A load share model for non-identical components of a k-out-of-m system

We consider a k-out-of-m load sharing system when the lifetimes of the components are not necessarily identically distributed random variables. For such systems, a model for the load sharing phenomenon through the exponentiated conditional survival functions of ordered failure times is proposed. This model is more general than the load sharing model with identically distributed component lifetimes and leads to a different family of distributions for ordered random variables. A general expression for the reliability of the system is given. The computations of the reliability for a two component parallel load sharing system corresponding to the exponential and Weibull distributions are discussed. For illustrative purpose, we discuss the inference procedures for a two component parallel load sharing system corresponding to the exponential distributions. A simulation study is carried out to assess the proposed estimation and testing procedures. The applicability of the proposed load sharing model is shown through two data sets.     

Assessing the reliability of a nanocomponent using nanocrack growth

In nanoscience and nanotechnology, much attention has been given to the dual problem of designing nanocomponents with novel physical properties and how such nanocomponents can be fabricated. Receiving less attention has been the question of the nanocomponent's reliability; how does a nanocomponent fail and how long does a nanocomponent survive under typical operating conditions? High reliability is necessary to guarantee the advancement and utilization of nanocomponents due to the fact that they account for a high proportion of costs of newly designed nanosystems as well as multiscale systems. A nanocomponent is a component that is made of atoms, and its reliability is determined by these atoms. There are situations where it is hard or impossible to extract information from a nanocomponent about its relationship to its atoms. In this article, we assess the nanocomponent's reliability by using its physical properties. Specifically, it is known that nanocrack growth involves considerable statistical variability and such variability should be accounted for assessing growth. In this paper, we first provide a stochastic nanocrack growth model and then evaluate the reliability of a nanocomponent based on this model. Various properties of this model are obtained. We also evaluate the reliability of a nanocomponent under different assumptions on our proposed growth model. This paper is a modification of the extensive literature on modeling fatigue cracks in materials on a larger scale, applied to nanoscale where growth is not a function of cumulative stress on the component but related to the time to first exceedance of a threshold. Copyright © 2013 John Wiley & Sons, Ltd.     

负载分担并联可修系统的可靠性分析

针对负载分担可修的并联系统模型,考虑了控制器可修,修理工多人的情形,并且在将控制器作为关键部件优先维修的规则下,对模型进行了可靠性分析.最后用一个实例,求得一些常见的系统可靠性指标,并结合部件的失效率和修复率进行了深入讨论,在系统不可修时求得其可靠度和平均寿命.     

基于综合重要度的动车组多部件系统机会维修策略研究

针对我国动车组列车现行维修方式,提出基于综合重要度序列的动车组多部件系统机会维修策略,对提高系统可靠度贡献大的关键部件进行准时优先维修。建立部件综合重要度指数计算模型,并依据其对部件维修优先级进行排序。以维修总成本最低为目标计算单部件最优维修周期及时刻,以系统维修总成本最低为目标,以关键部件的维修时刻为系统停机时刻建立考虑重要度的多部件系统机会维修模型。算例选取某型动车组四级修时更换的四部件系统为研究对象,讨论机会维修里程窗的大小及其偏移量对维修效果的影响,对比结果表明,考虑综合重要度的机会维修策略能够在维修费用基本持平的条件下,保证对系统可靠性贡献大的关键部件的可靠性,进而保证系统的整体可靠性。     

Reliability Importance and Invariant Optimal Allocation

The reliability importance of a component is a partial derivative of the system reliability with respect to this component reliability. When all components are i.i.d., the reliability importance is called the B-importance. Relationships between reliability allocation and the reliability importance for general coherent systems are explored. The invariant optimal allocation is an allocation related only to the relative ordering rather than the magnitude of the component reliabilities. A strong heuristic method (LK heuristic) is developed to search for an ideal allocation through the application of the reliability importance.The following conclusions are drawn: if there exists an invariant optimal allocation for a system, the optimal allocation is to assign component reliabilities according to the B-importance ordering. Furthermore, the allocation generated by the LK heuristic is the optimal allocation.     

A general model for consecutive-k-out-of-n: F repairable system with exponential distribution and (k−1)-step Markov dependence

In this paper, a general model for consecutive-k-out-of-n: F repairable system with exponential distribution and (k−1)-step Markov dependence is introduced. The lifetime of a component is an exponential random variable, its parameter depends on the number of consecutive failed components that precede the component. The repair time is also an exponential random variable. A priority repair rule on the basis of the system failure risk is adopted. Then the transition density matrix of the system is determined. Some reliability indices, including the system availability, rate of occurrence of failures and reliability are evaluated accordingly. For the demonstration of the model and methodology, a linear system example and a circular system example are investigated.     

