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The assessment of rolling bearing reliability is vital for ensuring mechanical operational safety and minimizing maintenance costs. Due to the difficulty in obtaining data on the performance degradation and failure time of rolling bearings, traditional methods for reliability assessment are challenged. This paper introduces a novel hybrid method for the reliability assessment of rolling bearings, combining the convolutional neural network (CNN)‐convolutional block attention module (CBAM)‐ bidirectional long short‐term memory (BiLSTM) network with the Wiener process. The approach comprises three distinct stages: Initially, it involves acquiring two‐dimensional time‐frequency representations of bearings at various operational phases using Continuous Wavelet Transform. Subsequently, the CNN‐CBAM‐BiLSTM network is employed to establish health index (HI) for the bearings and to facilitate the extraction of deep features, serving as input for the Wiener process. The final stage applies the Wiener process to evaluate the bearings’ reliability, characterizing the HI and quantifying uncertainties. The experiment is performed on bearing degradation data and the results indicate the effectiveness and superiority of the proposed hybrid method. [ABSTRACT FROM AUTHOR]

This paper proposes a new way of modelling imperfect maintenance in degradation models, by assuming that maintenance affects only a part of the degradation process. More precisely, the global degradation process is the sum of two dependent Wiener processes with drift. Maintenance has an effect of the ARD1$ARD_1$‐type on only one of these processes: it reduces the degradation level of a quantity which is proportional to the amount of degradation of this process accumulated since previous maintenance. Two particular cases of the model are considered: perturbed ARD1$ARD_1$ and partial replacement models. The usual ARD1$ARD_1$ model is also a specific case of this new model. The system is regularly inspected in order to measure the global degradation level. Two observation schemes are considered. In the complete scheme, the degradation levels are measured both between maintenance actions and at maintenance times (just before and just after). In the general scheme, the degradation levels are measured only between maintenance actions. The maximum likelihood estimation of the model parameters is studied for both observation schemes in both particular models. The quality of the estimators is assessed through a simulation study. [ABSTRACT FROM AUTHOR]

Electromagnets are often used in indirect control for industrial applications. The ability of an electromagnet to control objects should decrease with performance degradation. And electromagnets product poses a danger to people and objects in the working environment. So, it is very difficult to analyze the reliability of electromagnetic performance degradation because of the complicated working condition. Failure Mode and Effect Analysis (FMEA) is the most commonly used tool for product reliability analysis. The new version of FMEA uses integer as evaluation value, which cannot represent the hesitation psychology of the evaluator. The Action Priority (AP) table of the FMEA describes the relationship between the evaluation of influencing factors and the risk level of the failure mode, which provides rules for determining the risk level of the failure mode. However, the AP table may result in multiple failure modes having the same ranking, which does not align with the intention of FMEA to prevent failures. Therefore, this paper proposes a reliability analysis method for electromagnetic performance degradation based on FMEA and FIS. Firstly, the Double Hierarchy Hesitant Fuzzy Linguistic Term Set (DHHFLTS) is used as the evaluation language to describe the hesitation psychology of evaluators. Secondly, the AP table of FMEA is used as FIS fuzzy inference rule. In this way, the idea of FMEA to determine the risk level of failure mode is retained and the problem of FIS fuzzy rule making is overcome. Then, FIS defuzzification AP table inference results to determine the risk ranking of failure modes. This avoids situations where the order of failure modes is equal. Finally, a performance degradation model of the electromagnet is constructed based on the Wiener process, and the calculation results of the new method are verified. [ABSTRACT FROM AUTHOR]

This study addresses the problem of performance reliability degradation and lifetime prediction in complex systems with high reliability but insufficient information. It comprehensively considers the effects of various uncertainties, such as measurement, cognitive, and stochastic uncertainties, and proposes a generalized normal grey cloud Bayesian Wiener process (GNGCBWP) stochastic degradation model. First, based on the historical degradation information of the system, the interval grey number sequence of the degradation increment is constructed, and the performance degradation path of the system is analyzed to determine the degradation model type. Then, combining the normal grey cloud and Bayesian estimation theory, the relevant definitions and theorems of generalized normal grey cloud Bayesian estimation (GNGCBE) are proposed. Finally, the parameter estimation results obtained using the GNGCBE method are substituted into the grey Wiener process degradation model to dynamically analyze performance reliability degradation and predict the remaining useful life (RUL) in real‐time. And the validity and scientificity of the proposed model is verified through a case study of laser equipment. Moreover, the comparison results of the models indicate that the proposed model has advantages in dynamic analysis of performance reliability degradation and real‐time RUL prediction for highly reliable complex systems with limited or poor degradation information. It can significantly reduce the impact of multiple uncertainties on the analysis results and improve the accuracy and reliability of the final prediction results. [ABSTRACT FROM AUTHOR]

