。通过对7075-T6和LY12CZ铝合金缺口试件的随机振动疲劳寿命进行预测,结果表明该方法较准确地预测了两种缺口试件随机振动下的疲劳寿命。     

Discrete stochastic optimization using variants of the stochastic ruler method

We present two random search methods for solving discrete stochastic optimization problems. Both of these methods are variants of the stochastic ruler algorithm. They differ from our earlier modification of the stochastic ruler algorithm in that they use different approaches for estimating the optimal solution. Our new methods are guaranteed to converge almost surely to the set of global optimal solutions under mild conditions. We discuss under what conditions these new methods are expected to converge faster than the modified stochastic ruler algorithm. We also discuss how these methods can be used for solving discrete optimization problems when the values of the objective function are estimated using either transient or steady‐state simulation. Finally, we present numerical results that compare the performance of our new methods with that of the modified stochastic ruler algorithm when applied to solve buffer allocation problems. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Adaptive random search for continuous simulation optimization

We present, analyze, and compare three random search methods for solving stochastic optimization problems with uncountable feasible regions. Our adaptive search with resampling (ASR) approach is a framework for designing provably convergent algorithms that are adaptive and may consequently involve local search. The deterministic and stochastic shrinking ball (DSB and SSB) approaches are also convergent, but they are based on pure random search with the only difference being the estimator of the optimal solution [the DSB method was originally proposed and analyzed by Baumert and Smith]. The three methods use different techniques to reduce the effects of noise in the estimated objective function values. Our ASR method achieves this goal through resampling of already sampled points, whereas the DSB and SSB approaches address it by averaging observations in balls that shrink with time. We present conditions under which the three methods are convergent, both in probability and almost surely, and provide a limited computational study aimed at comparing the methods. Although further investigation is needed, our numerical results suggest that the ASR approach is promising, especially for difficult problems where the probability of identifying good solutions using pure random search is small. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

基于排队论的反舰导弹突防概率研究

根据水面舰艇对海导弹攻击中作战指挥的需要,提出了基于排队论中随机服务理论的反舰导弹突防概率解算模型.综合研究了目标舰艇编队采用各种手段进行抗击帮助条件下,反舰导弹突防概率的计算问题,并且结合想定装备参数进行了算例分析.为指挥员实施导弹攻击提供辅助决策和量化支持.     

随机-非概率模型下的船体结构屈服强度可靠性分析

针对在役舰船船体载荷、材料属性的随机特性和实船勘验得出的腐蚀损伤下船体抗力区间特性,提出一种基于随机概率理论和区间非概率理论的随机-非概率可靠性分析模型,分别从区间变量随机化和随机变量区间化两个角度给出该模型的可靠性指标求解方法。基于该模型对某舰船船体结构屈服强度进行可靠性分析,结果表明:该模型既体现了结构变量的客观不确定性又减弱了评估结果的盲目保守性,对于既含有随机变量又含有区间变量的在役舰船的可靠性评估具有很强的适用性。     

Assessing the value of demand sharing in supply chains

We consider the problem of assessing the value of demand sharing in a multistage supply chain in which the retailer observes stationary autoregressive moving average demand with Gaussian white noise (shocks). Similar to previous research, we assume each supply chain player constructs its best linear forecast of the leadtime demand and uses it to determine the order quantity via a periodic review myopic order‐up‐to policy. We demonstrate how a typical supply chain player can determine the extent of its available information in the presence of demand sharing by studying the properties of the moving average polynomials of adjacent supply chain players. The retailer's demand is driven by the random shocks appearing in the autoregressive moving average representation for its demand. Under the assumptions we will make in this article, to the retailer, knowing the shock information is equivalent to knowing the demand process (assuming that the model parameters are also known). Thus (in the event of sharing) the retailer's demand sequence and shock sequence would contain the same information to the retailer's supplier. We will show that, once we consider the dynamics of demand propagation further up the chain, it may be that a player's demand and shock sequences will contain different levels of information for an upstream player. Hence, we study how a player can determine its available information under demand sharing, and use this information to forecast leadtime demand. We characterize the value of demand sharing for a typical supply chain player. Furthermore, we show conditions under which (i) it is equivalent to no sharing, (ii) it is equivalent to full information shock sharing, and (iii) it is intermediate in value to the two previously described arrangements. Although it follows from existing literature that demand sharing is equivalent to full information shock sharing between a retailer and supplier, we demonstrate and characterize when this result does not generalize to upstream supply chain players. We then show that demand propagates through a supply chain where any player may share nothing, its demand, or its full information shocks (FIS) with an adjacent upstream player as quasi‐ARMA in—quasi‐ARMA out. We also provide a convenient form for the propagation of demand in a supply chain that will lend itself to future research applications. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 515–531, 2014     

数学模拟中产生正态随机数的方法研究

针对在火灾烟气和其他气态物质扩散的模拟研究中经常遇到正态分布的随机数的产生问题进行研究,探讨了特殊分布随机数的产生方法。特别给出了正态分布随机数的产生算法及其代码,并进行了验证。结果表明了所述产生正态随机数算法的可行性和可靠性。     

Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems

We consider the classical problem of whether certain classes of lifetime distributions are preserved under the formation of coherent systems. Under the assumption of independent and identically distributed (i.i.d.) component lifetimes, we consider the NBUE (new better than used in expectation) and NWUE (new worse than used in expectation) classes. First, a necessary condition for a coherent system to preserve the NBUE class is given. Sufficient conditions are then obtained for systems satisfying this necessary condition. The sufficient conditions are satisfied for a collection of systems which includes all parallel systems, but the collection is shown to be strictly larger. We also prove that no coherent system preserves the NWUE class. As byproducts of our study, we obtain the following results for the case of i.i.d. component lifetimes: (a) the DFR (decreasing failure rate) class is preserved by no coherent systems other than series systems, and (b) the IMRL (increasing mean residual life) class is not preserved by any coherent systems. Generalizations to the case of dependent component lifetimes are briefly discussed.