基于系统可靠性的组件综合重要度变化机理分析

重要度理论是一种重要的系统薄弱环节识别和评估方法,被广泛应用于系统可靠性设计优化、维修资源分配、维修决策以及风险分析等领域。本文以组件状态转移率为纽带,分析了组件综合重要度对系统可靠性的影响机理,识别对系统可靠性变化影响最大的组件,综合重要度评估了单位时间内系统可靠性的变化。首先给出综合重要度的定义;其次讨论系统可靠性的组件重要度表示方法;最后在串联和并联系统中,分析综合重要度随着组件状态转移率的变化机理。     

NBUE分布类应力-强度模型的概率上界

研究应力-强度模型的结构的可靠性分析,当元件应力变量分布属于NBUE类,强度变量服从指数分布,给出了应力-强度模型中概率的上界,由此讨论了n个元件组成系统的应力-强度模型概率上界.     

The signal model: A model for competing risks of opportunistic maintenance

This paper presents a competing risks reliability model for a system that releases signals each time its condition deteriorates. The released signals are used to inform opportunistic maintenance. The model provides a framework for the determination of the underlying system lifetime from right-censored data, without requiring explicit assumptions about the type of censoring to be made. The parameters of the model are estimated from observational data by using maximum likelihood estimation. We illustrate the estimation process through a simulation study. The proposed signal model can be used to support decision-making in optimising preventive maintenance: at a component level, estimates of the underlying failure distribution can be used to identify the critical signal that would trigger maintenance of the individual component; at a multi-component system level, accurate estimates of the component underlying lifetimes are important when making general maintenance decisions. The benefit of good estimation from censored data, when adequate knowledge about the dependence structure is not available, may justify the additional data collection cost in cases where full signal data is not available.     

面向任务保障的多组件系统效益优化策略

为了保障系统在执行任务期间高可靠、高效益的运行,从系统效益的角度出发,构建了系统可靠性模型,采用边际效应思想构建了效益重要度,提出了一种面向任务保障的多组件系统效益优化策略。当系统可靠度下降到设定阈值时,计算系统各组件的效益重要度,选择效益重要度最大的组件进行备件分配,如此进行迭代,直到完成任务保障,形成最优的备件分配序列。通过该策略实现了以运行效益最优为目标,以系统可靠度和任务保障时长为约束的备件分配序列。最后,通过数值仿真验证了该策略的可行性。     

Optimization of component reliability in the design phase of capital goods

We introduce a quantitative model to support the decision on the reliability level of a critical component during its design. We consider an OEM who is responsible for the availability of its systems in the field through service contracts. Upon a failure of a critical part in a system during the exploitation phase, the failed part is replaced by a ready-for-use part from a spare parts inventory. In an out-of-stock situation, a costly emergency procedure is applied. The reliability levels and spare parts inventory levels of the critical components are the two main factors that determine the downtime and corresponding costs of the systems. These two levels are decision variables in our model. We formulate the portions of Life Cycle Costs (LCC) which are affected by a component’s reliability and its spare parts inventory level. These costs consist of design costs, production costs, and maintenance and downtime costs in the exploitation phase. We conduct exact analysis and provide an efficient optimization algorithm. We provide managerial insights through a numerical experiment which is based on real-life data.     

Hybrid block replacement and inspection policies for a multi-component system with heterogeneous component lives

Novel replacement policies that are hybrids of inspection maintenance and block replacement are developed for an n identical component series system in which the component parts used at successive replacements arise from a heterogeneous population. The heterogeneous nature of components implies a mixed distribution for time to failure. In these circumstances, a hybrid policy comprising two phases, an early inspection phase and a later wear-out replacement phase, may be appropriate. The policy has some similarity to burn-in maintenance. The simplest policy described is such a hybrid and comprises a block-type or periodic replacement policy with an embedded block or periodic inspection policy. We use a three state failure model, in which a component may be good, defective or failed, in order to consider inspection maintenance. Hybrid block replacement and age-based inspection, and opportunistic hybrid policies will also arise naturally in these circumstances and these are briefly investigated. For the simplest policy, an approximation is used to determine the long-run cost and the system reliability. The policies have the interesting property that the system reliability may be a maximum when the long-run cost is close to its minimum. The failure model implies that the effect of maintenance is heterogeneous. The policies themselves imply that maintenance is carried out more prudently to newer than to older systems. The maintenance of traction motor bearings on underground trains is used to illustrate the ideas in the paper.     

Reliability stochastic optimization for a series system with interval component reliability via genetic algorithm

This paper deals with chance constraints based reliability stochastic optimization problem in the series system. This problem can be formulated as a nonlinear integer programming problem of maximizing the overall system reliability under chance constraints due to resources. The assumption of traditional reliability optimization problem is that the reliability of a component is known as a fixed quantity which lies in the open interval (0, 1). However, in real life situations, the reliability of an individual component may vary due to some realistic factors and it is sensible to treat this as a positive imprecise number and this imprecise number is represented by an interval valued number. In this work, we have formulated the reliability optimization problem as a chance constraints based reliability stochastic optimization problem with interval valued reliabilities of components. Then, the chance constraints of the problem are converted into the equivalent deterministic form. The transformed problem has been formulated as an unconstrained integer programming problem with interval coefficients by Big-M penalty technique. Then to solve this problem, we have developed a real coded genetic algorithm (GA) for integer variables with tournament selection, uniform crossover and one-neighborhood mutation. To illustrate the model two numerical examples have been solved by our developed GA. Finally to study the stability of our developed GA with respect to the different GA parameters, sensitivity analyses have been done graphically.     

