Reliability and Condition-Based Maintenance Analysis of Deteriorating Systems Subject to Generalized Mixed Shock Model

For successful commercialization of evolving devices (e.g., micro-electro-mechanical systems, and biomedical devices), there must be new research focusing on reliability models and analysis tools that can assist manufacturing and maintenance of these devices. These advanced systems may experience multiple failure processes that compete against each other. Two major failure processes are identified to be deteriorating or degradation processes (e.g., wear, fatigue, erosion, corrosion) and random shocks. When these failure processes are dependent, it is a challenging problem to predict reliability of complex systems. This research aims to develop reliability models by exploring new aspects of dependency between competing risks of degradation-based and shock-based failure considering a generalized mixed shock model, and to develop new and effective condition-based maintenance policies based on the developed reliability models. In this research, different aspects of dependency are explored to accurately estimate the reliability of complex systems. When the degradation rate is accelerated as a result of withstanding a particular shock pattern, we develop reliability models with a changing degradation rate for four different shock patterns. When the hard failure threshold reduces due to changes in degradation, we investigate reliability models considering the dependence of the hard failure threshold on the degradation level for two different scenarios. More generally, when the degradation rate and the hard failure threshold can simultaneously transition multiple times, we propose a rich reliability model for a new generalized mixed shock model that is a combination of extreme shock model, δ-shock model and run shock model. This general assumption reflects complex behaviors associated with modern systems and structures that experience multiple sources of external shocks. Based on the developed reliability models, we introduce new condition-based maintenance strategies by including various maintenance actions (e.g., corrective replacement, preventive replacement, and imperfect repair) to minimize the expected long-run average maintenance cost rate. The decisions for maintenance actions are made based on the health condition of systems that can be observed through periodic inspection. The reliability and maintenance models developed in this research can provide timely and effective tools for decision-makers in manufacturing to economically optimize operational decisions for improving reliability, quality and productivity.Industrial Engineering, Department o

Modèles de fiabilité et de maintenance prédictive de systèmes sujets à des défaillances interactives