The use of Constant‐stress accelerated degradation tests (CSADT) modeling is an effective way to assess the reliability of products. However, when conducting reliability experiments, the data collected may come from various sources such as different manufacturing batches, equipment, and operators. This can result in reduced accuracy of the test evaluations. In this research paper, we propose optimal designs for the Wiener constant‐stress accelerated degradation model that take into account the heterogeneity of manufacturing batches and individual differences. Our goal is to minimize the variability of the mean time to failure (MTTF) while working within a specified budget, test time, and available test units. To achieve this, we utilize particle swarm optimization (PSO) to find the best solution based on a complex objective function. We also compare our model with others using degradation data from LEDs, showing that our model has a better goodness‐of‐fit. Finally, we present examples of optimal CSADT plans under different constraints and conduct sensitivity analysis. [ABSTRACT FROM AUTHOR]

Remaining useful life prediction (RUL) is a critical procedure in the application of prognostics and health management for devices or systems. It is difficult to predict the RUL in a time‐varying external environment. Specifically, many mechanical systems typically experience various operating conditions, which have impacts on the degradation process and degradation rate. In particular, the linear degradation modeling of the Wiener process‐based RUL prediction method has attracted considerable attention recently. However, the dependency of degradation rate and operating conditions is generally ignored in the current degradation modeling, which leads to inaccurate issues in the RUL prediction. Therefore, to solve the above issues, a novel RUL prediction method based on the Wiener process considering parameter dependence is proposed in this paper. At first, a linear Wiener process degradation model considering parameter dependence is constructed to describe the dependency of the drift coefficient and operating conditions. Secondly, the probability density function of RUL is derived under the concept of first hit time. After that, the collaboration between the Bayesian update and expectation maximization algorithm is introduced to update and estimate the model parameters. Finally, the validity and applicability of the proposed method are verified by a numerical simulation and three case studies of bearings. [ABSTRACT FROM AUTHOR]

In the traditional switching policy of a standby system, the standby unit is switched to the normal operation state only after the active unit fails. In contrast, in satellite engineering, a new periodic switching strategy is used by technicians in the satellite gyroscope standby system. Due to the performance degradation of the gyroscope in the long‐term operation and standby process, satellites may fail on orbit. For this problem, an operation optimization model is established for a two‐unit warm standby degradation system considering the periodic switching strategy. First, the degradation process of the units is described by a multiphase Wiener process. Second, based on the first‐hitting time theory, the analytic expressions of reliability and mean time to failure (MTTF) of the degradation system are derived. Third, the optimal periodic switching interval is determined to maximize the system MTTF by using the particle swarm optimization algorithm (PSO). Finally, a numerical example of a gyroscope warm standby subsystem is provided to validate the proposed model. [ABSTRACT FROM AUTHOR]

The improved modified extended tanh‐function approach was used to study optical stochastic soliton solutions and other exact stochastic solutions for the nonlinear Schrödinger‐Hirota equation with multiplicative white noise. The derived solutions include stochastic bright solitons, stochastic singular solitons, stochastic periodic solutions, stochastic singular periodic solutions, stochastic exponential solutions, stochastic rational solutions, and stochastic Jacobi elliptic doubly periodic solutions. Constraints on the parameters were taken into account to ensure the existence of the obtained stochastic soliton solutions. Additionally, selected solutions were presented graphically to illustrate the physical characteristics of the stochastic solutions. In this paper, we used Mathematica (11.3) packages to find the coefficients and Matlab (R2015a) packages to plot the graphs. [ABSTRACT FROM AUTHOR]

Summary: In this study, we demonstrate that engineered topological features can distinguish time series sampled from different stochastic processes with different noise characteristics, in both balanced and unbalanced sampling schemes. We compare our classification results against the results of the same classification on features coming from descriptive statistics and the wavelet transform. We conclude that machine learning models built on engineered topological features alone perform consistently better than those built on the standard statistical and wavelet features for time series classification tasks. We also apply dimension reduction techniques to our engineered features and compare the result of our classification models before and after dimensionality reduction. Finally, we also show that in our calculations of the engineered topological features, employing parallel computing methods does yield significant improvements in run time and memory footprint. [ABSTRACT FROM AUTHOR]

For high‐reliability and long‐life electronic devices, reliability analyses based on degradation data with small sample sizes are an outstanding question. Recently, increasing attention has been paid to the abundant historical degradation data. Exploiting the information in these historical data efficiently and integrating them to benefit the current reliability analysis is an important issue. This study proposes a new integrating method for the historical and current degradation data based on the Wiener process by considering the consistency of failure mechanisms between the different batches of degradation data. Simulation studies show that the new method has superior reliability estimation, and is robust to the assumption of consistent failure mechanisms. Finally, the proposed method is used to analyze a real data set consisting of the metal‐oxide‐semiconductor field‐effect transistor (MOSFET) degradation data. [ABSTRACT FROM AUTHOR]