A deteriorating cold standby repairable system with priority in use

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. In this system, it is assumed that the working time distributions and the repair time distributions of the two components are both exponential and component 1 is given priority in use. After repair, component 2 is “as good as new” while component 1 follows a geometric process repair. Under these assumptions, using the geometric process and a supplementary variable technique, some important reliability indices such as the system availability, reliability, mean time to first failure (MTTFF), rate of occurrence of failure (ROCOF) and the idle probability of the repairman are derived. A numerical example for the system reliability R(t) is given. And it is considered that a repair-replacement policy based on the working age T of component 1 under which the system is replaced when the working age of component 1 reaches T. Our problem is to determine an optimal policy T^∗ such that the long-run average cost per unit time of the system is minimized. The explicit expression for the long-run average cost per unit time of the system is evaluated, and the corresponding optimal replacement policy T^∗ can be found analytically or numerically. Another numerical example for replacement model is also given.     

The impact of fleet size on performance-based incentive management

Performance-based contracting (PBC) is envisioned to lower the asset ownership cost while ensuring desired system performance. System availability, widely used as a performance metric in such contracts, is affected by multiple factors such as equipment reliability, spares stock, fleet size, and service capacity. Prior studies have either focussed on ensuring parts availability or advocating the reliability allocation during design. This paper investigates a single echelon repairable inventory model in PBC. We focus on reliability improvement and its interaction with decisions affecting service time, taking into account the operating fleet size. The study shows that component reliability in a repairable inventory system is a function of the operating fleet size and service rate. A principal-agent model is further developed to evaluate the impact of the fleet size on the incentive mechanism design. The numerical study confirms that the fleet size plays a critical role in determining the penalty and cost sharing rates when the number of backorders is used as the negative incentive scheme.     

An effective immune based two-phase approach for the optimal reliability-redundancy allocation problem

Highly reliable systems can reduce loss of money and time in practice. System reliability can be enhanced by: (i) increasing component reliabilities and/or (ii) providing redundancy at the component level. A trade-off between these two options is necessary for nonlinear-constrained reliability optimization. The problem of maximizing system reliability through component reliability choices and component redundancy is called as reliability-redundancy allocation problem, and it is a difficult but realistic nonlinear mixed-integer optimization problem. In this paper, under nonlinear constraints of weight, cost, and volume, we propose a new immune based two-phase approach to solve the reliability-redundancy allocation problem. In the first phase, an immune based algorithm (IA) is developed to solve the allocation problem, and in the second phase we present a new procedure to improve the solutions by IA. Numerical results of four benchmark problems are reported and compared. As shown, the solutions by the new proposed approach are all superior to those best solutions by typical approaches in the literature.     

Reliability and covariance estimation of weighted k-out-of-n multi-state systems

In the literature of reliability engineering, reliability of the weighted k-out-of-n system can be calculated using component reliability based on the structure function. The calculation usually assumes that the true component reliability is completely known. However, this is not the case in practical applications. Instead, component reliability has to be estimated using empirical sample data. Uncertainty arises during this estimation process and propagates to the system level. This paper studies the propagation mechanism of estimation uncertainty through the universal generating function method. Equations of the complete solution including the unbiased system reliability estimator and the corresponding unbiased covariance estimator are derived. This is a unified approach. It can be applied to weighted k-out-of-n systems with multi-state components, to weighted k-out-of-n systems with binary components, and to simple series and parallel systems. It may also serve as building blocks to derive estimators of system reliability and uncertainty measures for more complicated systems.     

Reversed hazard function of uncertain lifetime

Reversed hazard function is widely applied in reliability analysis. This paper considers the human uncertainty in a system, and employs uncertain variable to model the lifetime of a component. Concepts of mean residual life and residual entropy are proposed to describe a failed system, and their relationships with the reversed hazard function are discussed. In addition, this paper provides some applications of reversed hazard function to the mean past lifetime and past entropy.     

利用隐蔽的系统寿命数据估计元件的可靠性

考虑由一个成败型元件和一个指数寿命型元件组成的串联系统。本文利用隐蔽的系统一次性检测数据估计元件的可靠性，给出元件可靠性的极大似然估计和区门估计，给出了算例。     

Reliability-based measures and prognostic analysis of a K-out-of-N system in a random environment

In this paper, we study reliability based measures and prognostic problems of a K-out-of-N system in which the failure process of each component depends not only on its intrinsic characteristic but also on its operating environment conditions. The system reliability and the expected remaining useful lifetime are calculated. Under the periodic inspection policy, the system asymptotic availability is derived. We aim at providing explicit expressions for these quantities. The model allows us to incorporate the observation information of the environment in the evaluation of the system performances. Numerical examples show the efficiency and accuracy of our method by comparing with the Monte-Carlo simulations. It is pointed out that the environment condition has significant effect on the system reliability based measures and the system prognostic analysis.