This article presents a methodology for modeling degradation signals from components functioning under dynamically evolving environment conditions. In situ sensor signals related to the degradation process are utilized as well as the environment conditions, to predict and update, in real-time, the distribution of a component’s residual lifetime. The model assumes that the time-dependent rate at which a component’s degradation signal increases (or decreases) is affected by the severity of the current environmental or operational conditions. These conditions are assumed to evolve as a continuous-time Markov chain. Unique to the proposed model is the union of historical data with real-time, sensor-based data to update the signal parameters, environment parameters, and the residual lifetime distribution of the component within a Bayesian framework.

Degradation modeling for real-time estimation of residual lifetimes in dynamic environments

Monotone optimal replacement policies for a Markovian deteriorating system in a controllable environment

We present transient and asymptotic reliability indices for a single-unit system that is subject to Markov-modulated shocks and wear. The transient results are derived from the (transform) solution of an integro-differential equation describing the joint distribution of the cumulative degradation process and the state of the modulating process. Additionally, we prove the asymptotic normality of a properly centered and time-scaled version of the cumulative degradation at time t. This asymptotic result leads to a simple normal approximation for a properly centered and space-scaled version of the system's lifetime distribution. Two numerical examples illustrate the quality of the normal approximation. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 56: 563-576, 2009 In this article, we investigate transient and asymptotic reli- ability indices for a single-unit system that degrades over time due to normal wear induced by its operating environment and randomly occurring shocks that cause additional damage to the system. The wear rate and shock arrival rate are both modulated by an external process (the random environment) which is modeled as a continuous-time, regenerative stochas- tic process {Zt : t ≥ 0}. At time zero, the device begins its lifetime in perfect working order but degrades over time under the influence of its random environment and shock damage until the cumulative degradation reaches a fixed threshold x, at which time it fails. We denote this random time until failure by Tx. Derived herein are transform expressions for the cumulative distribution function (c.d.f.) of Tx and its nth moment (n ≥ 1) when the environment is assumed to evolve as a time-homogeneous Markov process. The main transient results are obtained by showing that the joint distribution of the cumulative degradation level and the environment state conditionally satisfies an integro-differential equation. This equation leads to the Laplace-Stieltjes transform (LST) of the lifetime distribution function and the LST of its moments. We additionally investigate a scaled version of the unit's lifetime with the aim of developing simple approximations that allow us to circumvent (numerical) Laplace transform inversion.

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On a Markov‐modulated shock and wear process

In this study, we introduce reliability models for a device with two dependent failure processes: soft failure due to degradation and hard failure due to random shocks, by considering the declining hard failure threshold according to changes in degradation. Owing to the nature of degradation for complex devices such as microelectromechanical systems, a degraded system is more vulnerable to force and stress during operation. We address two different scenarios of the changing hard failure threshold due to changes in degradation. In Case 1, the initial hard failure threshold value reduces to a lower level as soon as the overall degradation reaches a critical value. In Case 2, the hard failure threshold decreases gradually and the amount of reduction is proportional to the change in degradation. A condition-based maintenance model derived from a failure limit policy is presented to ensure that a device is functioning under a certain level of degradation. Finally, numerical examples are illustrated to explain the developed reliability and maintenance models, along with sensitivity analysis. Copyright © 2016 John Wiley & Sons, Ltd.

Reliability Analysis and Condition-based Maintenance for Failure Processes with Degradation-dependent Hard Failure Threshold

Shock and wear models under policy N using phase-type distributions

A trivariate stochastic process is considered, describing a sequence of random shocks {Xn } at random intervals {Y n} with random system state {Jn }. The triviariate stochastic process satisfies a Markov renewal property in that the magnitude of shocks and the shock intervals are correlated pairwise and the corresponding joint distributions are affected by transitions of the system state which occur after each shock according to a Markov chain. Of interest is a system lifetime terminated whenever a shock magnitude exceeds a prespecified level z. The distribution of system lifetime, its moments and a related exponential limit theorem are derived explicitly. A similar transform analysis is conducted for a second type of system lifetime with system failures caused by the cumulative magnitude of shocks exceeding a fixed level z.

Analysis of Markov renewal shock models

On a generalized m/g/1 queue with service degradation/enforcement

Parametric simulation models are developed for structural analysis of voting behaviors in public referendum. By decomposing the residents into eight groups, a mechanism is established to construct transition probability matrices defined on three states (0: undecided; 1: YES; 2: NO), thereby capturing behavioral patterns of the residents in forming their individual opinions toward the voting date. This approach enables one to devise a strategy concerning how to transform the formation of the eight residential groups so as to achieve a target voting result. The validity is tested through eight real cases of Japan and a mock public referendum.

Development of Parametric Simulation Models for Structural Analysis of Voting Behaviors in Public Referendum

Convergence properties of the block Gauss-Seidel algorithm applied to ergodic Markov chains are discussed in this paper. This algorithm is one of the most prevalent methods for computing ergodic probability vectors of large-scale Markov chains. We will provide necessary and sufficient conditions for global geometric convergence of this algorithm. To apply this algorithm, the state space of a Markov process is decomposed into mutually exclusive and exhaustive lumps. The convergence properties depend on this lumping. It is also shown that there exists at least one set of lumps, for any ergodic stochastic matrix, which assures geometric convergence of the algorithm.

Necessary and sufficient conditions for global geometric convergence of block gauss-seidel iteration algorithm applied to markov chains

Media planning problems for japanese newspaper considering page space

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