A new age‐ and state‐dependent degradation process with possibly negative increments

A generalized system reliability model based on survival signature and multiple competing failure processes

Reliability assessment has been widely used and studied as one of the important roles in equipment operation and maintenance. Multivariate competing degradation models have been extensively studied, but some non-competing multivariate degradation processes still exist in reality. In this paper, we present a method of reliability assessment based on Wiener process which considering non-competing relationship. The multivariate degradation process studied in this paper consists of two degradation indicators. The Wiener process was applied to model two degradation indicators separately. Bayesian method is used for parameter estimation of unknown parameters of degradation models and quantification of uncertainty. A case study of spool valve is used for the demonstration and validation of the model presented in this paper.

Considering the dynamic diffusion in degradation process, we propose an integrated Wiener process with a nonlinear drift and a stochastic volatility for degradation modelling. In our model, the drift and stochastic volatility are estimated nonparametrically to avoid the model misspecification issue. The key innovation of this study is the estimation of stochastic volatility which adopts the functional principal component analysis method and applies it to bipower variance. This estimation approach is able to effectively capture both cross-unit variations and time-varying features within the diffusion process. Also, the proposed model can reduce the estimation bias caused by jump points, which are common phenomenon in degradation process. Furthermore, the distribution of remaining useful life and the mean time to failure are both obtained in explicit forms. Finally, the proposed model and the nonparametric estimation method are illustrated by two simulation experiments and two real cases.

Reliability assessment method based on performance degradation data has been proven to be useful when dealing with products characterized as long-life and highly reliable. However, this method can hardly be applied when measurement of performance degradation is technically difficult or costly. To tackle this problem, this paper proposes to utilize the measurement data which are related to the performance degradation, namely, marker data. It is assumed that the degradation process is modeled with Wiener process, and that the marker is the integral of the performance degradation. We first estimate the parameters of the Wiener process using marker data and then conduct the reliability assessment. A simulated example is presented to demonstrate the proposed method.

Remaining useful life (RUL) prediction is a core technology for equipment operation and health management, and the degradation process of most equipment generally has a long-term correlation. To address this issue, we propose a method to quantify the uncertainty of RUL prediction based on a temporal convolutional network (TCN)-transformer- Wiener Process (WP) degradation model. We give a new generalized RUL prediction framework that employs TCN-Transformer to fit device degradation trends, which can adaptively adjust the fitting of degradation trends. WP is introduced, and the concept of first hitting time (FHT) gives an approximate expression for the probability density function (PDF) of the remaining lifetime of the model, further quantifying the uncertainty of the RUL prediction results. Finally, verification and analysis on the bearing dataset and the tool holder power head degradation dataset, and by comparing with other existing popular methods demonstrated the accuracy and stability of the proposed RUL prediction method. This innovative method provides a robust solution for RUL prediction, offering significant contributions to improving maintenance strategies and operational efficiency.

In this paper, a novel approach is proposed to determine target reliability index based on modeling performance degradation of concrete structures as a stochastic process. First, the Wiener process with drift is used to simulate the degradation process of relative dynamic elastic modulus of concrete, and the drift coefficient and diffusion coefficient of Wiener process are estimated according to the experimental data of degradation of relative dynamic elastic modulus. Then, based on the relations between concrete compressive strength, dynamic elastic modulus, and relative dynamic elastic modulus, the relationship between compressive strength and the amount of degradation of relative dynamic elastic modulus are deduced, and then, the statistical parameters of concrete compressive strength under different service time can be calculated. Finally, based on the established limit state equation of flexural capacity of the weak section and the statistical parameters of compressive strength at different times, the reliability index of a structure under different service life is calculated. On the other hand, according to the drift Wiener process model of relative dynamic elastic modulus degradation of concrete, the time‐varying failure probability of structural durability degradation is calculated based on the first‐passage failure probability formula of drift Wiener process. Taking a concrete plant structure as an example, the time‐varying reliability index calculated based on the limit state equation and the time‐varying failure probability obtained based on the first‐passage failure probability analysis of drift Wiener process are compared, and then the recommended values of target reliability index of structural bearing capacity are comprehensively determined.

Accelerated degradation testing (ADT) is an efficient tool to conduct material service reliability and safety evaluations by analyzing performance degradation data. Traditional stochastic process models are mainly for linear or linearization degradation paths. However, those methods are not applicable for the situations where the degradation processes cannot be linearized. Hence, in this paper, a general ADT model based on the Wiener process is proposed to solve the problem for accelerated degradation data analysis. The general model can consider the unit-to-unit variation and temporal variation of the degradation process, and is suitable for both linear and nonlinear ADT analyses with single or multiple acceleration variables. The statistical inference is given to estimate the unknown parameters in both constant stress and step stress ADT. The simulation example and two real applications demonstrate that the proposed method can yield reliable lifetime evaluation results compared with the existing linear and time-scale transformation Wiener processes in both linear and nonlinear ADT analyses.

Accelerated degradation is a pivotal section for lithium cells for a long cycle life. Wiener process as an important part of stochastic process, plays a key role for the accelerated degradation analysis. In general, the basic Wiener process is modeled with the constant drift rate and diffusion parameter. That indicates the lithium-ion batteries have the same degradation process for the same stress and the complexity of the algorithm is reduced. However, due to the differences in production processes and materials, the individual variations exist. The general Wiener process ignores the individual variations. That leads to reduction of algorithm accuracy. To improve the algorithm accuracy, this paper proposes a Wiener model for the accelerated degradation analysis, considering individual variation. The accelerated model with individual variation is modeled. First, degradation model parameters for each sample are estimated separately. Then, the varieties in the estimation results of each sample parameters are analyzed. That provides the theoretical reference for the parameters of Wiener process. In addition, the coefficient of variation is used as a measure of drift rate and diffusion parameters. Meanwhile, combining with the Wiener process and accelerated model, parameters are optimized by the `maximum likelihood estimation (MLE). Finally, the proposed model is demonstrated for the effectiveness by a practical example.

