Multi-state homogeneous Markov models in reliability analysis

In the standard Markov technique applied to reliability analysis, components are characterized by two states: an up state and a down state. The present paper explores the possibility of studying system reliability, by modelling each component with a multi-state homogeneous Markov model (MHMM). It is shown that this approach is of value both in approximating non-exponential probability distributions and in helping to build up suitable models for physical processes. Examples are presented which illustrate how the multi-state technique fits many practical situations. Finally some open problems on this topic are suggested.     

Mathematical models for marginal reliability analysis

The present paper deals with some mathematical techniques which are now available for the evaluation of the marginal reliability of a system. In particular the characteristics of both exact methods and approximate ones are examined including, among these last ones, also methods of more recent use and recent extensions of know ones. Moreover, some among the most efficient numerical methods are discussed. Some examples are reported during the exposition in order to better illustraté the different features and, when possible, to compare the techniques     

Neural network realization of Markov reliability and fault-tolerance models

A feed-forward recursive neural network consisting of 2n neurons forming 2 layers, n neurons in each layer, is set to represent a discrete-time n-state Markov model of a fault-tolerant hardware. A quadratic energy function for the neural net is presented and the appropriate update equations for the weights are derived using the least mean square gradient-descent technique.     

Splitting-based importance-sampling algorithm for fast simulationof Markov reliability models with general repair-policies

Markov chains with small transition probabilities occur while modeling the reliability of systems where the individual components are highly reliable and quickly repairable. Complex inter-component dependencies can exist and the state space involved can be huge, making these models analytically and numerically intractable. Naive simulation is also difficult because the event of interest (system failure) is rare, so that a prohibitively large amount of computation is needed to obtain samples of these events. An earlier paper (Juneja et al., 2001) proposed an importance sampling scheme that provides large efficiency increases over naive simulation for a very general class of models including reliability models with general repair policies such as deferred and group repairs. However, there is a statistical penalty associated with this scheme when the corresponding Markov chain has high probability cycles as may be the case with reliability models with general repair policies. This paper develops a splitting-based importance-sampling technique that avoids this statistical penalty by splitting paths at high probability cycles and thus achieves bounded relative-error in a stronger sense than in previous attempts     

Cellular-automata models for reliability analysis of systems onsilicon

Reliability issues are important during the design of VLSI integrated circuits built on silicon, due to several design constraints-higher performance and frequency, device miniaturization, higher levels of on-chip integration-that must be satisfied by the final product. Digital designs are usually subject to failures due to the increased operating temperature caused by their high power dissipation. This paper addresses the problem of analyzing the reliability with respect to power consumption of digital systems constructed with CMOS technology. The solution is simulation-based, and relies on a new, cellular automaton-based model which is particularly suitable for identifying the power characteristics of a sequential design. The model is discussed in detail; it provides a homogeneous representation of all the components of the circuit. Primary inputs, flip-flops, primary outputs, and their related cones of combinational logic are modeled in the same way by means of cellular automaton cells. The model is used to analyze reliability of sequential VLSI circuits. To prove the applicability of the model, we report experimental results on some standard benchmarks taken from the literature     

ECG signal analysis through hidden Markov models

This paper presents an original hidden Markov model (HMM) approach for online beat segmentation and classification of electrocardiograms. The HMM framework has been visited because of its ability of beat detection, segmentation and classification, highly suitable to the electrocardiogram (ECG) problem. Our approach addresses a large panel of topics some of them never studied before in other HMM related works: waveforms modeling, multichannel beat segmentation and classification, and unsupervised adaptation to the patient's ECG. The performance was evaluated on the two-channel QT database in terms of waveform segmentation precision, beat detection and classification. Our waveform segmentation results compare favorably to other systems in the literature. We also obtained high beat detection performance with sensitivity of 99.79% and a positive predictivity of 99.96%, using a test set of 59 recordings. Moreover, premature ventricular contraction beats were detected using an original classification strategy. The results obtained validate our approach for real world application.     

