An information‐based burn‐in procedure for minimally repaired items from mixed population

Burn‐in is a method used to eliminate the initial failures in field use. In this paper, we will consider an information‐based burn‐in procedure for repairable items, which is completely new type of burn‐in procedure. By this procedure, based on the operational (failure and repair) history of the items observed during burn‐in procedure, those with poor reliability performance are eliminated. From a probabilistic point of view, this burn‐in procedure utilizes the information contained in the ‘random paths’ of the corresponding point processes. A general formulation of the model will be suggested, and under the suggested framework, two‐stage optimization procedure for determining optimal burn‐in procedures will be studied in detail. Copyright © 2016 John Wiley & Sons, Ltd.     

Objective Bayesian analysis for competing risks model with Wiener degradation phenomena and catastrophic failures

In this paper, the objective Bayesian method is applied to investigate the competing risks model involving both catastrophic and degradation failures. By modeling soft failure as the Wiener degradation process, and hard failures as a Weibull distribution, we obtain the noninformative priors (Jefferys prior and two reference priors) for the parameters. Moreover, we show that their posterior distributions have good properties and we propose Gibbs sampling algorithms for the Bayesian inference based on the Jefferys prior and two reference priors. Some simulation studies are conducted to illustrate the superiority of objective Bayesian method. Finally, we apply our methods to two real data examples and compare the objective Bayesian estimates with the other estimates.     

Bounds to optimal burn‐in and optimal work size

Burn‐in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, we consider the problem of determining the optimal burn‐in time and optimal work size maximizing the long‐run average amount of work saved per time unit in the computer applications. Assuming that the underlying lifetime distribution of the computer has an initially decreasing or/and eventually increasing failure rate function, an upper bound for the optimal burn‐in time is derived for each fixed work size and a uniform (with respect to the burn‐in time) upper bound for the optimal work size is also obtained. Furthermore, it is shown that a non‐trivial lower bound for the optimal burn‐in time can be derived if the underlying lifetime distribution has a large initial failure rate. Copyright © 2005 John Wiley & Sons, Ltd.     

专职修理工多重休假且修理设备可更换的k/n(G)表决系统研究

讨论专职修理工多重休假,修理设备可发生失效且可更换的k/n（G）表决可修系统.当系统中没有故障部件时,专职修理工开始一次休假,在此期间,若有工作部件发生故障,则立即指派普通修理工修理故障部件,一直持续到系统中无故障部件或专职修理工休假回来.利用马尔可夫过程理论和矩阵解法,给出了系统瞬态和稳态下的可用度和故障频度、可靠度、系统首次故障前的平均时间、修理设备处于更换状态的概率等指标的表达式.在此基础上,基于不同的初始条件研究了相关指标随时间的变化情况.最后,特殊情形的讨论验证了所得结果的正确性.     

Flexibility in a Stackelberg leadership with differentiated goods

We study the effects of product differentiation in a Stackelberg model with demand uncertainty for the first mover. We do an ex-ante and ex-post analysis of the profits of the leader and of the follower firms in terms of product differentiation and of the demand uncertainty. We show that even with small uncertainty about the demand, the follower firm can achieve greater profits than the leader, if their products are sufficiently differentiated. We also compute the probability of the second firm having higher profit than the leading firm, subsequently showing the advantages and disadvantages of being either the leader or the follower firm.     

A complex discrete warm standby system with loss of units

A redundant complex discrete system is modelled through phase type distributions. The system is composed of a finite number of units, one online and the others in a warm standby arrangement. The units may undergo internal wear and/or accidental external failures. The latter may be repairable or non-repairable for the online unit, while the failures of the standby units are always repairable. The repairability of accidental failures for the online unit may be independent or not of the time elapsed up to their occurrence. The times up to failure of the online unit, the time up to accidental failure of the warm standby ones and the time needed for repair are assumed to be phase-type distributed. When a non-repairable failure occurs, the corresponding unit is removed. If all units are removed, the system is then reinitialized. The model is built and the transient and stationary distributions determined. Some measures of interest associated with the system, such as transition probabilities, availability and the conditional probability of failure are achieved in transient and stationary regimes. All measures are obtained in a matrix algebraic algorithmic form under which the model can be applied. The results in algorithmic form have been implemented computationally with Matlab. An optimization is performed when costs and rewards are present in the system. A numerical example illustrates the results and the CPU (Central Processing Unit) times for the computation are determined, showing the utility of the algorithms.     

A discrete-time model of failure and repair

In this paper the authors introduce and study a model of failures and repairs of units with discrete lifetimes. They suppose that a unit has a sequence of tasks to perform and that its lifetime is measured by the number of tasks performed before its final, fatal failure. Upon a failure the unit may be repaired (with some probability) and then it may attempt again to perform the current task. The unit dies when (with some probability) a repair cannot be completed. We derive some stochastic comparisons of pairs of such models. The stochastic comparisons are then applied for obtaining results regarding the inheritance of several aging properties by the repaired unit. Various examples illustrate the applicability of the model. Some variants of the model of this paper can be viewed as discrete analogues of the notion of imperfect repair.     

