Reliability Modelling of Multiple Repairable Units

This paper proposes a model selection framework for analysing the failure data of multiple repairable units when they are working in different operational and environmental conditions. The paper provides an approach for splitting the non‐homogeneous failure data set into homogeneous groups, based on their failure patterns and statistical trend tests. In addition, when the population includes units with an inadequate amount of failure data, the analysts tend to exclude those units from the analysis. A procedure is presented for modelling the reliability of a multiple repairable units under the influence of such a group to prevent parameter estimation error. We illustrate the implementation of the proposed model by applying it on 12 frequency converters in the Swedish railway system. The results of the case study show that the reliability model of multiple repairable units within a large fleet may consist of a mixture of different stochastic models, that is, the homogeneous Poisson process/renewal process, trend renewal process, non‐homogeneous Poisson process and branching Poisson processes. Therefore, relying only on a single model to represent the behaviour of the whole fleet may not be valid and may lead to wrong parameter estimation. Copyright © 2015 John Wiley & Sons, Ltd.     

Beyond its cost, the value of maintenance: An analytical framework for capturing its net present value

Maintenance planning and activities have grown dramatically in importance across many industries and are increasingly recognized as drivers of competitiveness if managed appropriately. Correlated with this observation is the proliferation of maintenance optimization techniques in the technical literature. But while all these models deal with the cost of maintenance (as an objective function or a constraint), only a handful addresses the notion of value of maintenance, and seldom in an analytical or quantitative way.In this paper, we propose that maintenance has intrinsic value and argue that existing cost-centric models ignore an important dimension of maintenance, namely its value, and in so doing, they can lead to sub-optimal maintenance strategies. We develop a framework for capturing and quantifying the value of maintenance activities. Our framework is based on four key components. First, we consider systems that deteriorate stochastically and exhibit multi-state failures, and model their state evolution using Markov chains and directed graphs. Second, we consider that the system provides a flow of service per unit time. This flow in turn is “priced” and a discounted cash flow is calculated resulting in a present value (PV) for each branch of the graph—or “value trajectory” of the system. Third as the system ages or deteriorates, it migrates towards lower PV branches of the graph, or lower value trajectories. Fourth, we conceptualize maintenance as an operator (in a mathematical sense) that raises the system to a higher PV branch in the graph. We refer to the value of maintenance as the incremental PV between the pre- and post-maintenance branches of the graphs minus the cost of maintenance. The framework presented here offers rich possibilities for future work in benchmarking existing maintenance strategies based on their value implications, and in deriving new maintenance strategies that are “value-optimized.”     

Reliability analysis for new technology-based transmitters

The reliability analysis of new technology-based transmitters has to deal with specific issues: various interactions between both material elements and functions, undefined behaviours under faulty conditions, several transmitted data, and little reliability feedback. To handle these particularities, a “3-step” model is proposed, based on goal tree-success tree (GTST) approaches to represent both the functional and material aspects, and includes the faults and failures as a third part for supporting reliability analyses. The behavioural aspects are provided by relationship matrices, also denoted master logic diagrams (MLD), with stochastic values which represent direct relationships between system elements. Relationship analyses are then proposed to assess the effect of any fault or failure on any material element or function. Taking these relationships into account, the probabilities of malfunction and failure modes are evaluated according to time. Furthermore, uncertainty analyses tend to show that even if the input data and system behaviour are not well known, these previous results can be obtained in a relatively precise way. An illustration is provided by a case study on an infrared gas transmitter. These properties make the proposed model and corresponding reliability analyses especially suitable for intelligent transmitters (or “smart sensors”).     

