Bayesian enhanced decision making for deteriorating repairable systems with preventive maintenance

Since a system and its components usually deteriorate with age, preventive maintenance (PM) is often performed to restore or keep the function of a system in a good state. Furthermore, PM is capable of improving the health condition of the system and thus prolongs its effective age. There has been a vast amount of research to find optimal PM policies for deteriorating repairable systems. However, such decisions involve numerous uncertainties and the analyses are typically difficult to perform because of the scarcity of data. It is therefore important to make use of all information in an efficient way. In this article, a Bayesian decision model is developed to determine the optimal number of PM actions for systems which are maintained according to a periodic PM policy. A non‐homogeneous Poisson process with a power law failure intensity is used to describe the deteriorating behavior of the repairable system. It is assumed that the status of the system after a PM is somewhere between as good as new for a perfect repair and as good as old for a minimal repair, and for failures between two preventive maintenances, the system undergoes minimal repairs. Finally, a numerical example is given and the results of the proposed approach are discussed after performing sensitivity analysis. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Optimal production and maintenance policy for imperfect production systems

A joint optimization of the production run length and preventive maintenance (PM) policy is studied for a deteriorating production system where the in‐control period follows a general probability distribution with non‐decreasing failure rate. In the literature, the sufficient conditions for the optimality of the equal‐interval PM schedule is explored to derive an optimal production run length and an optimal number of PM actions. Nevertheless, an exhaustive search may arise. In this study, based on the assumption that the conditions for the optimality of the equal‐interval PM schedule hold, we derive some structural properties for the optimal production/PM policy, which increases the efficiency of the solution procedure. These analyses have implications for the practical application of the production/PM model to be more available in practice. A numerical example of gamma shift distribution with non‐decreasing failure rates is used to illustrate the solution procedure, leading to some insight into the management process. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Optimal joint preventive maintenance and production policies

We study joint preventive maintenance (PM) and production policies for an unreliable production‐inventory system in which maintenance/repair times are non‐negligible and stochastic. A joint policy decides (a) whether or not to perform PM and (b) if PM is not performed, then how much to produce. We consider a discrete‐time system, formulating the problem as a Markov decision process (MDP) model. The focus of the work is on the structural properties of optimal joint policies, given the system state comprised of the system's age and the inventory level. Although our analysis indicates that the structure of optimal joint policies is very complex in general, we are able to characterize several properties regarding PM and production, including optimal production/maintenance actions under backlogging and high inventory levels, and conditions under which the PM portion of the joint policy has a control‐limit structure. In further special cases, such as when PM set‐up costs are negligible compared to PM times, we are able to establish some additional structural properties. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

On‐line parameter estimation for a partially observable system subject to random failure

In this paper, we study the on‐line parameter estimation problem for a partially observable system subject to deterioration and random failure. The state of the system evolves according to a continuous time homogeneous Markov process with a finite state space. The system state is not observable, except for the failure state. The information related to the system state is available at discrete times through inspections. A recursive maximum likelihood (RML) algorithm is proposed for the on‐line parameter estimation of the model. The RML algorithm proposed in the paper is considerably faster and easier to apply than other RML algorithms in the literature, because it does not require projection into the constraint domain and calculation of the gradient on the surface of the constraint manifolds. The algorithm is illustrated by an example using real vibration data. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

模糊推理在软件维护性评估和预测中的应用

摘要：在基于活动的质量模型维护性分析方法基础上,对贝叶斯方法进行了扩展,将模糊推理技术与现有的贝叶斯方法进行比较,开发了一个基于模糊推理的系统来对软件维护性进行量化评估和预测,描述了模糊技术在维护性评估和预测准确度方面的优势．     

Bayesian testing strategies for software with an operational profile

We consider a software reliability model where the failure rate of each fault depends on the specific operation performed. The software is tested in a given sequence of test cases for fixed durations of time to collect data on failure times. We present a Bayesian analysis of software failure data by treating the initial number of faults as a random variable. Our analysis relies on the Markov Chain Monte Carlo methods and is used for developing optimal testing strategies in an adaptive manner. Two different models involving individual and common faults are analyzed. We illustrate an implementation of our approach by using some simulated failure data. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:747–763, 2001     

