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• A system subject to both shocks and environment-affected degradation is investigated. • Maintenance actions related to randomly evolving environments are considered. • Explicit formulas for the cumulative distribution function of first passage time and system availability are derived. • A Monte Carlo simulation algorithm for computing the system first passage time is provided. • A detailed case study is conducted to demonstrate derived formulas. Many systems or devices may experience degradation and shocks simultaneously whose behaviors may have discrepancies in different system operating environments. In this paper, a reliability model is developed for systems subject to both sudden shocks and natural wear processes in randomly evolving environments. The natural wear behavior of the system under different environment is governed by a distinct Gamma process. The system fails when the overall degradation which contains the natural wear and the cumulative damage caused by previous arrival shocks hits a preset threshold. To calculate the cumulative distribution function of the first passage time, the explicit computation formula based on analytical methods and the simulation algorithm based on Monte Carlo simulation methods are provided, which could verify each other. Further, a corrective replacement policy is considered in the case where the environment switching process takes place only when the system is functioning, and then the formula for the system availability is analytically derived. Finally, a study case of the lithium-ion battery is given to illustrate the proposed model and obtained results. [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]

Due to the complex structures and the multi-functionality of modern products, there are usually two or more performance characteristics which can reflect a product's degradation states. The degradation processes corresponding to these performance characteristics are dependent in general, which brings challenges to the degradation data analysis. In this paper, a gamma process based degradation model is developed for the bivariate dependent degradation data, where the dependency between the two degradation processes is captured by a common random effect naturally. The expectation maximization algorithm is employed to estimate the model parameters. Then, a real-time prediction method for a product's remaining useful life is proposed using the Bayesian method. Finally, both the simulation study and the case study are provided for illustration, whose results demonstrate that the proposed model as well as the corresponding inference methods does work well. • A gamma process based bivariate degradation model is proposed. • The dependency between the two PCs is captured by a common random effect naturally. • The MLEs of the model parameters are obtained via the EM algorithm. • Analytical formulas are presented for the RUL prediction. • The effectiveness is validated via simulation and case studies. [ABSTRACT FROM AUTHOR]

• Developing degradation-based and duration-based mission abort policies based on a two-stage degradation process. • Deriving mission reliability and system survivability under the proposed stochastic failure process and mission abort policies. • Investigating the optimal mission abort policies balancing the tradeoff between mission reliability and system survivability. • Providing a detailed comparison of the cost-saving performance of the two proposed abort policies numerically. Various safety-critical systems such as aircrafts, submarines and space stations are required to perform missions continually in harsh environment. To enhance the survivability of such systems, a mission can be aborted when the mission completion becomes problematic and a rescue procedure is immediately initiated. This paper investigates the optimal mission abort policy based on a two-stage Gamma process which can be separated into normal and defective stages. Degradation-based abort policy where a mission is aborted if the system degradation level is higher than a threshold and duration-based abort policy where a mission is aborted if the duration in defective stage is larger than a threshold are considered. The mission success probability and system survivability under these two policies are evaluated and the optimal mission abort thresholds balancing the tradeoff between the mission success probability and system survivability are investigated. A numerical example on an unmanned aerial vehicle (UAV) is presented to illustrate the applicability of the proposed abort policies. [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]