Reliability and Failure Probability Functions of the m-Consecutive-k-out-of-n: F Linear and Circular Systems

في هذه الورقة ، تم دراسة الانواع الخطية والدائرية  للنظام m لعدد k التتابعي  من n من المكونات، حيث تم تصنيف عناصر فضاء عينة فشل مكونات النظام الى تجمعين من التصنيفات، الأول للحالات التي يكون فيها النظام في حالة العمل والآخر للحالات التي يكون فيها النظام وصل لمرحلة الفشل، ومن ثم  تم استخدام هذه التصنيفات لحساب دالة كثافة احتمال موثوقية النظام ودالة كثافة احتمال فشل النظام، وفي النهاية تم اقتراح خوارزمية رياضية لحساب ذلك، تتضمن عمليات التصنيفات هذه وكيفية حساب الدالتين المذكورين من خلال عملية التصنيف.The m-consecutive-k-out-of-n: F linear and circular system consists of n sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least m non-overlapping runs of consecutive-k failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly m-consecutive-k-out-of-n: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided

RESTART Simulation of Non-Markov Consecutive-K-Out-of-N: F Repairable Systems

The reliability of consecutive-k-out-of-n: F repairable systems and (k−1)-step Markov dependence is studied. The model analyzed in this paper is more general than those of previous studies given that repair time and component lifetimes are random variables that follow a general distribution. The system has one repair service which adopts a priority repair rule based on system failure risk. Since crude simulation has proved to be inefficient for highly dependable systems, the RESTART method was used for the estimation of steady-state unavailability, MTBF and unreliability. Probabilities up to the order of 10−16 have been accurately estimated with little computational effort. In this method, a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of a rare event (e.g., a system failure) is higher. The main difficulty for the application of this method is to find a suitable function, called the importance function, to define the regions. Given the simplicity involved in changing some model assumptions with RESTART, the importance function used in this paper could be useful for dependability estimation of many systems

Integrated analysis of error detection and recovery

An integrated modeling and analysis of error detection and recovery is presented. When fault latency and/or error latency exist, the system may suffer from multiple faults or error propagations which seriously deteriorate the fault-tolerant capability. Several detection models that enable analysis of the effect of detection mechanisms on the subsequent error handling operations and the overall system reliability were developed. Following detection of the faulty unit and reconfiguration of the system, the contaminated processes or tasks have to be recovered. The strategies of error recovery employed depend on the detection mechanisms and the available redundancy. Several recovery methods including the rollback recovery are considered. The recovery overhead is evaluated as an index of the capabilities of the detection and reconfiguration mechanisms

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

Markov chain Monte Carlo methods for parameter identification in systems biology models

First, I would like to thank Prof. Dr. Achim Tresch for giving me the opportunity to write this thesis and to work on three fascinating projects. I really appreciate all the fruitful discussions, his constant support and the excellent working atmosphere. I would also like to thank Prof. Dr. Patrick Cramer for being my doctoral supervisor. Furthermore, I would like to thank all the other members of my dissertation committee (Prof. Dr. Rainer Spang

Analysis of Embedded Controllers Subject to Computational Overruns

Microcontrollers have become an integral part of modern everyday embedded systems, such as smart bikes, cars, and drones. Typically, microcontrollers operate under real-time constraints, which require the timely execution of programs on the resource-constrained hardware. As embedded systems are becoming increasingly more complex, microcontrollers run the risk of violating their timing constraints, i.e., overrunning the program deadlines. Breaking these constraints can cause severe damage to both the embedded system and the humans interacting with the device. Therefore, it is crucial to analyse embedded systems properly to ensure that they do not pose any significant danger if the microcontroller overruns a few deadlines.However, there are very few tools available for assessing the safety and performance of embedded control systems when considering the implementation of the microcontroller. This thesis aims to fill this gap in the literature by presenting five papers on the analysis of embedded controllers subject to computational overruns. Details about the real-time operating system's implementation are included into the analysis, such as what happens to the controller's internal state representation when the timing constraints are violated. The contribution includes theoretical and computational tools for analysing the embedded system's stability, performance, and real-time properties.The embedded controller is analysed under three different types of timing violations: blackout events (when no control computation is completed during long periods), weakly-hard constraints (when the number of deadline overruns is constrained over a window), and stochastic overruns (when violations of timing constraints are governed by a probabilistic process). These scenarios are combined with different implementation policies to reduce the gap between the analysis and its practical applicability. The analyses are further validated with a comprehensive experimental campaign performed on both a set of physical processes and multiple simulations.In conclusion, the findings of this thesis reveal that the effect deadline overruns have on the embedded system heavily depends the implementation details and the system's dynamics. Additionally, the stability analysis of embedded controllers subject to deadline overruns is typically conservative, implying that additional insights can be gained by also analysing the system's performance