This paper evaluates the remaining useful life (RUL) for the accelerated Wiener process with mixed random effects and measurement errors. In the discussed model, the random effects are included in both the drift and diffusion parameters of the Wiener process to model the heterogeneity among different degradation paths of products. The measurement errors are introduced to describe the inaccuracy during the measurement process. The effect of the accelerated stress level is included in the drift parameter. The expectation‐maximization (EM) algorithm is applied to obtain the estimation of the model parameters. The expressions of the probability density functions (PDFs) and cumulative distribution functions (CDFs) of the lifetime and RUL distributions of products under the normal usage stress level are derived theoretically. Finally, an example of stress relaxation data is used to illustrate the effectiveness of the developed model and method. [ABSTRACT FROM AUTHOR]

Dissolution studies are a fundamental component of pharmaceutical drug development, yet many studies rely upon the f1 and f2 model‐independent approach that is not capable of accounting for uncertainty in parameter estimation when comparing dissolution profiles. In this paper, we deal with the issue of uncertainty quantification by proposing several model‐dependent approaches for assessing the similarity of two dissolution profiles. We take a statistical modeling approach and allow the dissolution data to be modeled using either a Dirichlet distribution, gamma process model, or Wiener process model. These parametric forms are shown to be reasonable assumptions that are capable of modeling dissolution data well. Furthermore, based on a given statistical model, we are able to use the f1 difference factor and f2 similarity factor to test the equivalency of two dissolution profiles via bootstrap confidence intervals. Illustrations highlighting the success of our methods are provided for both Monte Carlo simulation studies, and real dissolution data sets. [ABSTRACT FROM AUTHOR]

In this paper, we propose degradation test sampling plans (DTSPs) used to determine the acceptability of a product in a Wiener process model. A test statistic and the acceptance criterion based on Wiener process parameter estimates are proposed. The design of a degradation test is investigated using a model incorporating test cost constraint to minimize the asymptotic variance of the proposed test statistic. Some important variables, including the sample size, measurement frequency, and the total test time, are chosen as decision variables in a degradation test plan. The asymptotic variance of the test statistic and the approximate functional forms of the optimal solutions are derived. A search algorithm is also represented in a flow chart for the purpose of finding the optimal DTSPs. In addition, we assess the minimum cost requirement for the result of the test procedure to satisfy the minimum requirements for the producer's risk and the consumer's risk. When the given test budget is not large enough, we suggest some methods to find appropriate solutions. Finally, a numerical example is used to illustrate the proposed methodology. Optimum DTSPs are obtained and tabulated for some combinations of commonly used producer and consumer risk requirements. A sensitivity analysis is also conducted to investigate the sensitivity of the obtained DTSPs to the cost parameters used. [ABSTRACT FROM AUTHOR]

The evidential variable shows the powerful ability on the parameter description, so we have cooperated it with the linear Wiener process to model linear degradation processes. However, the degradation paths of some products exhibit two‐phase patterns over the running time, which cannot be modeled by the linear Wiener process. Hence, it is developed into an associated evidential variable‐based two‐phase Wiener process. In order to utilize the proposed model, the related evidence obtaining, evidence fusion and performance inference approaches are constructed. A simulation study and an actual case are performed to verify the superiorities of the proposed method. The proposed method provides higher accuracies of the useful life, degradation, and reliability evaluations, due to utilizing the evidential variable and considering the two‐phase degradation conditions. [ABSTRACT FROM AUTHOR]

In this paper, a simplified Wiener structure (SWS) for single‐input‐single‐output (SISO) Wiener processes and an identification method based on Gaussian mixture model (GMM) and expectation maximization (EM) algorithm are proposed. The vast majority of industrial processes can be regarded as approximately monotonic non‐linear processes. Approximately, a monotonic characteristic is introduced into the non‐linear module and a rich dynamic characteristic is added into the linear module of the Wiener model. Thus, SWS is exploited and has strong generalization ability. Because GMM can describe the arbitrary distribution of sample data in theory, it is used to accurately describe the output data, including the system error term of SWS. Hence, a statistical model (Equation (17)) is obtained. Then, the EM algorithm is introduced to identify the parameters of the statistical model that contains the parameters of SWS. In the end, two numerical examples demonstrate the effectiveness of both the SWS and the GMM‐EM‐based iterative offline identification algorithm. [ABSTRACT FROM AUTHOR]

Summary: We propose a low‐complexity graph‐based iterative algorithm for the detection of coherent optical OFDM signals in the presence of residual carrier frequency offset and phase noise. We exploit the circular properties of the frequency offset and phase noise and derive graphical messages using the Gaussian probability density function. The proposed algorithm shows similar error rate performance as the existing algorithm at a much lower implementation complexity. [ABSTRACT FROM AUTHOR]