An optimal burn‐in policy based on a degradation model

Burn‐in tests help manufacturers detect defective items and remove them before being sold to customers. In a competitive marketplace, cost is a major consideration and not employing a burn‐in test may result in higher and needless expenses. With this in mind, we consider degradation‐based burn‐in tests in which the degradation path follows a Wiener process and weak items are identified when the process crosses a piecewise linear function. We also study linear functions as a special case of such a piecewise linear barrier. Within this setup, we apply a cost model to determine the optimal burn‐in test. Finally, we discuss an illustrative example using GaAs laser degradation data and present an optimal burn‐in test for it.     

Bayesian inference for the power law process

The power law process has been used to model reliability growth, software reliability and the failure times of repairable systems. This article reviews and further develops Bayesian inference for such a process. The Bayesian approach provides a unified methodology for dealing with both time and failure truncated data. As well as looking at the posterior densities of the parameters of the power law process, inference for the expected number of failures and the probability of no failures in some given time interval is discussed. Aspects of the prediction problem are examined. The results are illustrated with two data examples.     

基于Markov更新过程的城市交通网络级联失效评价模型

根据路段单元状态与其功能之间的关系,给出了路段单元状态的‘失效—非失效’二态表示方法,进一步根据网络中路段单元之间的连接关系,提出了道路交通网络‘级联失效’态的定义及识别方法;利用更新理论及Markov链相关理论,分析了道路交通网络级联失效态—非级联失效态持续时间随机变化的概率分布规律,给出了对假想分布的未知参数进行估计及对假想分布进行假设检验的方法,并提出了以失效次数及转移概率为主要评价参数的交通网络级联失效评价模型。以一个实际路网为例,对模型进行了标定,将标定好的模型评价结果与实际观察结果进行了比对,结果显示模型具有较好的实用性。     

Hierarchical production control of a flexible manufacturing system

A hierarchical production control framework for a flexible manufacturing system is proposed. The machines in the system are subject to failures in a wide spectrum band. At first, failures are clustered near some discrete points on the failure spectrum in order to define the hierarchical model. Each level in the hierarchy corresponds to a discrete point on the failure spectrum. At each level, faster varying failures are modelled by their mean behaviour, and more slowly varying failures are treated as static. Then, a hierarchical controller of multiple time scale type is proposed. System control at each level is based on the work of Kimemia and Gershwin. Simulation results conclude the paper.     

The final answer to the complexity of a basic problem in resilient network design

To provide resilience to failures of the multi-commodity flow network, either in the failure-free state flows can be routed along multiple paths and over-dimensioned, or whenever a failure occurs flows can be restored along unaffected paths. The complexity of the network design depends on the selected method of providing resilience and on a number of design options—whether single or multiple commodities and single- or multi-element failures are considered, if the reaction to failures is dependent or independent on the failure, which mechanism of capacity release and reuse is applied, etc. For almost all combinations of those choices either the corresponding design problem has already been shown to be NP-hard or a compact linear programming formulation of the problem has been provided. The only case that has resisted an answer is when flows are restored in a state-dependent manner using the stub release mechanism. In this paper it is proved that the corresponding network design problem is NP-hard even for a single commodity and for single-element failures. The proof is based on the reduction of the Hamiltonian path problem.     

AN AGENT‐BASED EVENT DRIVEN FORAGING MODEL

ABSTRACT. A game‐theoretic foraging model is developed in an agent‐based framework. The animal's environment is described in terms of agents representing prey, predators and the habitat. The animal has two modes of behavior for each agent: tactical mode behaviors alter the outcomes of the events and strategic mode behaviors alter the probability of future events. Possible event outcomes are represented as utilities which have both benefit and cost components. The probabilities of successful behaviors are tracked via short‐term (tactical), intermediate‐term (strategic) and long‐term (reference) memories. Probabilities change continually through the moment‐to‐moment events, and switches in behavior occur when the expected utility of one behavior exceeds that of another. At the switch point, the expected utilities of the behaviors are equivalent; through this property the model parameters can be calibrated from behavioral experiments. A bluegill foraging study on giving‐up time is used to calibrate the model and then habitat foraging is simulated. Problems with interpreting behavioral studies without fully characterizing the multiple scales of interactions with agents are discussed.     