Consecutive k-within-m-out-of-n:F system with exchangeable components

As a generalization of k-out-of-n:F and consecutive k-out-of-n:F systems, the consecutive k-within-m-out-of-n:F system consists of n linearly ordered components such that the system fails iff there are m consecutive components which include among them at least k failed components. In this article, the reliability properties of consecutive k-within-m-out-of-n:F systems with exchangeable components are studied. The bounds and approximations for the survival function are provided. A Monte Carlo estimator of system signature is obtained and used to approximate survival function. The results are illustrated and numerics are provided for an exchangeable multivariate Pareto distribution

Characterization of real-time computers

A real-time system consists of a computer controller and controlled processes. Despite the synergistic relationship between these two components, they have been traditionally designed and analyzed independently of and separately from each other; namely, computer controllers by computer scientists/engineers and controlled processes by control scientists. As a remedy for this problem, in this report real-time computers are characterized by performance measures based on computer controller response time that are: (1) congruent to the real-time applications, (2) able to offer an objective comparison of rival computer systems, and (3) experimentally measurable/determinable. These measures, unlike others, provide the real-time computer controller with a natural link to controlled processes. In order to demonstrate their utility and power, these measures are first determined for example controlled processes on the basis of control performance functionals. They are then used for two important real-time multiprocessor design applications - the number-power tradeoff and fault-masking and synchronization

A Combined Numerical and Experimental Approach for Rolling Bearing Modelling and Prognostics

