Shock models under a Markovian arrival process

A device submitted to shocks arriving randomly and causing damage is considered. Every shock can be fatal or not. The shocks follow a Markovian arrival process. When the shock is fatal, the device is instantaneously replaced. The Markov process governing the shocks is constructed, and the stationary probability vector calculated. The probability of the number of replacements during a time is determined. A particular case in which the fatal shock occurs after a fixed number of shocks is introduced, and a numerical application is performed. The expressions are in algorithmic form due to the use of matrix-analytic methods. Computational aspects are introduced. This model extends others previously considered in the literature.     

Reliability analysis for devices subject to competing failure processes based on chance theory

This paper studies the reliability for devices subject to independent competing failure processes of degradation and shocks in an uncertain random environment. The continuous degradation is governed by an uncertain process, and external shocks arrive according to an uncertain random renewal reward process, in which the inter-arrival times of shocks and the shock sizes are assumed to be random variables and uncertain variables, respectively. The device reliability is defined as the chance measure that the uncertain degradation signals do not exceed a soft failure threshold L, and the uncertain random shocks do not cause the device failure. The device reliability is obtained by employing chance theory under four different shock patterns. Finally, a case study on a gas insulated transmission line is carried out to show the implementation of the proposed model.     

System availability in a shock model under preventive repair and phase‐type distributions

A device that can fail by shocks or ageing under policy N of maintenance is presented. The interarrival times between shocks follow phase‐type distributions depending on the number of cumulated shocks. The successive shocks deteriorate the system, and some of them can be fatal. After a prefixed number k of nonfatal shocks, the device is preventively repaired. After a fatal shock the device is correctively repaired. Repairs are as good as new, and follow phase‐type distributions. The system is governed by a Markov process whose infinitesimal generator, stationary probability vector, and availability are calculated, obtaining well‐structured expressions due to the use of phase‐type distributions. The availability is optimized in terms of the number k of preventive repairs. Copyright © 2009 John Wiley & Sons, Ltd.     

Opportunistic Maintenance for Multi-component Shock Models

This paper is concerned with opportunistic maintenance on a multi-component cumulative damage shock model with stochastically dependent components. A component fails when its cumulative damage exceeds a given threshold, and any such a failure creates a maintenance opportunity, and triggers a simultaneous repair on all the components, including the non-failed ones, such that damages accumulated at various components are reduced to certain degrees. Utilizing the coupling method, stochastic maintenance comparisons on failure occurrences under different model parameters are obtained. Some positive dependence properties of this multi-component shock model are also presented.Lirong Cui: Supported by the NSF of China grant 70371048.Haijun Li: Supported in part by the NSF grant DMI 9812994.     

A reliability system under different types of shock governed by a Markovian arrival process and maintenance policy K

A reliability system subject to shocks producing damage and failure is considered. The source of shocks producing failures is governed by a Markovian arrival process. All the shocks produce deterioration and some of them failures, which can be repairable or non-repairable. Repair times are governed by a phase-type distribution. The number of deteriorating shocks that the system can stand is fixed. After a fatal failure the system is replaced by another identical one. For this model the availability, the reliability, and the rate of occurrence of the different types of failures are calculated. It is shown that this model extends other previously published in the literature.     

Reliability modeling for mutually dependent competing failure processes due to degradation and random shocks

Many systems are subject to two mutually dependent competing risks namely degradation and random shocks, and they can fail due to two competing modes of failure, soft and hard failure. Soft failure occurs when the total degradation performance, including continuous degradation and sudden degradation increments caused by random shocks, exceeds a certain critical threshold level. Hard failure occurs when the magnitude of any shock (extreme shock model) or the accumulated damage of shocks (cumulative shock model) is beyond some strength threshold level, which is affected by the temporal degradation performance. From viewpoints of Stress-Strength models and Cumulative damage/shock model, a realistic reliability model is developed in this article for mutually dependent competing failure processes due to degradation and random shocks. Finally, a numerical example of Micro-Electro-Mechanical System (MEMS) is conducted to illustrate the implementation and effectiveness of the proposed model.     

Ultrasonic evaluation of anisotropic damage in multiaxially textile-reinforced thermoplastic composites made from hybrid yarns

The basic damage and failure models of multiaxially reinforced composites with a thermoplastic matrix are presented and verified. Within the framework of continuum damage mechanics, a phenomenological model is introduced, where the damage is defined as a change in the elasticity tensor. For damage identification, a specific ultrasonic device was developed. A combination of an immersion set-up and a contact coupling device formed a system for an efficient determination of stiffness-tensor components from convenient sets of velocity measurements. Linked to a tensile machine, it allowed us to measure the anisotropic damage of the new materials group caused by tensile loading. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 221–234, March–April, 2006.     

Damage models for multi-component systems

A series system of n components is subject to a damage process. The damage to each component is cumulative and when it exceeds a certain threshold the component, and hence the device, fails. For various optimality criteria related to system lifetime and system reliability, we find the optimal allocation of resources among the components where the total resources are limited and the allocation of the resources determines the threshold level of each component. Various inventory-type applications are noted.     

Reliability of a multi-state system subject to shocks using phase-type distributions

The reliability of a multi-state system is considered. The system is subject to both internal wear-out and external shocks causing damage that cumulates as shocks follow one another. As a consequence of this cumulating damage, the system wear-out process can be affected.     