Analyzing maintenance strategies by agent-based simulations: A feasibility study

Thoroughly planned and implemented maintenance strategies save time and cost. However, the integration of maintenance work into reliability analysis is difficult as common modeling techniques are often not applicable due to state explosion which calls for restrictive model assumptions and oversimplification. From authors’ point of view, agent-based modeling (ABM) of technical and organizational systems is a promising approach to overcome such problems. But since ABM is not well established in reliability analysis its feasibility in this area still has to be demonstrated. For this purpose ABM is compared with Markov chains, namely by analyzing the reliability of a maintained n-unit system with dependent repair events, applying both modeling approaches. Although ABM and Markov chains lead to the same numerical results, the former points out the potentiality of an improved system state handling. This is demonstrated by extending the ABM with operators as additional “agents” featuring their location (x;y) availability (0;1) and different maintenance strategies. This extension highlights the capability of ABM to analyze complex emergent system behavior and allows a systematic refinement and optimization of the maintenance strategies.     

“System-of-systems” approach for interdependent critical infrastructures

The study of the interdependencies within critical infrastructures (CI) is a growing field of research as the importance of potential failure propagation among infrastructures may lead to cascades affecting all supply networks. New powerful methods are required to model and describe such “systems-of-systems” (SoS) as a whole. An overall model is required to provide security and reliability assessment taking into account various kinds of threats and failures. A significant challenge associated with this model may be to create “what-if” scenarios for the analysis of interdependencies. In this paper the interdependencies between industrial control systems (ICS), in particular SCADA (Supervisory Control and Data Acquisition), and the underlying critical infrastructures to address the vulnerabilities related to the coupling of these systems are analyzed. The modeling alternatives for system-of-systems, integrated versus coupled models, are discussed. An integrated model contains detailed low level models of (sub)systems as well as a high level model, covering all hierarchical levels. On the other hand, a coupled model aggregates different simulated outputs of the low level models as inputs at a higher level. Strengths and weaknesses of both approaches are analyzed and a model architecture for SCADA and the “system under control” are proposed. Furthermore, the HLA simulation standard is introduced and discussed in this paper as a promising approach to represent interdependencies between infrastructures. To demonstrate the capabilities of the HLA standard for the interdependencies study, an exemplary application and some first results are also briefly presented in this paper.     

考虑维修场所的动车组多部件双目标成组维修研究

为探究维修场所选择对动车组多部件维修策略制定的影响,综合考虑维修方式、维修场所类别和维修人员等因素,以减少维修成本和维修时间为目标,建立了考虑维修场所的动车组多部件双目标成组维修模型。首先,在两级非完美维修方式的基础上,引入维修场所对维修方式的约束,通过维修场所的选择进一步选择维修方式。然后,提出一种部件维修任务分配算法,实现了维修人员与部件维修任务的优化匹配,使得系统维修时间最短;同时,将该算法引入到遗传算法中,用于求解考虑维修场所和系统维修时间的成组维修模型。实例分析表明,所提出的维修策略在满足动车组部件可靠度要求的前提下,减少了系统的维修成本和维修时间。研究结果可为合理制定动车组维修策略提供理论参考。     

Uncertain process–based reliability and maintenance modeling for systems under mutually dependent degradation and shock processes

For the systems that experience competing failure processes, an uncertain process–based degradation model is developed to describe the systems. The competing degradation process is composed of internal continuous degradation and external shocks, and the mutual dependence between them is considered. When the magnitude of the internal degradation exceeds the threshold, the soft failure occurs. While for the shock processes involving the randomness and the subjective information, we adopt the uncertain random renewal reward process to characterize it. Hard failure occurs when the damage of the shock process exceeds the strength threshold of the system. By using the belief reliability metric, the reliability of the degraded system is defined as the chance measure that neither soft failure nor hard failure occurs. And the effect of the degradation-shock dependence on the system reliability is performed by the parametric studies. Then the proposed degradation model is introduced into the preventive maintenance strategy to minimize the average maintenance cost. Using the microelectromechanical systems as an example, the effectiveness of the constructed degradation model and maintenance strategy is illustrated, and the proposed model can characterize the system degradation process in a superior way to the stochastic process model. These methods can be applied to other similar degraded systems and provide support for maintenance decisions.     