RÉSUMÉ: L’interaction des défaillances est une thématique qui prend une ampleur considérable dans le monde de la recherche industrielle moderne. Les systèmes sont de plus en plus complexes et leurs fonctionnements et défaillances sur le long terme sont sujets à diverses sources d’influence internes et externes. Les actifs physiques en particulier sont soumis à l’impact du temps, de l’environnement et du rythme de leur utilisation. Connaître ces sources d’influence n’est pas suffisant car il importe de comprendre quelles sont les relations qui les lient afin de planifier de façon efficiente la maintenance des actifs. En effet, cette dernière peut s’avérer très couteuse et sa mauvaise planification peut conduire à l’utilisation de systèmes dangereux pouvant engendrer des évènements catastrophiques. La fiabilité est un vaste domaine. Elle propose une large panoplie de modèles mathématiques qui permettent de prédire le fonctionnement et les défaillances des actifs physiques. Ceci dit, les concepts des modèles les plus appliqués à ce jour se basent sur des hypothèses parfois simplistes et occultent bien souvent certaines relations de dépendances qui régissent un système. L’interaction des défaillances dans le cadre des dépendances stochastiques est abordée par de nombreux travaux de recherches. Par contre, la compréhension et l’implémentation de ces travaux demeurent un défi pour les spécialistes en maintenance qui ont besoin de modèles réalistes pour une maintenance préventive efficace. Cette thèse traite de la fiabilité et la maintenance prédictive des actifs physiques en exploitation et sujets à divers modes de défaillance interactifs. Elle établit avant tout l’importance d’accorder une attention particulière à l’interaction des défaillances dans le domaine de la fiabilité et de la maintenance. Dans une revue de littérature, les concepts et les méthodes de modélisation et d’optimisation en fiabilité et en maintenance préventive sont présentés. Les divers types de dépendances dans un système sont discutés. Un cas d’application, à savoir celui des ponceaux en béton, est proposé. Les travaux entrepris par la suite fournissent avant tout un cadre pour la modélisation de la fiabilité incluant l’interaction des défaillances. A cette fin, une étude comparative des modèles existants les plus pertinents est effectuée de points de vue conceptuel, méthodologique et applicatif. Le cadre étant défini, un modèle basé sur les chocs extrêmes et les chaînes de Markov est construit afin de valoriser le caractère séquentiel des défaillances interactives. Cette proposition est améliorée pour prendre en compte la dégradation du système. Une stratégie de maintenance prédictive est conséquemment développée. Toutes ces approches sont appliquées à un ensemble de ponceaux en béton observés sur plusieurs années. Cela permet d’expliquer les dépendances entre l’occurrence de déplacements et l’occurrence de fissures dans une structure. Tous ces concepts et résultats sont finalement discutés afin de déterminer des perspectives réalistes pour une étude approfondie de l’interactivité d’un point de vue fiabiliste et dans un but stratégique pour la planification de la maintenance.----------ABSTRACT: Failure interaction is a subject gaining growing attention in the world of modern industrial research. Systems are becoming increasingly complex. Their life cycles are subject to various internal and external influences. Physical assets in particular are impacted by time, environment and usage. Knowing these sources of influence is not enough. Indeed, it is important to understand the relationships between them in order to plan effectively for the maintenance of assets. Maintenance can be quite expensive. Thus, poor planning can lead to dangerous systems that could cause catastrophic events. Reliability engineering offers a wide range of mathematical models to predict failures. That being said, the concepts of the most widely applied models in the industry are often based on simplistic assumptions and tend to overlook certain dependencies within a system. Failure interaction in the context of stochastic dependencies is largely addressed in the literature. However, understanding and implementing the proposed approaches remains a challenge for maintenance specialists that need realistic models for efficient maintenance planning. This thesis focuses on the reliability and predictive maintenance of physical assets subject to interactive failure modes. First of all, it emphasizes the importance of paying particular attention to failure interaction. In a literature review, the concepts and methods for modeling and optimizing reliability and preventive maintenance are presented. The diverse dependencies in a system are discussed. A case study is proposed, namely concrete culverts. Subsequently, the research provides a framework for modeling reliability that integrates the interaction of failures. To this end, the most relevant models in the literature are comparatively studied from a conceptual, methodological and applicative point of view. In the defined framework, a model based on extreme shocks and Markov processes is built in order to represent the sequential nature of interactive failures. This approach is extended to take into account the natural degradation of a system. A predictive maintenance strategy is consequently developed. All these models are applied to a set of concrete culverts observed over several years. The dependences between the occurrence of displacements and the occurrence of cracks in a structure are explained through these approaches. Finally, these concepts and results are discussed in order to determine realistic perspectives for in-depth studies of the impact of failure interaction on reliability and for strategic maintenance plannin

Optimization of maintenances following proof tests for the final element of a safety-instrumented system

2019 The Authors Safety-instrumented systems (SISs) have been widely installed to prevent accidental events and mitigate their consequences. Mechanical final elements of SISs often become vulnerable with time due to degradations, but the particulars in SIS operations and assessment impede the adaption of state-of-art research results on maintenances into this domain. This paper models the degradation of SIS final element as a stochastic process. Based on the observed information during a proof test, it is essential to determine an optimal maintenance strategy by choosing a preventive maintenance (PM) or corrective maintenance (CM), as well deciding what degree of mitigation of degradation is enough in case of a PM. When the reasonable initiation situation of a PM and the optimal maintenance degree are identified, lifetime cost of the final element can be minimized while keeping satisfying the integrity level requirement for the SIS. A numerical example is introduced to illustrate how the presenting methods are used to examine the effects of maintenance strategies on cost and the average probability of failure on demands (PFDavg) of a SIS. Intervals of the upcoming tests thus can be updated to provide maintenance crews with more clues on cost-effective tests without weakening safety