Rolling-element bearings are widely employed components which cover a major role in the NVH behaviour of the mechanical systems in which they are inserted. Therefore, it is crucial to thoroughly understand their fundamental properties and accurately quantify their most relevant parameters. Moreover, their inevitable failure due to contact fatigue leads to the necessity of correctly describing their dynamic behaviour. In fact, they permit to develop diagnostic and prognostic schemes, which are heavily requested in the nowadays industrial scenario due to their increasingly important role in the development of efficient maintenance strategies. As a result, throughout the years several techniques have been developed by researchers to address different challenges related to the modelling of these components. Within this context, this thesis aims at improving the available methods and at proposing novel approaches to tackle the modelling of rolling-element bearings both in case of static and dynamic simulations. In particular, the dissertation is divided in three major topics related to this field, i.e. the estimation of bearing radial stiffness trough the finite-element method, the lumped-parameter modelling of defective bearings and the development of physics-based prognostic models. The first part of the thesis deals with the finite-element simulations of rolling-element bearings. In particular, the investigation aims at providing an efficient procedure for the generation of load-dependent meshes. The method is developed with the primary objective of determining the radial stiffness of the examined components. In this regard, the main contribution to the subject is the definition of mesh element dimensions on the basis of analytical formulae and in the proposed methodology for the estimation of bearing stiffness. Then, the second part describes a multi-objective optimization technique for the estimation of unknown parameters in lumped parameter models of defective bearings. In fact, it was observed that several parameters which are commonly inserted in these models are hardly measurable or rather denoted by a high degree of uncertainty. On this basis, an optimization procedure aimed at minimizing the difference between experimental and numerical results is proposed. The novelty of the technique lies in the approach developed to tackle the problem and its peculiar implementation in the context of bearing lumped-parameter models. Lastly, the final part of the dissertation is devoted to the development of physics-based prognostic models. Specifically, two models are detailed, both based on a novel degradation-related parameter, i.e. the Equivalent Damaged Volume (EDV). An algorithm capable of extracting this quantity from experimental data is detailed. Then, EDV values are used as input parameters for two prognostic models. The first one aims at predicting the bearing vibration under different operative conditions with respect to a given reference deterioration history. On the other hand, the objective of the second model is to predict the time until a certain threshold on the equivalent damaged volume is crossed, regardless of the applied load and the shaft rotation speed. Therefore, the original aspect of this latter part is the development of prognostic models based on a novel indicator specifically introduced in this work. Results obtained from all proposed models are validated through analytical methods retrieved from the literature and by comparison with data acquired on a dedicated test bench. To this end, a test rig which was set-up at the Engineering Department of the University of Ferrara was employed to perform two type of tests, i.e. stationary tests on bearings with artificial defects and run-to-failure tests on initially healthy bearings. The characteristics of acceleration signals acquired during both tests are extensively discussed.I cuscinetti a rotolamento sono componenti meccanici che influenzano in maniera considerevole il comportamento dinamico dei sistemi all’interno dei quali sono montati. Pertanto, è di fondamentale importanza possedere strumenti atti alla stima dei loro parametri più rilevanti e avere a disposizione modelli dedicati allo studio delle loro caratteristiche dinamiche. Questo aspetto è di estrema importanza soprattutto nell’ottica dello sviluppo di schemi di diagnostica e prognostica, i quali sono sempre più richiesti all’interno dello scenario industriale odierno. In questo contesto, questa tesi si propone di migliorare le tecniche numeriche già esistenti e di fornire nuovi approcci per la modellazione dei cuscinetti a rotolamento sia nel caso di problemi statici che dinamici. Nello specifico, il lavoro tratta in maniera dettagliata tre diversi argomenti relativi a questo tema, ossia la stima della rigidezza radiale tramite il metodo agli elementi finiti, la modellazione a parametri concentrati di cuscinetti con difetti e lo sviluppo di modelli di prognostica physics-based. La prima parte della tesi concerne la simulazione di cuscinetti a rotolamento tramite il metodo ad elementi finiti. In particolare, lo studio si propone di fornire una procedura per la generazione di griglie le cui dimensioni dipendano dal carico applicato. Il metodo è sviluppato con l’obbiettivo di stimare in maniera computazionalmente efficace la rigidezza radiale del componente in esame. Pertanto, il contributo principale sul tema dato da questa prima parte riguarda il metodo analitico che permette di definire a priori le dimensioni degli elementi che costituiscono la mesh e la metodologia utilizzata per la stima della rigidezza. La seconda parte descrive una procedura di ottimizzazione multi obbiettivo per la stima dei parametri incogniti all’interno dei modelli a parametri concentrati di cuscinetti con difetti. Questa esigenza nasce dall’osservazione che numerosi parametri tipicamente inseriti in questa tipologia di modelli sono difficilmente misurabili oppure caratterizzati da un alto grado di incertezza. Perciò, nella seconda parte viene introdotta una tecnica innovativa che consente di stimare i parametri di modello che minimizzano la differenza fra risultati numerici e sperimentali in diverse condizioni di funzionamento. Infine, l’ultima parte è dedicata allo sviluppo di modelli di prognostica physics-based. A tal riguardo, vengono dettagliati due modelli basati su un nuovo indicatore di degrado del cuscinetto, denominato Equivalent Damaged Volume (EDV). Questo indicatore viene calcolato durante il funzionamento del cuscinetto tramite un algoritmo dedicato. I valori così ottenuti sono poi utilizzati come dati di input per i due modelli prognostici. Il primo mira a predire la vibrazione del cuscinetto in condizioni operative diverse rispetto ad una storia di degrado di riferimento. Diversamente, il secondo modello permette di prevedere il tempo rimanente prima del superamento di una soglia critica di volume equivalente danneggiato, indipendentemente da carico applicato e velocità di rotazione. Dunque, l’aspetto originale di quest’ultima parte ricade nello sviluppo di tecniche prognostiche basate su un nuovo indicatore introdotto ad-hoc in questo lavoro. I risultati ottenuti da tutti i modelli proposti sono validati grazie a metodi analitici di letteratura e a dati acquisiti in laboratorio per mezzo di un banco prova installato presso il Dipartimento di Ingegneria dell’Università di Ferrara. Il banco prova è stato utilizzato per realizzare due tipologie di prove, ossia test stazionari su cuscinetti che presentano difetti artificiali e prove di tipo run-to-failure su cuscinetti inizialmente sani. Le caratteristiche dei segnali di accelerazione acquisiti in entrambe le prove sono discussi in maniera esaustiva

Studies in condition based maintenance using proportional hazards models with imperfect observations

Introduction and literature review -- Preliminary notations -- problem statement -- Optimal inspection period and replacement policy for CBM with imperfect information using PHM -- Problem formulation -- Formulation of the POMDP -- Long-run average cost and total long-run average cost -- Optimal inspection period -- Numerical example -- Evaluating the remaining life for equipment with unobservable states -- Practical implications -- Model assumptions -- Development of parameter estimation methods for a condition based maintenance with indirect observations -- Proposed model -- Parameters' estimation -- Optimal inspection interval and optimal replacement policy -- Reliability function and mean residual life -- Estimation of the model's parameter