A robust model for a leader–follower competitive facility location problem in a discrete space

This paper aims at determining the optimal locations for the leader’s new facilities under the condition that the number of the follower’s new facilities is unknown for the leader. The leader and the follower have some facilities in advance. The first competitor, the leader, opens p new facilities in order to increase her own market share. On the other hand, she knows that her competitor, the follower, will react to her action and locate his new facilities as well. The number of the follower’s new facilities is unknown for the leader but it is assumed that the leader knows the probability of opening different numbers of the follower’s new facilities. The leader aims at maximizing her own market share after the follower’s new facilities entry. The follower’s objective is also to maximize his own market share. Since the number of the follower’s new facilities is unknown for leader, “Robust Optimization” is used for maximizing the leader’s market share and making the obtained results “robust” in various scenarios in terms of different numbers of the follower’s new facilities. The optimal locations for new facilities of both the leader and the follower are chosen among pre-determined potential locations. It is assumed that the demand is inelastic. The customers probabilistically meet their demands from all different facilities and the demand level which is met by each facility is computed by Huff rule. The computational experiments have been applied to evaluate the efficiency of the proposed model.     

Analysis of a system with minimal repair and its application to replacement policy

The periodic replacement with minimal repair at failures is studied by many authors, however, there is not a clear definition for minimal repair. This paper defines a minimal repair in the term of the failure rate and devices some probability quantities and reliability properties. As an application of these results, the replacement model where a system is replaced at time T or at nth failure are considered and the optimum policies are discussed.     

Impact of compressor failures on gas transmission network capability

National Grid, the gas operator in the United Kingdom, has experienced challenges in evaluating the capability of its gas transmission network to maintain function in the event of risks particularly to withstand the impact of compressor failures. We propose a mathematical programming model to support the operator in dealing with the problem. Several solution techniques are developed to solve the various versions of the problem efficiently. In the case of little data on compressor failure, an uncertainty theory is applied to solve this problem if the compressor failures are independent; while a robust optimisation technique is developed to solve it when they are not. Otherwise, when there are data on compressor failure, Monte Carlo simulation is applied to find the expected capability of the gas transmission network. Computational experiments, carried out on a case study at National Grid, demonstrate the efficiency of the proposed model and solution techniques. A further analysis is performed to determine the impact of compressor failures and suggest efficient maintenance policies for National Grid.     

Optimal burn-in for maximizing reliability of repairable non-series systems

Burn-in is a manufacturing process applied to products to eliminate early failures in the factory before the products reach the customers. Various methods have been proposed for determining an optimal burn-in time of a non-repairable system or a repairable series system, assuming that system burn-in improves all components in the system. In this paper, we establish the trade-off between the component reliabilities during system burn-in and develop an optimal burn-in time for repairable non-series systems to maximize reliability. One impediment to expressing the reliability of a non-series system is in that successive failures during system burn-in cannot be described precisely because a failed component is not detected until the whole system fails. For approximating the successive failures of a non-series system during system burn-in, we considered two types of repair: minimal repair at the time of system failure, and repair at the time of component or connection failure. The two types of repair provide bounds on the optimal system burn-in time of non-series systems.     

Estimation in a Discrete Reliability Growth Model Under an Inverse Sampling Scheme

This paper develops a discrete reliability growth (RG) model for an inverse sampling scheme, e.g., for destructive tests of expensive single-shot operations systems where design changes are made only and immediately after the occurrence of failures. For qi, the probability of failure at the i-th stage, a specific parametric form is chosen which conforms to the concept of the Duane (1964, IEEE Trans. Aerospace Electron. Systems, 2, 563-566) learning curve in the continuous-time RG setting. A generalized linear model approach is pursued which efficiently handles a certain non-standard situation arising in the study of large-sample properties of the maximum likelihood estimators (MLEs) of the parameters. Alternative closed-form estimators of the model parameters are proposed and compared with the MLEs through asymptotic efficiency as well as small and moderate sample size simulation studies.     

A condition based maintenance model for a two-unit series system

This paper discusses a condition based maintenance model with exponential failures and fixed inspection intervals for a two-unit system in series. The condition of each unit, such as vibration or heat, is monitored at equidistant time intervals. The condition indicator variables for each unit are used to decide whether to repair an individual unit or to overhaul the whole system. After a maintenance action is performed the monitored condition indicator variable takes on its initial value. Each unit can fail only once within an inspection interval and when one or both units fail the system fails. The probability of failure is exponential and the failure rate is dependent on the condition. The cost to be minimized is the long-run average cost of maintenance actions and failures. We study the optimal solution to this problem obtained via dynamic programming.     

On the Brown–Proschan model when repair effects are unknown

A device is repaired after failure. The Brown–Proschan (BP) model assumes that the repair is perfect with probability p and minimal with probability (1−p). Theoretical results usually suppose that each repair effect (perfect or minimal repair) is known. However, this is not generally the case in practice. In this paper, we study the behavior of the BP model when repair effects are unknown. In this context, the main features of the failure process are derived: distribution functions of times between failures, failure intensity, likelihood function, etc. We propose to estimate the repair efficiency parameter p and the parameters of the first time to failure distribution with the likelihood function or equivalently the EM algorithm. We also propose to combine a moment estimation of the scale parameter and a maximum likelihood estimation of other parameters. Copyright © 2010 John Wiley & Sons, Ltd.