Condition-based maintenance—an extensive literature review

This paper presents an extensive literature review on the field of condition-based maintenance (CBM). The paper encompasses over 4000 contributions, analysed through bibliometric indicators and meta-analysis techniques. The review adopts Factor Analysis as a dimensionality reduction, concerning the metric of the co-citations of the papers. Four main research areas have been identified, able to delineate the research field synthetically, from theoretical foundations of CBM; (i) towards more specific implementation strategies (ii) and then specifically focusing on operational aspects related to (iii) inspection and replacement and (iv) prognosis. The data-driven bibliometric results have been combined with an interpretative research to extract both core and detailed concepts related to CBM. This combined analysis allows a critical reflection on the field and the extraction of potential future research directions

Some contributions to maintenance and accelerated degradation test under complex failure process

Ph.DDOCTOR OF PHILOSOPH

Condition-based maintenance for systems with aging and cumulative damage based on proportional hazards model

This paper develops a condition-based maintenance (CBM) policy for systems subject to aging and cumulative damage. The cumulative damage is modeled by a continuous degradation process. Different from previous studies which assume that the system fails when the degradation level exceeds a specific threshold, this paper argues that the degradation itself does not directly lead to system failure, but increases the failure risk of the system. Proportional hazards model (PHM) is employed to characterize the joint effect of aging and cumulative damage. CBM models are developed for two cases: one assumes that the distribution parameters of the degradation process are known in advance, while the other assumes that the parameters are unknown and need to be estimated during system operation. In the first case, an optimal maintenance policy is obtained by minimizing the long-run cost rate. For the case with unknown parameters, periodic inspection is adopted to monitor the degradation level of the system and update the distribution parameters. A case study of Asphalt Plug Joint in UK bridge system is employed to illustrate the maintenance policy.The work described in this paper was partially supported by a theme-based project grant (T32-101/15-R) of University Grants Council, and a Key Project (71532008) supported by National Natural Science Foundation of China

Modeling dependent competing failure processes with degradation-shock dependence

In this paper, we develop a new reliability model for dependent competing failure processes (DCFPs), which accounts for degradation-shock dependence. This is a type of dependence where random shock processes are influenced by degradation processes. The degradation-shock dependence is modeled by assuming that the intensity function of the nonhomogeneous Poisson process describing the random shock processes is dependent on the degradation processes. The dependence effect is modeled with reference to a classification of the random shocks in three “zones” according to their magnitudes, damage zone, fatal zone, and safety zone, with different effects on the system's failure behavior. To the best of the authors’ knowledge, this type of dependence has not yet been considered in reliability models. Monte Carlo simulation is used to calculate the system reliability. A realistic application is presented with regards to the dependent failure behavior of a sliding spool, which is subject to two dependent competing failure processes, wear and clamping stagnation. It is shown that the developed model is capable of describing the dependent competing failure behaviors and their dependence

The analysis of initial probability distribution in Markov Chain model for lifetime estimation

Fatigue crack growth is a stochastic phenomenon due to the uncertainties factors such as material properties, environmental conditions and geometry of the component. These random factors give an appropriate framework for modelling and predicting a lifetime of the structure. In this paper, an approach of calculating the initial probability distribution is introduced based on the statistical distribution of initial crack length. The fatigue crack growth is modelled and predicted by a Markov Chain associated with a classical deterministic crack Paris law. It has been used in calculating the transition probabilities matrix to represent the physical meaning of fatigue crack growth problem. The equation of Paris law provides information regarding the stress intensity factor and material properties in predicting the crack growth rate. The data from the experimental work under constant amplitude loading was analyzed using the Markov Chain model. The results provide a reliable prediction and show excellent agreement between proposed model and experimental result. The reliability of the model can be an effective tool for safety analysis of structure