Mean residual life and increasing convex comparison of shock models

Two devices are subjected to shocks arriving according to a general counting process. Let M₁ and M₂ be the random number of shocks that cause the failure of the first and the second device, respectively. We find conditions on the counting process such that the mean residual life ordering, the increasing convex ordering and the expectation ordering between M₁ and M₂ are preserved in the random lifetimes of the two devices.     

Burn-in by environmental shocks for two ordered subpopulations

Burn-in is a widely used engineering method of elimination of defective items before they are shipped to customers or put into field operation. In conventional burn-in procedures, components or systems are subject to a period of simulated operation prior to actual usage. Then those which failed during this period are scrapped and discarded. In this paper, we assume that the population of items is composed of two ordered subpopulations and the elimination of weak items by using environmental shocks is considered. Optimal severity levels of these shocks that minimize the defined expected costs are investigated. Some illustrative examples are discussed.     

Identifiability issues in dynamic stress–strength modeling

In many real-life scenarios, system reliability depends on dynamic stress–strength interference, where strength degrades and stress accumulates concurrently over time. In some other cases, shocks appear at random time points, causing damage which is only effective at the instant of shock arrival. In this paper, we consider the identifiability problem of a system under deterministic strength degradation and stochastic damage due to shocks arriving according to a homogeneous Poisson process. We provide conditions under which the models are identifiable with respect to lifetime data only. We also consider current status data and suggest to collect additional information and discuss the issues of model identifiability under different data configurations.     

Availability of inspected systems subject to shocks – A matrix algorithmic approach

We examine the limiting average availability of a maintained system that deteriorates due to random shock process and as a response to its usage (wear out). System’s failures are not self-announcing, hence, failures must be detected via inspection. We consider randomly occurring shocks that arrive according to a Poisson process and cumulatively damage the system. Two models are considered: in Model 1 the shock and wear out processes are independent of the external environment and in Model 2, the shocks arrival rate, the shock magnitudes and the wear out rate are governed by a random environment which evolves as a Markov process. We obtain the system’s availability for both models.     

On the influence of the lamella's elasticity on self-excited vibrations in gearboxes

Eek noise in a gearbox of a vehicle drivetrain is a phenomenon, which can arise while shifting between gears and which is not accepted by customers. Beneath audible squeaking, it can cause damage of mechanical components. There is a wide range of possible reasons for the occurrence of this effect, which strongly depends on properties of the considered gearbox (physical parameters, geometry, operation, …). From the mathematical point of view, the occurrence can be predicted using linear stability analysis of the stationary behaviour of a physically motivated gearbox model. The components of a gearbox are clutch discs being in contact, gears and elastically supported shafts. In this contribution, a rigid multibody model of the device [4] is extended by the elastic modelling of the motor's side disc (rotating Kirchhoff plate). The aim of the overall system is to analyze the shifting process. The analysis reveals that beneath instability mechanisms which are known from systems with rigid bodies, new instabilities occur incorporating of out-of-plane vibrations of the plate. In a reasonable parameter region, the first two unsymmetrical modes of the lamella have the main contribution to the instability. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the topologic structure of economic complex networks: Empirical evidence from large scale payment network of Estonia

This paper presents the first topological analysis of the economic structure of an entire country based on payments data obtained from Swedbank. This data set is exclusive in its kind because around 80% of Estonia's bank transactions are done through Swedbank; hence, the economic structure of the country can be reconstructed. Scale-free networks are commonly observed in a wide array of different contexts such as nature and society. In this paper, the nodes are comprised by customers of the bank (legal entities) and the links are established by payments between these nodes. We study the scaling-free and structural properties of this network. We also describe its topology, components and behaviors. We show that this network shares typical structural characteristics known in other complex networks: degree distributions follow a power law, low clustering coefficient and low average shortest path length. We identify the key nodes of the network and perform simulations of resiliency against random and targeted attacks of the nodes with two different approaches. With this, we find that by identifying and studying the links between the nodes is possible to perform vulnerability analysis of the Estonian economy with respect to economic shocks.     

Simultaneous life testing in a random environment

Examined here is a class of multivariate lifetime distributions generated by a physical model in which a group of like devices is simultaneously exposed to a random wear or damage environment. This random wear is represented by a nonnegative stochastic process with independent increments. Associated with each device is a random threshold and the device fails when the wear attains this threshold. It is shown that tied failure times occur with positive probability. Algorithms are developed to obtain the probabilistic properties of various random variables associated with the joint failure time vector. In particular, these algorithms are used to find the probability of obtaining a specific tie configuration and the large sample behavior of the number of distinct failure times.     

Self-similar strong shocks in non-uniform atmosphere

The propagation of strong shocks in an atmosphere of variable density at rest is studied. The energy gain of the flow enveloped by the shock is assumed to be time-dependent. Analytical and numerical solutions of the similarity flows behind such shocks are obtained.     

One-dimensional nonlinear motions in electroelastic solids: Characteristics and shock waves

The general balance laws and jump relations of the nonlinear electroelasticity of anisotropic dielectrics presented in a previous work are systematically used to characterize and classify infinitesimal discontinuities and electroelastic shocks that can propagate in a simplified one-dimensional model. In particular, the characteristic speeds are obtained, the thermodynamical behavior of weak electroelastic shocks is established, and a classification of electroelastic shocks is given when the material admits a quadratic energy (so-called neo-Hookean case). The Hugoniot jump equation plays the fundamental role in the second point while electric switch-on and switch-off shocks can be exhibited in the classification. The work paves the way for a fully three-dimensional study in anisotropic ferroelectrics and ceramics.