Approximate Kalman-Bucy filter for continuous-time semi-Markov jump linear systems

The aim of this paper is to propose a new numerical approximation of the Kalman-Bucy filter for semi-Markov jump linear systems. This approximation is based on the selection of typical trajectories of the driving semi-Markov chain of the process by using an optimal quantization technique. The main advantage of this approach is that it makes pre-computations possible. We derive a Lipschitz property for the solution of the Riccati equation and a general result on the convergence of perturbed solutions of semi-Markov switching Riccati equations when the perturbation comes from the driving semi-Markov chain. Based on these results, we prove the convergence of our approximation scheme in a general infinite countable state space framework and derive an error bound in terms of the quantization error and time discretization step. We employ the proposed filter in a magnetic levitation example with markovian failures and compare its performance with both the Kalman-Bucy filter and the Markovian linear minimum mean squares estimator

Techniques for the Fast Simulation of Models of Highly dependable Systems

With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable system

Formal analysis techniques for gossiping protocols

We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them

An Optimal Replacement Problem of A Semi-Markovian Deteriorating System

This paper discusses an optimal replacement problem of a multi-state system when the deterioration of the system state is described by a semi-Markov process. It is assumed that the system has operating costs and replacement costs depending on its states. The problem is to derive a replacement policy which minimizes the expected average cost per unit time over the infinite horizon. Moreover, under some reasonable conditions reflecting the physical and economical meaning of the deterioration, we show that an optimal replacement policy has a monotone structure

Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields

This book covers a broad range of research results in the field of Markov and Semi-Markov chains, processes, systems and related emerging fields. The authors of the included research papers are well-known researchers in their field. The book presents the state-of-the-art and ideas for further research for theorists in the fields. Nonetheless, it also provides straightforwardly applicable results for diverse areas of practitioners

Petri-Net Simulation Model of a Nuclear Component Degradation Process

International audienceMulti physical state modeling (MPSM) is a novel approach being investigated for estimating the reliability of components and systems in the context of probabilistic risk assessment (PRA). The approach integrates multi-state modeling, which describes the degradation process by transitions among discrete states (e.g. initial, micro-crack, rupture, etc) and physical modeling by (physical) equations that govern the degradation process. In practice, the degradation process is non-Markovian and its transition rates are time-dependent and influenced by external factors such as temperature and stress. Under these conditions, it is in general difficult to derive the state probabilities analytically. On the contrary, Petri nets provide a flexible modeling framework for describing degradation processes with arbitrary transition rates. In this paper, we build a Petri net in support of Monte Carlo simulation of the stochastic aging behavior of a nuclear component undergoing stress corrosion cracking. The results are compared with analytical results derived in a previous work of literature

On the computation of some interval reliability indicators for semi-markov systems

none4In this paper, we computed general interval indicators of availability and reliability for systems modelled by time non-homogeneous semi-Markov chains. First, we considered durationdependent extensions of the Interval Reliability and then, we determined an explicit formula for the availability with a given window and containing a given point. To make the computation of the window availability, an explicit formula was derived involving duration-dependent transition probabilities and the interval reliability function. Both interval reliability and availability functions were evaluated considering the local behavior of the system through the recurrence time processes. The results are illustrated through a numerical example. They show that the considered indicators can describe the duration effects and the age of the multi-state system and be useful in real-life problems.openD'amico G.; Manca R.; Petroni F.; Selvamuthu D.D'Amico, G.; Manca, R.; Petroni, F.; Selvamuthu, D

Modelo de apoio à decisão para a manutenção condicionada de equipamentos produtivos

Doctoral Thesis for PhD degree in Industrial and Systems EngineeringIntroduction: This thesis describes a methodology to combine Bayesian control chart and CBM (Condition-Based Maintenance) for developing a new integrated model. In maintenance management, it is a challenging task for decision-maker to conduct an appropriate and accurate decision. Proper and well-performed CBM models are beneficial for maintenance decision making. The integration of Bayesian control chart and CBM is considered as an intelligent model and a suitable strategy for forecasting items failures as well as allow providing an effectiveness maintenance cost. CBM models provides lower inventory costs for spare parts, reduces unplanned outage, and minimize the risk of catastrophic failure, avoiding high penalties associated with losses of production or delays, increasing availability. However, CBM models need new aspects and the integration of new type of information in maintenance modeling that can improve the results. Objective: The thesis aims to develop a new methodology based on Bayesian control chart for predicting failures of item incorporating simultaneously two types of data: key quality control measurement and equipment condition parameters. In other words, the project research questions are directed to give the lower maintenance costs for real process control. Method: The mathematical approach carried out in this study for developing an optimal Condition Based Maintenance policy included the Weibull analysis for verifying the Markov property, Delay time concept used for deterioration modeling and PSO and Monte Carlo simulation. These models are used for finding the upper control limit and the interval monitoring that minimizes the (maintenance) cost function. Result: The main contribution of this thesis is that the proposed model performs better than previous models in which the hypothesis of using simultaneously data about condition equipment parameters and quality control measurements improve the effectiveness of integrated model Bayesian control chart for Condition Based Maintenance.Introdução: Esta tese descreve uma metodologia para combinar Bayesian control chart e CBM (Condition- Based Maintenance) para desenvolver um novo modelo integrado. Na gestão da manutenção, é importante que o decisor possa tomar decisões apropriadas e corretas. Modelos CBM bem concebidos serão muito benéficos nas tomadas de decisão sobre manutenção. A integração dos gráficos de controlo Bayesian e CBM é considerada um modelo inteligente e uma estratégica adequada para prever as falhas de componentes bem como produzir um controlo de custos de manutenção. Os modelos CBM conseguem definir custos de inventário mais baixos para as partes de substituição, reduzem interrupções não planeadas e minimizam o risco de falhas catastróficas, evitando elevadas penalizações associadas a perdas de produção ou atrasos, aumentando a disponibilidade. Contudo, os modelos CBM precisam de alterações e a integração de novos tipos de informação na modelação de manutenção que permitam melhorar os resultados.Objetivos: Esta tese pretende desenvolver uma nova metodologia baseada Bayesian control chart para prever as falhas de partes, incorporando dois tipos de dados: medições-chave de controlo de qualidade e parâmetros de condição do equipamento. Por outras palavras, as questões de investigação são direcionadas para diminuir custos de manutenção no processo de controlo.Métodos: Os modelos matemáticos implementados neste estudo para desenvolver uma política ótima de CBM incluíram a análise de Weibull para verificação da propriedade de Markov, conceito de atraso de tempo para a modelação da deterioração, PSO e simulação de Monte Carlo. Estes modelos são usados para encontrar o limite superior de controlo e o intervalo de monotorização para minimizar a função de custos de manutenção.Resultados: A principal contribuição desta tese é que o modelo proposto melhora os resultados dos modelos anteriores, baseando-se na hipótese de que, usando simultaneamente dados dos parâmetros dos equipamentos e medições de controlo de qualidade. Assim obtém-se uma melhoria a eficácia do modelo integrado de Bayesian control chart para a manutenção condicionada

Hybrid Stochastic Models for Remaining Lifetime Prognosis

The United States Air Force is developing its next generation aircraft and is seeking to reduce the risk of catastrophic failures, maintenance activities, and the logistics footprint while improving its sortie generation rate through a process called autonomic logistics. Vital to the successful implementation of this process is remaining lifetime prognosis of critical aircraft components. Complicating this problem is the absence of failure time information; however, sensors located on the aircraft are providing degradation measures. This research has provided a method to address at least a portion of this problem by uniting analytical lifetime distribution models with environment and/or degradation measures to obtain the remaining lifetime distribution