Recursive algorithms for estimation of hidden Markov models andautoregressive models with Markov regime

This paper is concerned with recursive algorithms for the estimation of hidden Markov models (HMMs) and autoregressive (AR) models under the Markov regime. Convergence and rate of convergence results are derived. Acceleration of convergence by averaging of the iterates and the observations are treated. Finally, constant step-size tracking algorithms are presented and examined     

Importance and sensitivity analysis in assessing system reliability

After reviewing various importance concepts adopted in reliability, the authors propose a method for sensitivity analysis. The method uses the heuristically based generalized perturbation theory (GPT) methodology, widely adopted in reactor-physics studies. The concept of importance of a state in the Markov model representation of systems is introduced. The resulting formulations apply to any response of interest in reliability analysis. The relationship between the GPT method and Birnbaum importance is given     

Approximate Markov Modeling of High-Reliability Telecommunications Systems

The reliability model of a system with redundancy but only a single repairman is Markov only if the component failure rates and the repair rate are constants. This paper introduces a method with which a reliability analyst can formulate an approximate (time-homogeneous) Markov model for a system with 1-out-of-2 redundancy when repair is nonexponential (repair rate is time-dependent). This approximate model yields accurate steady-state predictions of system reliability when time-to-repair is orders of magnitude smaller than timeto-component-failure, as is typical in high-reliability telecommunications systems. Transition rates and error bounds for the approximate model are given based on the first three moments of the repair time distribution. An application of the method is shown for the system in which repair time is composed of a "next day" parts delivery phase followed by an on-site repair phase.     

Hidden Markov models for character recognition

A hierarchical system for character recognition with hidden Markov model knowledge sources which solve both the context sensitivity problem and the character instantiation problem is presented. The system achieves 97-99% accuracy using a two-level architecture and has been implemented using a systolic array, thus permitting real-time (1 ms per character) multifont and multisize printed character recognition as well as handwriting recognition.     

一个计算无圈有向网络可靠度的新算法

本文对无圈有向网络的可靠度计算进行了研究。提出了加权有序根树的概念，给出了路径集合的一种特殊排序方法，导出一个计算无圈有向网络可靠度的拓扑公式。在该公式的基础上提出了一个新的计算无圈有向网络可靠度的不交积和算法，算法可以生成简洁的可靠度表达式，从而可以有效地计算无圈有向网络的可靠度。同时验证了算法的有效性。     

Training approach for hidden Markov models

The authors propose a new training approach based on maximum model distance (MMD) for HMMs. MMD uses the entire training set to estimate the parameters of each HMM, while the traditional maximum likelihood (ML) only uses those data labelled for the model. Experimental results showed that significant error reduction can be achieved through the proposed approach. In addition, the relationship between MMD and corrective training was discussed, and we have proved that the corrective training is a special case of the MMD approach     

Universal classification for hidden Markov models

Binary hypotheses testing using empirically observed statistics is studied in the Neyman-Pearson formulation for the hidden Markov model (HMM). An asymptotically optimal decision rule is proposed and compared to the generalized likelihood ratio test (GLRT), which has been shown in earlier studies to be asymptotically optimal for simpler parametric families. The proof of the main theorem is provided. The result can be applied to several types of HMMs commonly used in speech recognition and communication applications. Several applications are demonstrated     

Thermal reliability prediction and analysis for high-density electronic systems based on the Markov process

Thermal-mechanical fatigue is one of the main failure modes for electronic systems, particularly for high-density electronic systems with high-power components. Thermal reliability estimation and prediction have been an increasing concern for improving the safety and reliability of electronic systems. In this paper, we propose a stochastic process prediction model to estimate the thermal reliability of an electronic system based on Markov theory. We first divided the high-density electronic systems into four modules: the energy transformation and protection module, the electronic control module, the connection module, and the signal transmission and transformation module. By integrating failure and repair characteristics of the four modules, a stochastic model of thermal reliability analysis and prediction for a whole electronic system was built based on the Markov process. The feature parameters of thermal reliability evaluation, including thermal reliability, thermal failure probability, mean time between thermal faults, and thermal stable availability, were derived based on our comprehensive model. Finally, we applied the model to an indoor electronic system of DC frequency conversion conditioning. The thermal reliability was estimated and predicted using tested failure and debugging repair data. Effective methods for improving thermal reliability are presented and analyzed based on the comprehensive Markov model.     

