Search

• In a shock environment, the system's self-healing mechanism is considered. • The damage evolution effect of shock is proposed. • In a dynamic self-healing environment, two competing failure modes are presented. • The change in degradation rates is considered. We consider a system subject to two distinct failure modes, i.e., a soft failure subject to gradual degradation, and a hard failure caused by cumulative shocks, whichever comes first. This type of systems has wide applications and has been extensively studied in the literature. However, little attention has been paid to the dynamic self-healing mechanism in such systems. With the emergence of intelligent systems and complex architectures, materials with intrinsic self-healing mechanism have the ability to recover damage under external random shocks. In order to illustrate practical significance of the proposed model, reinforced concrete beams (RC-beam) with self-healing capsules in dependent competing failure processes due to cumulative crack evolution effect and rebar performance degradation are taken as the application background. In this paper, the change of degradation rates and damage evolution effect are considered based on the design of critical failure threshold and self-healing mechanism. This study proposes a novel reliability model for a system experiencing dependent competing degradation and cumulative shock failure in a dynamic self-healing environment. A procedure is developed to evaluate the reliability based on this model. We demonstrate the fitness of proposed model through numerical simulation and sensitivity analysis. [ABSTRACT FROM AUTHOR]

Highlights • Degradation-shock dependences are considered by two SEPs. • The general path model and the Wiener process model are applied to the dependent competing failure processes. • Analytical results of the reliability indexes are achieved for models 1 and 2. • Simulations are adopted to obtain the system reliability and lifetime pdf for models 3 and 4. Abstract In this research, reliability models are developed for systems or devices subject to dependent competing soft and hard failure processes with degradation-shock dependences. The new models in this paper extend previous researches by considering novel shock effect patterns (SEPs) resulting from multiple species of external shocks. A soft failure occurs when overall degradation level exceeds the soft failure threshold. Meanwhile, a hard failure occurs when the transmitted shock size exceeds the hard failure threshold. The dependences between the soft and hard failure processes are considered in terms of two different SEPs, degradation level and degradation rate. For SEP I, the shocks can increase the degradation level. Thus, the soft failure is indicated by the overall degradation level comprising of the internal continuous degradation and the additional damage caused by shocks. For SEP II, the shocks can increase the degradation rate of the soft failure process. Specifically, in this research four reliability models focusing on different stochastic processes and SEPs are developed. Closed-form reliability formulas are derived for the general path models, while simulation methods are adopted to get the reliability for the Wiener process models. Finally, numerical examples are given to illustrate the models and the approaches. [ABSTRACT FROM AUTHOR]

Highlights • Three types of thresholds including alarm line and two different failure thresholds are used to model the system reliability. • Two degradation process models, Wiener-Gamma and Gamma-Gamma, are developed. • Explicit formulas for the system reliability in terms of duration thresholds for the degradation models are presented. Abstract Stochastic degradation process models are developed in terms of cumulative degradation signals of systems under three types of thresholds including alarm line and two different failure thresholds. One of the failure thresholds corresponds to the degradation amount, and the other corresponds to the duration. We assume that the degradation process can be separated into two distinctive stages by a change-point which is the first passage time of the degradation process with respect to the alarm line. For simplicity, the first stage is regarded as an age-dependent (or non-stationary) Wiener process or an age-dependent (or non-stationary) Gamma process, and the second stage is regarded as an age-dependent (or non-stationary) Gamma process; thus, two special degradation models, Wiener-Gamma and Gamma-Gamma, are constructed. Specially, two-stage stationary Wiener-Gamma and Gamma-Gamma models can be viewed as special cases. The system reliability is defined as the probability that the degradation signals do not exceed a failure threshold and the duration of exceeding the alarm line is less than the duration threshold. Some reliability results including two cases in terms of duration thresholds (constants and random variables) are derived. The moments of lifetime are also given based on the results. In addition, simulation is carried out to verify the given results. And some numerical examples are presented to illustrate the results obtained in the paper. [ABSTRACT FROM AUTHOR]

Wiener degradation processes with fixed failure threshold have recently received extensive applications due to their desirable mathematical properties. However, a system may experience various environments during the overall degradation life cycle. This may lead to abrupt changes of both the failure thresholds and drift parameters due to the fluctuation of endurance of the deterioration system. Motivated by the practical needs of such multi-phase degradation systems, in this paper, a multi-phase degradation model based on the Wiener process is developed to describe the phenomenon of abrupt changes of failure thresholds and drift parameters. Both the two-phase and multi-phase ( n  ≥ 3) cases are considered under changing failure thresholds and drift parameters in this paper. Analytical expression of system reliability is given for the Wiener process model with two successive different failure thresholds. Meanwhile, a recursive formula is developed to get the analytical expression of system reliability for the Wiener process model with multiple successive different failure thresholds ( n  ≥ 3). In addition, simulation procedures are carried out to verify the given results. And some numerical examples are presented to illustrate the proposed model. [ABSTRACT FROM AUTHOR]