The Method of Manufactured Universes for validating uncertainty quantification methods

The Method of Manufactured Universes is presented as a validation framework for uncertainty quantification (UQ) methodologies and as a tool for exploring the effects of statistical and modeling assumptions embedded in these methods. The framework calls for a manufactured reality from which “experimental” data are created (possibly with experimental error), an imperfect model (with uncertain inputs) from which simulation results are created (possibly with numerical error), the application of a system for quantifying uncertainties in model predictions, and an assessment of how accurately those uncertainties are quantified. The application presented in this paper manufactures a particle-transport “universe”, models it using diffusion theory with uncertain material parameters, and applies both Gaussian process and Bayesian MARS algorithms to make quantitative predictions about new “experiments” within the manufactured reality. The results of this preliminary study indicate that, even in a simple problem, the improper application of a specific UQ method or unrealized effects of a modeling assumption may produce inaccurate predictions. We conclude that the validation framework presented in this paper is a powerful and flexible tool for the investigation and understanding of UQ methodologies.     

Establishment and Analysis of the Fault Tree for the Oil Transfer Pump System in CNPC Work Zone

The reliability of the equipment is very important for the large petrochemical industry, especially for oil pump as the core component of driving equipment. In order to reduce the loss of the enterprise brought by equipment failure, it is need to find those reasons which may lead to equipment failure and take some preventive measures as early as possible. This article analyzes the failure of the oil transfer pump system in CNPC work zone systematically, qualitatively and quantitatively, using the fault tree analysis method. Then 105 groups of minimal cut sets are found, and the probability of system failure after a certain time operation is calculated by using Weibull distribution. Combined with specific requirements of reliability, the work zone may make a scientific decision of plant maintenance cycle according to the conclusion.     

The use of lifetime functions in the optimization of interventions on existing bridges considering maintenance and failure costs

In the last decade, it became clear that life-cycle cost analysis of existing civil infrastructure must be used to optimally manage the growing number of aging and deteriorating structures. The uncertainties associated with deteriorating structures require the use of probabilistic methods to properly evaluate their lifetime performance. In this paper, the deterioration and the effect of maintenance actions are analyzed considering the performance of existing structures characterized by lifetime functions. These functions allow, in a simple manner, the consideration of the effect of aging on the decrease of the probability of survival of a structure, as well as the effect of maintenance actions. Models for the effects of proactive and reactive preventive maintenance, and essential maintenance actions are presented. Since the probability of failure is different from zero during the entire service life of a deteriorating structure and depends strongly on the maintenance strategy, the cost of failure is included in this analysis. The failure of one component in a structure does not usually lead to failure of the structure and, as a result, the safety of existing structures must be analyzed using a system reliability framework. The optimization consists of minimizing the sum of the cumulative maintenance and expected failure cost during the prescribed time horizon. Two examples of application of the proposed methodology are presented. In the first example, the sum of the maintenance and failure costs of a bridge in Colorado is minimized considering essential maintenance only and a fixed minimum acceptable probability of failure. In the second example, the expected lifetime cost, including maintenance and expected failure costs, of a multi-girder bridge is minimized considering reactive preventive maintenance actions.     

Modelling and Simulation of Scraper Reliability for Maintenance

A scraper conveyor is a kind of heavy machinery which can continuously transport goods and widely used in mines,ports and store enterprises.Since scraper failure rate directly affects production costs and production capacity,the evaluation and the prediction of scraper conveyor reliability are important for these enterprises.In this paper,the reliabilities of different parts are classified and discussed according to their structural characteristics and different failure factors.Based on the component’s time-to-failure density function,the reliability model of scraper chain is constructed to track the age distribution of part population and the reliability change of the scraper chain.Based on the stress-strength interference model,considering the decrease of strength due to fatigue failure,the dynamic reliability model of such component as gear,axis is developed to observe the change of the part reliability with the service time of scraper.Finally,system reliability model of the scraper is established for the maintenance to simulate and calculate the scraper reliability.     