Mathematical maintenance models of vehicles’ equipment

Dissertation for obtaining a scientific degree of Doctor of Philosophy within the specialty 05.22.20 «Maintenance and repair of vehicles». – National Aviation University, Kyiv, 2018.The thesis addresses the critical scientific problem of creating the appropriate maintenance models for digital avionics systems and degrading equipment of vehicles, which increases the operational effectiveness of such systems significantly. The thesis research includes the analysis of the current state and models of digital avionics maintenance. The study describes the necessity for developing the mathematical maintenance models for redundant digital avionics systems, considering the discontinuous nature of their operation, continuous nature of in-flight testing, possibility of both permanent and intermittent failures and organization of several maintenance levels using various diagnostic tools for detecting both failure types. Another focus of the thesis is the analysis of modern trends and mathematical models of condition-based maintenance (CBM) of vehicles’ equipment. The necessity of developing new CBM mathematical models for degrading equipment of vehicles, considering the probabilities of correct and incorrect decisions when checking system suitability for use in the upcoming operation interval, and the possibility of joint determination of the optimum inspection schedule and replacement thresholds for systems that affect and do not affect safety have been substantiated. The scientific novelty of the primary results obtained in the course of the thesis research is as follows: 1. For the first time, mathematical models to evaluate the operational reliability indicators of continuously monitored line replaceable units/line replaceable modules (LRUs/LRMs) and redundant avionics systems over both finite and infinite time interval, which, unlike known models, consider the characteristics of both permanent and intermittent 2failures, have been developed. These models allow evaluating the impact of intermittent failures on the availability and mean time between unscheduled removals (MTBUR) of LRU/LRM. 2. For the first time, generalized expressions to calculate the average maintenance costs of redundant avionics systems, considering the impact of permanent and intermittent failures, have been developed for alternative maintenance options that differ by the number of maintenance levels (one, two or three), which allows choosing the optimal maintenance option during warranty and post-warranty periods. 3. For the first time, a mathematical model of CBM, based on condition monitoring at scheduled times has been developed, which, unlike the known models, considers the probabilities of correct and incorrect decisions made when checking system suitability. This model allows formulating the criteria of determining the optimal replacement threshold for each inspection time and substantially reduce the likelihood of system failure in the forthcoming interval of operation. 4. For the first time, generalized mathematical expressions to calculate the effectiveness indicators of CBM over a finite time interval, as well as the criteria of joint optimization of the inspection schedule and replacement thresholds for systems that affect or do not affect the safety, have been developed. These results allow significantly improve the availability, reduce average maintenance costs and reduce the number of inspections. The practical value of the results obtained in the thesis is as follows: 1. The techniques to calculate probabilistic and time-related indicators of maintenance effectiveness for digital avionics LRUs/LRMs over finite and infinite operating intervals have been developed. The proposed procedures allow to estimate the availability, operational reliability function (ORF), and mean time between unscheduled removals (MTBUR) of LRUs/LRMs during warranty and post-warranty maintenance periods for both federated avionics (FA) and integrated modular avionics (IMA) architectures; 2. A technique for minimizing the warranty maintenance cost of the redundant digital avionics systems has been developed, demonstrating (through the example of the ADIRS system of the Airbus A380 aircraft) that in the case of the optimal option of warranty maintenance, the average maintenance cost per aircraft decreases by 28 %; 33. A technique for minimizing the post-warranty maintenance cost of the redundant digital avionics systems has been developed. It demonstrates (through the example of the ADIRS system of the Airbus A380 aircraft) that a three-level maintenance option with an intermittent fault detector (IFD) at I and D levels, is optimal as it reduces the total expected maintenance costs by 11 times compared to a one-level option, and by over 8.5 times compared to a two-level option without IFD; 4. A technique for determining the optimal replacement thresholds when monitoring the condition of the degrading system at scheduled times has been developed, which allows to significantly reduce the system failure probability in the forthcoming interval of operation. 5. A technique for joint determination of the optimal replacement threshold and periodicity of suitability checking when monitoring the system condition has been developed, which allows to substantially increase the availability of systems while significantly reducing the number of inspections. The results of the thesis research may be used in the development and maintenance of FA and IMA systems, as well as degrading equipment of vehicles