Derivation of Markov models for effectiveness analysis of adaptable software architectures for mobile computing

Adaptable software architectures (SA) have been suggested as a viable solution for the design of distributed applications that operate in a mobile computing environment to cope with the high heterogeneity and variability of this environment. Mobile code techniques can be used to implement this kind of SA since they allow us to dynamically modify the load of the hosting nodes and the internode traffic to adapt to the resources available in the nodes and to the condition of the (often wireless) network link. However, moving code among nodes has a cost (e.g., in terms of network traffic and consumed energy for mobile nodes), so designing an adaptable SA based on mobile code techniques requires a careful analysis to determine its effectiveness from the early design stages. In this respect, our main contribution consists of a methodology, called ASAP (adaptable software architectures performance), to automatically derive, starting from a design model of a mobility-based SA, a Markov model whose solution provides insights about the most effective adaptation strategy based on code mobility in a given execution environment. We assume that the SA model is expressed using the Unified Modeling Language (UML) because of its widespread use in software design, also suggesting some extension to this formalism to better express the "mobility structure" of the application, i.e., which are the mobile components, and the possible targets of their movement.     

Numerical methods for reliability evaluation of Markov closedfault-tolerant systems

This paper compares three numerical methods for reliability calculation of Markov, closed, fault-tolerant systems which give rise to continuous-time, time-homogeneous, finite-state, acyclic Markov chains. The authors consider a modified version of Jensen's method (a probabilistic method, also known as uniformization or randomization), a new version of ACE (acyclic Markov chain evaluator) algorithm with several enhancements, and a third-order implicit Runge-Kutta method (an ordinary-differential-equation solution method). Modifications to Jensen's method include incorporating stable calculation of Poisson probabilities and steady-state detection of the underlying discrete-time Markov chain. The new version of Jensen's method is not only more efficient but yields more accurate results. Modifications to ACE algorithm are proposed which incorporate scaling and other refinements to make it more stable and accurate. However, the new version no longer yields solution symbolic with respect to time variable. Implicit Runge-Kutta method can exploit the acyclic structure of the Markov chain and therefore becomes more efficient. All three methods are implemented. Several reliability models are numerically solved using these methods and the results are compared on the basis of accuracy and computation cost     

Asymptotic smoothing errors for hidden Markov models

In this paper, the asymptotic smoothing error for hidden Markov models (HMMs) is investigated using hypothesis testing ideas. A family of HMMs is studied parametrised by a positive constant /spl epsiv/, which is a measure of the frequency of change. Thus, when /spl epsiv//spl rarr/0, the HMM becomes increasingly slower moving. We show that the smoothing error is O(/spl epsiv/). These theoretical predictions are confirmed by a series of simulations.     

Phased-mission system reliability under Markov environment

The authors show how to determine the reliability of a multi-phase mission system whose configuration changes during consecutive time periods, assuming failure and repair times of components are exponentially distributed and redundant components are repairable as long as the system is operational. The mission reliability is obtained for 3 cases, based on a Markov model. (1) Phase durations are deterministic; the computational compact set model is formulated and a programmable solution is developed using eigenvalues of reduced transition-rate matrices. (2) Phase durations are random variables of exponential distributions and the mission is required to be completed within a time limit; the solution is derived as a recursive formula, using the result of case 1 and mathematical treatment-a closed-form solution would be prohibitively complex and laborious to program. (3) Phase durations are random variables and there is no completion time requirement; the solution is derived similarly to case 1 using moment generating functions of phase durations. Generally, reliability problems of phased-mission systems are complex. The authors' method provides exact solutions which can be easily implemented on a computer     

Reduced-complexity estimation for large-scale hidden Markov models

In this paper, we address the problem of reduced-complexity estimation of general large-scale hidden Markov models (HMMs) with underlying nearly completely decomposable discrete-time Markov chains and finite-state outputs. An algorithm is presented that computes O(/spl epsi/) (where /spl epsi/ is the related weak coupling parameter) approximations to the aggregate and full-order filtered estimates with substantial computational savings. These savings are shown to be quite large when the chains have blocks with small individual dimensions. Some simulation studies are presented to demonstrate the performance of the algorithm.     

Hidden Markov models for multiaspect target classification

This article presents a new approach for target identification, in which we fuse scattering data from multiple target-sensor orientations. The multiaspect data is processed via hidden Markov model (HMM) classifiers, buttressed by physics-based feature extraction. This approach explicitly accounts for the fact that the target-sensor orientation is generally unknown or “hidden”. Discrimination results are presented for measured scattering data