For the accelerated degradation test (ADT) of lithium-ion battery, the degradation path models are usually applied with the fixed parameters. To optimize the degradation path models, so many battery cells are required for the ADT models based on the degradation path. However, for some lithium-ion batteries with long cycle life and high reliability, the samples are limited due to experimental cost constraints. Meanwhile, owing to the differences in raw materials and manufacturing processes, it is easy to observe variations among the degradation path of lithium-ion battery cells. Fortunately, Wiener process model considering the individual difference can express the variations and be modeled with limited samples for lithium-ion battery. Motivated by this issue, an improved method with random effects Wiener process (REWP) is proposed in this article. First, to verify the degradation process following the Wiener process, the Shapiro-Wilk test is carried out on the basis of a significance level of 0.05. Second, we analyze the varieties of every lithium-ion battery cell. To select a suitable Wiener process model, we apply the coefficient of variation as a measure of random parameters selection for Wiener process. Meanwhile, the maximum likelihood estimation (MLE) is used to optimize parameters of the proposed model. Next, the three different REWP models and general Wiener process model are compared. Finally, to demonstrate the proposed method, the lithium-ion battery cells used for a spacecraft in low Earth orbit (LEO) are conducted for ADTs. The results suggest that the REWP model has a better performance for assessing reliability of lithium-ion battery with long cycle life.

Existing strategies for forecasting the remaining lifespan of deteriorating equipment are not suitable for situations where the measurement intervals for the deteriorating equipment are unevenly distributed, and the monitoring data's measurement frequency does not align with historical data. Moreover, they have not taken into account the fluctuation of adaptive drift parameters during the period of decline. In light of this, a nonlinear prediction model for the remaining lifespan of deteriorating equipment that incorporates historical observational data, based on adaptive drift parameters, is proposed. Initially, the degradation process is described using a real-time state-space model with drift parameters adjusted using historical data to establish a nonlinear degradation model following the Wiener process. Subsequently, an analytical expression for the remaining life in terms of first-passage time is derived, and the parameters of the model are determined through the expectation maximization algorithm. Finally, the proposed method's efficacy and applicability are confirmed using degradation data from a reset spring under impact.

Proactive maintenance and spare parts ordering are two fundamental components for prognostics and health management of system. To achieve timely proactive maintenance and spare parts ordering, it is necessary to forecast the demand of spare parts accurately according to the system's operating state. In this paper, a degradation modeling based method is proposed to adaptively forecast the demand of spare parts. Specifically, the system's lifetime is predicted in a probability form by modeling its degradation process as a Wiener process. To achieve adaptive lifetime estimation, the degradation rate parameter is recursively updated by Kalman filtering algorithm and then the lifetime is derived by considering the updated degradation rate parameter. Based on the lifetime distribution, the demand distribution of spare parts in a future time span can be forecasted by evaluating the convolution of the lifetime distribution. Finally, a case study for gyro's data is provided to illustrate the implementation of the proposed method.

Brushless DC motors are widely used, and their working temperatures, regarding as degradation processes, are nonlinear and multistage. It is necessary to establish a nonlinear degradation model. In this research, our study was based on accelerated degradation data of motors, which are their working temperatures. A multistage Wiener model was established by using the transition function to modify linear model. The normal weighted average filter (Gauss filter) was used to improve the results of estimation for the model parameters. Then, to maximize likelihood function for parameter estimation, we used numerical optimization method- the simplex method for cycle calculation. Finally, the modeling results show that the degradation mechanism changes during the degradation of the motor with high speed. The effectiveness and rationality of model are verified by comparison of the life distribution with widely used nonlinear Wiener model, as well as a comparison of QQ plots for residual. Finally, predictions for motor life are gained by life distributions in different times calculated by multistage model.

Owing to operating condition changing, physical mutation, and sudden shocks, degradation trajectories usually exhibit multi-phase features, and the abrupt jump often appears at the changing time, which makes the traditional methods of lifetime estimation unavailable. In this paper, we mainly focus on how to estimate the lifetime of the multi-phase degradation process with abrupt jumps at the change points under the concept of the first passage time (FPT). Firstly, a multi-phase degradation model with jumps based on the Wiener process is formulated to describe the multi-phase degradation pattern. Then, we attain the lifetime’s closed-form expression for the two-phase model with fixed jump relying on the distribution of the degradation state at the change point. Furthermore, we continue to investigate the lifetime estimation of the degradation process with random effect caused by unit-to-unit variability and the multi-phase degradation process. We extend the results of the two-phase case with fixed parameters to these two cases. For better implementation, a model identification method with off-line and on-line parts based on Expectation Maximization (EM) algorithm and Bayesian rule is proposed. Finally, a numerical case study and a practical example of gyro are provided for illustration.

Reliability modeling of the bivariate deteriorating product with both monotonic and non-monotonic degradation paths

In this chapter we describe a simple degradation model based on the Wiener process. A failure occurs when the degradation reaches a given level for the first time. In this case, the time to failure is inverse Gaussian distributed. The parameters of the lifetime distribution can be estimated from observation of degradation only, from observation of failures, or from observation of both degradation increments and failure times. In the chapter, statistical methods for estimating the parameters of degradation processes for different data structures are developed and compared.