Integration of SPC and performance maintenance for supply chain system

In this paper, a supply chain system is viewed as a maintainable system, and the economic-statistical design of a likelihood ratio control chart with a maintenance application is considered for this system. The supply chain system is described by a three-state: normal state, warning state and failure state. A likelihood ratio control chart is used to monitor the system given that only categorical observations can be obtained. When the chart signals, a full inspection is performed to determine the actual system state (normal or warning), and preventive maintenance is immediately performed in the warning state. In addition, the supply chain system must be corrected upon failure (i.e. corrective maintenance), and should be maintained in a scheduled time (i.e. planned maintenance). A mathematical model is developed for the joint optimisation of the control chart parameters and planned maintenance time based on renewal theory. An example is presented to illustrate how to determine the optimal design parameters. We also investigate the effect of coefficients and statistical constraints on the decision variables and the expected cost.     

Dynamic reliability of digital-based transmitters

Dynamic reliability explicitly handles the interactions between the stochastic behaviour of system components and the deterministic behaviour of process variables. While dynamic reliability provides a more efficient and realistic way to perform probabilistic risk assessment than “static” approaches, its industrial level applications are still limited. Factors contributing to this situation are the inherent complexity of the theory and the lack of a generic platform. More recently the increased use of digital-based systems has also introduced additional modelling challenges related to specific interactions between system components. Typical examples are the “intelligent transmitters” which are able to exchange information, and to perform internal data processing and advanced functionalities. To make a contribution to solving these challenges, the mathematical framework of dynamic reliability is extended to handle the data and information which are processed and exchanged between systems components. Stochastic deviations that may affect system properties are also introduced to enhance the modelling of failures. A formalized Petri net approach is then presented to perform the corresponding reliability analyses using numerical methods. Following this formalism, a versatile model for the dynamic reliability modelling of digital-based transmitters is proposed. Finally the framework's flexibility and effectiveness is demonstrated on a substantial case study involving a simplified model of a nuclear fast reactor.     

Random Hazard in Reliability Problems

A class of models for system reliability is presented which (a) introduces the notion of random variability of environment, and hence of instantaneous failure rate or “hazard,” (b) leads to exponentially distributed system time to failure, and to exponentially distributed component time to failure when components are exposed to the environment in isolation, but (c) does not lead to a prediction of series system failure rate based on the usual procedure of adding component failure rates. If the usual procedure is followed, it is shown that underestimates of system reliability are obtained. A simple spares provisioning problem is investigated when such a model is assumed to hold.     

Nonparametric adaptive age replacement with a one-cycle criterion

Age replacement of technical units has received much attention in the reliability literature over the last four decades. Mostly, the failure time distribution for the units is assumed to be known, and minimal costs per unit of time is used as optimality criterion, where renewal reward theory simplifies the mathematics involved but requires the assumption that the same process and replacement strategy continues over a very large (‘infinite’) period of time. Recently, there has been increasing attention to adaptive strategies for age replacement, taking into account the information from the process. Although renewal reward theory can still be used to provide an intuitively and mathematically attractive optimality criterion, it is more logical to use minimal costs per unit of time over a single cycle as optimality criterion for adaptive age replacement. In this paper, we first show that in the classical age replacement setting, with known failure time distribution with increasing hazard rate, the one-cycle criterion leads to earlier replacement than the renewal reward criterion. Thereafter, we present adaptive age replacement with a one-cycle criterion within the nonparametric predictive inferential framework. We study the performance of this approach via simulations, which are also used for comparisons with the use of the renewal reward criterion within the same statistical framework.     