The main focus of this paper is on the development of reliability measures for a repairable multi-state system which operates under dynamic regimes under the discrete-time hypothesis. The switching process of regimes is governed by a Markov chain, and the functioning process of the system follows another Markov chain with different transition probability matrices under different regimes. In terms of two chains as above, a new Markov chain is constructed to depict the evolution process of the dynamic system. For the regime consideration, some novel reliability indices are essential and firstly introduced in this paper. By means of hierarchical partitions for the new state space, Ion-Channel modeling theory and discrete-time Markov chain, the traditional and novel reliability and availability functions for the system under random regimes are easily obtained with the closed form solutions, such as two types of system reliabilities, two types of system point availabilities, two types of system multiple-point availabilities and the associated system multi-interval availabilities and so on. In addition, some probability distributions of sojourn times we are interested in are discussed and computed here. Finally, a numerical example is given to illustrate the results obtained in the paper. [ABSTRACT FROM AUTHOR]

This paper studies a cold standby repairable system with working vacations and vacation interruptions. The repairman׳s multiple vacation, the working vacation policy and the vacation interruption policy are considered simultaneously. The lifetime of component follows a Phase-type (PH) distribution. The repair time in the regular repair period and the working vacation period are other two Phase-type distributions with different representations, and the successive vacation times are governed by a Markovian arrival process (MAP). For this system, a vector-valued Markov process is constructed. We obtain several important performance measures for the system in transient and stationary regimes applying the matrix-analytic method. Finally, a numerical example is given to illustrate the results obtained in the paper. [ABSTRACT FROM AUTHOR]

Abstract: A proof on the optimal arrangement of a linear consecutive-k-out-of- system, with , was given by Jalali et al. [2005. The optimal consecutive-k-out-of- line for . J. Statist. Plann. Inference 128, 281–287]. However, a corollary for the case was still incomplete. In this note we point out what is missing from the proof of that corollary and present a new proof using a different approach. [Copyright &y& Elsevier]

• A fixed change point model with a jump based on a Wiener process is developed. • The fixed change point model is extended to a random change point model. • Two phase changing patterns for the random change point model are proposed. • Analytical results of the system reliability indexes are given for Model 1 and the HPP case of PCP 2 in Model 2. A two-phase degradation system with a change point is commonly seen in many real-world degradation systems due to influence of internal mechanisms and external environments, such as lithium-ion batteries, light-emitting diodes (LEDs), plasma display panels (PDPs), and vacuum fluorescent displays (VFDs). Random jumps exist at the change points of the degradation processes. Motivated by this phenomenon, this paper attempts to model such kinds of systems based on the Wiener process. Specifically, In Model 1, a constant change point model is first considered. The analytical results of the system reliability, lifetime distribution, and the remaining useful lifetime (RUL) are obtained. Then, based on Model 1, a random change point model, i.e., Model 2, is proposed to explain the change point phenomenon which is influenced by the accumulative effect of a shock process. Two phase-change patterns (PCPs) are considered in Model 2. For PCP I, the change point is triggered when the number of shocks reaches a predetermined threshold. For PCP II, the change point is triggered when the accumulative shock damage exceeds the corresponding threshold. The system reliability indexes are studied by using analytical and simulation methods. Finally, several numerical examples are given to illustrate the approaches and results. [ABSTRACT FROM AUTHOR]

• A novel concept of repairable system's balanced condition is proposed. • The PH-distributions have been considered for Model 1. • Three effective maintenance policies are provided for case II of Model 2. • System reliability and availability indexes are derived for the two models. This paper considers a novel k -out-of- n : F repairable balanced system with m sectors. The characteristic of this balanced system is that the numbers of working components in the m sectors must keep the same at any time. Thus, some components should be shut down manually when the balance is broken. Specifically, two Markov repairable system models are proposed in this paper in terms of different restart mechanisms of shut down components. The excellent Markov process imbedding method is used to obtain the system reliabilities and availabilities. Phase-type (PH) distributions for the lifetime and repair time of the components in the first model are considered. For the second case of the second model, three different maintenance policies are proposed and their performances are compared through several numerical examples. To the best of our knowledge, the k -out-of- n : F repairable balanced system models proposed in the research of this paper are first reported in literature. Finally, numerical examples are given to illustrate the models and the approaches. [ABSTRACT FROM AUTHOR]

In engineering applications, system degradation is influenced by continuous degradation and random shocks simultaneously. In this paper, we study the reliability of a multi-component system with interacting components that are subject to both continuous degradation process and categorized shocks. By interacting components, we refer to the case where the degradation behavior of a particular component can influence that of another component. This is in contrast to previous works in the literature that typically assume independence in the degradation interaction in multi-component systems. Moreover, categorized shocks are assumed to selectively affect one or more components by either causing a sudden jump in the degradation level or accelerating the degradation rate, or both. Under these assumptions, we derive the reliability of a series system in a recursive way and propose a simulation method to approximate the failure time of k -out-of- n systems. An example of the MEMS (Micro-electro mechanical systems) oscillator, which is a typical system with interacting components subject to continuous degradation and categorized random shocks, is studied in the end to demonstrate the results obtained in this paper. [ABSTRACT FROM AUTHOR]