Asymptotic properties of imperfect repair models and estimation of repair efficiency

The aim of this articles is to study the asymptotic behavior of two imperfect repair models, called Arithmetic Reduction of Intensity and Arithmetic Reduction of Age models. These models have been proposed by Doyen and Gaudoin (Reliab Eng Syst Safe 84 (2004) 45–56) and include many usual virtual age models. First, it is proved that the failure intensity of these models is asymptotically almost surely equivalent to a deterministic increasing function with a cumulative error proportional to a logarithm. Second, the almost sure convergence and asymptotic normality of several estimators of repair efficiency are derived, when the wear‐out process without repair is known. Finally, the coverage rate of the asymptotic confidence intervals issued from those estimators is empirically studied. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

串联系统预防维修周期优化策略研究(英文)

针对串联系统建立了基于可靠性约束的预防性维修优化模型,该模型充分考虑到预防维修可以提高系统可靠性的同时,其故障率会随着维修次数的增加而上升,引入役龄回退因子对预防维修活动前后系统性能的动态变化进行了描述.通过实例验证了该优化模型的正确性与可用性,对模型作进一步的扩展,还可用于更一般复杂的串并联系统.     

Application of Markov renewal theory and semi-Markov decision processes in maintenance modeling and optimization of multi-unit systems

In this paper, a condition-based maintenance model for a multi-unit production system is proposed and analyzed using Markov renewal theory. The units of the system are subject to gradual deterioration, and the gradual deterioration process of each unit is described by a three-state continuous time homogeneous Markov chain with two working states and a failure state. The production rate of the system is influenced by the deterioration process and the demand is constant. The states of the units are observable through regular inspections and the decision to perform maintenance depends on the number of units in each state. The objective is to obtain the steady-state characteristics and the formula for the long-run average cost for the controlled system. The optimal policy is obtained using a dynamic programming algorithm. The result is validated using a semi-Markov decision process formulation and the policy iteration algorithm. Moreover, an analytical expression is obtained for the calculation of the mean time to initiate maintenance using the first passage time theory.     

A partial characterization of the optimal ordering/rationing policy for a periodic review system with two demand classes and backordering

We consider a finite horizon periodic review, single product inventory system with a fixed setup cost and two stochastic demand classes that differ in their backordering costs. In each period, one must decide whether and how much to order, and how much demand of the lower class should be satisfied. We show that the optimal ordering policy can be characterized as a state dependent (s,S) policy, and the rationing structure is partially obtained based on the subconvexity of the cost function. We then propose a simple heuristic rationing policy, which is easy to implement and close to optimal for intensive numerical examples. We further study the case when the first demand class is deterministic and must be satisfied immediately. We show the optimality of the state dependent (s,S) ordering policy, and obtain additional rationing structural properties. Based on these properties, the optimal ordering and rationing policy for any state can be generated by finding the optimal policy of only a finite set of states, and for each state in this set, the optimal policy is obtained simply by choosing a policy from at most two alternatives. An efficient algorithm is then proposed. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

基于高斯和粒子滤波的AUV水下地形辅助导航方法

针对自主式水下无人航行器(AUV)长时间潜航时的精确导航定位需求,以多波束测深系统为水下地形测量设备,提出一种基于贝叶斯估计的AUV水下地形匹配导航模型。针对贝叶斯滤波后验概率密度函数的求解问题,用高斯混合密度函数近似状态的后验概率密度函数,提出了基于高斯和粒子滤波的水下地形匹配导航方法。基于多波束测深数据的回放式仿真试验表明,提出的方法可以有效近似地形匹配的贝叶斯滤波模型,具有良好的实用性。     

精度鉴定与试验决策系统

本文综合运用序贯分析方法和Ｂａｙｅｓ方法,提出用序贯Ｂａｙｅｓ决策进行战略导弹的精度鉴定和试验设计,序贯Ｂａｙｅｓ决策中的损失函数不仅考虑了决策损失,还考虑了试验费用,这样即可将鉴定方法与试验方法结合起来考虑,给出最佳鉴定方案及试验次数。     