An integrated methodology for the dynamic performance and reliability evaluation of fault-tolerant systems

We propose an integrated methodology for the reliability and dynamic performance analysis of fault-tolerant systems. This methodology uses a behavioral model of the system dynamics, similar to the ones used by control engineers to design the control system, but also incorporates artifacts to model the failure behavior of each component. These artifacts include component failure modes (and associated failure rates) and how those failure modes affect the dynamic behavior of the component. The methodology bases the system evaluation on the analysis of the dynamics of the different configurations the system can reach after component failures occur. For each of the possible system configurations, a performance evaluation of its dynamic behavior is carried out to check whether its properties, e.g., accuracy, overshoot, or settling time, which are called performance metrics, meet system requirements. Markov chains are used to model the stochastic process associated with the different configurations that a system can adopt when failures occur. This methodology not only enables an integrated framework for evaluating dynamic performance and reliability of fault-tolerant systems, but also enables a method for guiding the system design process, and further optimization. To illustrate the methodology, we present a case-study of a lateral-directional flight control system for a fighter aircraft.     

Stopping time optimisation in condition monitoring

Automated condition monitoring of active components of a system can improve the cost-efficiency of preventive and corrective maintenance and the availability of the production system. The validity, reliability and correct interpretation of the signals obtained from the condition monitoring instrumentation is important for the realisation of the potential benefits. The utilisation of experts in the interpretation of the condition monitoring signals is therefore crucial.In the paper, a stopping time model is formulated, where experts' judgements on the remaining operating time of a component, given an indication of incipient failure, are utilised to arrive at optimal operational maintenance decisions. Optimality is defined in the sense of maximising expected utility. An expert model is also formulated, which utilises percentile information elicited from the experts. The modelling framework allows for the testing of different modelling assumptions which affect the decision outcomes.     

Comment on “A framework to practical predictive maintenance modeling for multi-state systems” by Tan C.M. and Raghavan N. [Reliab Eng Syst Saf 2008;93(8):1138-50]

“System-perspective” proposed by “A framework to practical predictive maintenance modeling for multi-state systems” by Tan C.M. and Raghavan N. [A framework to practical predictive maintenance modeling for multi-state systems. Reliab Eng Syst Saf 2008;93(8):1138-50] is a very useful method to evaluate and optimize the maintenance strategy for complex systems, especially for multi-state systems (MSS). The commented paper proposes an innovative process and modeling method to present imperfect maintenance effects on MSS, but there exist some incorrect points and misunderstandings. In this paper, these problems are pointed out and are attempted to be corrected under the original framework of the commented paper.     

基于修理设备可更换和修理延迟策略的两不同型部件冷贮备可修系统

考虑具有修理设备可失效可更换和修理延迟策略且由两个不同型部件组成冷贮备可修系统,利用Markov更新过程理论和全概率分解技术,得到了系统的稳态可用度、首次故障前平均时间、稳态故障频度以及系统等待修理的概率,并且通过引入修理设备的“广义忙期”,获得了修理设备的稳态不可用度和稳态更换频度．最后以数值实例分析了修理延迟时间和修理设备的失效率对系统可靠性指标的影响．在工程应用中特别感兴趣的是稳态可靠性数量指标,希望本文所得结果对系统的优化设计和更换维修提供有用的信息．     

Bootstrap Monte Carlo Simulation of Reliability and Confidence Level with Periodical Maintenance

The bootstrap Monte Carlo simulation (BMCS) is presented as a new method for determining the reliability and confidence level of a general technical system with periodical maintenance. The method can be implemented on the basis of pure samples of failure times or of the mean value distributions in combination with the corresponding sample size of reliability. The BMCS does not require special distribution types and facilitates both the prediction and demonstration of reliability.Firstly, the bootstrap method for determining a confidence interval of a distribution function is investigated in order to verify the use of BMCS as a new method. The confidence level calculated by bootstrapping is therefore to be compared with the confidence level based on the beta-distribution. The accuracy of the BMCS shall subsequently be investigated by observing a component with periodical renewal. The confidence level of the reliability with periodical renewal calculated using the BMCS will be compared with the confidence level determined using the method of moments. Finally, a parameter study is carried out, and a case study as well as the potential of the BMCS shall be presented.