求解不确定型车辆路径问题的弱鲁棒优化方法

为降低鲁棒优化模型最优解的保守性,以最小化违约车辆数和总惩罚成本为目标,建立针对旅行时间不确定的开放式车辆路径问题的弱鲁棒优化模型。对于不确定数据集的每个取值,该模型的最优解可以使其目标函数值始终不超过某数值,进而改善最优解的保守性。为提高启发式算法发现最优解的概率,提出一种自设计遗传算法对模型进行求解,其主要思想是利用粒子群算法搜索出可使遗传算法预期产生最好解的算法要素,并将其进行组合,从而产生新的遗传算法。采用新产生的遗传算法对模型继续求解,输出最好解。计算结果表明:与以往的鲁棒优化方法相比,弱鲁棒优化方法的最优解的保守性显著降低。     

连续动态贝叶斯网络实现多传感器融合跟踪

利用多传感器数据进行目标跟踪,关键是怎样将多传感器的数据合理应用来对系统的状态做出最佳估计。提出应用连续动态贝叶斯网络的方法,结合卡尔曼滤波器模型,实现用多传感器数据进行目标跟踪的方法,并对算法进行了推导和验证。仿真结果证明了提出的多传感器数据互相修正融合滤波方法具有良好的滤波效果,并能够弥补传感器数据缺失和抑制脉冲噪声。     

装备研制中的Bayesian网及其应用

针对装备研制过程中产生的大量试验和调试数据,提出采用Bayesian网挖掘各组成单元间的依赖关系,并对Bayesian网学习中基于信息论的方法进行了改进,使确定网络拓扑结构的过程更加客观.学习得到Bayesian网后,分析了其在失效源判定和发现设计缺陷等方面的应用.     

结合全局与局部信息的主动轮廓分割模型

针对传统的基于区域的主动轮廓模型在分割灰度不均匀图像和噪声图像存在效果不佳的问题,提出结合全局项与局部项的主动轮廓分割模型。全局项由CV(Chan-Vese)模型的保真项构成,局部项的构建考虑局部区域信息的同时引入反映图像灰度特性的局部熵信息。依据图像灰度的特点,选择合理的全局项和局部项参数,并加入正则项保证曲线在演化过程中保持平滑,保障分割结果的可靠性。通过变分水平集方法最小化能量泛函,依据梯度下降流迭代更新水平集,完成曲线演化。采用模拟图像和实际图像进行实验分析,结果表明,所提出的结合全局项和局部项的主动轮廓模型可以高效地分割噪声严重以及灰度分布不均匀的图像。     

A stochastic model for burn‐in procedures in accelerated environment

Burn‐in procedure is a manufacturing technique that is intended to eliminate early failures of system or product. Burning‐in a component or system means to subject it to a period of use prior to being used in field. Generally, burn‐in is considered expensive and so the length of burn‐in is typically limited. Thus, burn‐in is most often accomplished in an accelerated environment in order to shorten the burn‐in process. A new failure rate model for an accelerated burn‐in procedure, which incorporates the accelerated ageing process induced by the accelerated environmental stress, is proposed. Under a more general assumption on the shape of failure rate function of products, which includes the traditional bathtub‐shaped failure rate function as a special case, upper bounds for optimal burn‐in time will be derived. A numerical example will also be given for illustration. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Periodic replacement when minimal repair costs vary with time

A policy of periodic replacement with minimal repair at failure is considered for a complex system. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed at any intervening system failures. The cost of a minimal repair to the system is assumed to be a nonde-creasing function of its age. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the system. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited in the case where the system life distribution is strictly increasing failure rate (IFR).     

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     

基于风险评估的检测与修理决策模型

研究了基于故障风险的检测与维修策略，运用威布尔比例风险模型建立系统故障率与工作时间及所处状态的关系。分析了两类基于间接状态信息维修决策的风险，建立了系统检测及维修策略的决策树，通过比较检测与不检测情况下的期望费用确定最优的检测间隔。算例表明，所提出的方法能够有效控制系统运行风险，降低系统运行费用。