The degradation model and the remaining useful life (RUL) prediction are two key metrics for machine health prognostics. However, the precision of RUL prediction highly depends on the validity of the degradation model. Consequently, the uncertainty of RUL prediction based on the two‐phase degradation process may cause the estimated product reliability to differ from its actual value and lead to a faulty predictive maintenance strategy. However, recent studies have rarely compared the RUL predictions based on two‐phase and single‐phase degradation models. In this study, a real‐time RUL prediction approach was developed for a two‐phase linear Wiener degradation process. A two‐phase Wiener degradation model was proposed along with an estimation method for the change point and model parameters. Based on a state‐space model and Markov chain Monte Carlo, the drift coefficient of the degradation model was updated, and a real‐time RUL prediction model was developed. To examine whether the two‐phase Wiener degradation model was incorrectly assumed to be single‐phase, a case study was conducted to analyze RUL prediction based on the original and incorrect models. The results demonstrated that to obtain a more accurate RUL prediction, a sufficient number of samples should be used in addition to updating the drift coefficient of the degradation model when new measurement data are available. [ABSTRACT FROM AUTHOR]

Timely planning and scheduling of railway infrastructure maintenance interventions are crucial for increased safety, improved availability, and reduced cost. We propose a data‐driven decision‐support framework integrating track condition predictions with tactical maintenance planning and operational scheduling. The framework acknowledges prediction uncertainties by using a Wiener process‐based prediction model at the tactical level. We also develop planning and scheduling algorithms at the operational level. One algorithm focuses on cost‐optimisation, and one algorithm considers the multi‐component characteristics of the railway track by grouping track segments near each other for one maintenance activity. The proposed framework's performance is evaluated using track geometry measurement data from a 34 km railway section in northern Sweden, focusing on the tamping maintenance action. We analyse maintenance costs and demonstrate potential efficiency increases by applying the decision‐support framework. [ABSTRACT FROM AUTHOR]

Remaining useful life prediction (RUL) is a key component in the application of prognostics and health management associated with devices or systems. But such RUL predictions are cumbersome owing to complexities from external effects and internal degradation mechanisms within systems. Specifically, it is common for degradation processes to comprise distinct multiple stages rather than just one uniform stage in many mechanical systems. In particular, the two‐stage degradation modeling for RUL prediction based on the Wiener process with linear drift has received significant attention in recent years. However, negative effects of measurement errors and stochasticity of the degradation states are generally excluded from current degradation modeling, which causes inaccuracy problems that can impact system maintenance schedules and operational efficiency. Therefore, to solve such problems, measurement errors are considered in this paper and a two‐stage degradation model is proposed, in which an adaptive term is also characterized by the Wiener process. The transition probability density function (TPDF) of the degradation state at the two‐stage changing point is derived and an analytical solution for the RUL is obtained under the concept of the first hit time (FHT). A Kalman filter and smoothing algorithm are introduced to estimate variables, and the expectation maximization (EM) algorithm is applied to update and estimate model parameters. Finally, the effectiveness and applicability of the proposed model in RUL predictions are verified through numerical simulation and a case study of bearings. [ABSTRACT FROM AUTHOR]

This manuscript extends the literature on the application of geometric Brownian motion. Forecasted drift and diffusion terms estimated separately and recursively are plugged into the framework to forecast S&P500 index values. Expected index values are estimated from 100,000 simulated index values and probabilities. The results of comparing expected index values with actual values indicate that although reliable predictions of S&P500 index values can be obtained at monthly, quarterly, and annual frequencies, the reliability may decrease in that order. [ABSTRACT FROM AUTHOR]

Residual current device (RCD), the critical equipment to protect the safety of electrical users, are known to experience performance degrade over time during their use lifetime. Therefore, in order to promptly replace the RCD before failure, it is very important to predict its lifetime. In order to predict the remaining life of the RCD, a constant‐stress accelerated degradation test (CSADT) and a combination prediction model are proposed. First, the CSADT is conducted with temperature as the acceleration stress and the residual operating current as degradation characteristic. Then, based on the prediction result of pseudo failure life, a combination model of Wiener process and GM (1, 1) model is given. Finally, the remaining life of the RCD under normal use environment is extrapolated. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

We construct and study a test to detect possible change points in the regression parameters of a linear model when the model errors and covariates may exhibit heteroscedasticity. Being based on a new trimming scheme for the CUSUM process introduced in Horváth et al. (2020), this test is particularly well suited to detect changes that might occur near the endpoints of the sample. A complete asymptotic theory for the test is developed under the null hypothesis of no change in the regression parameter, and consistency of the test is also established in the presence of a parameter change. Monte Carlo simulations show that our test is comparable to existing methods when the errors are homoscedastic. In contrast, existing methods developed for homoscedastic data are demonstrated to be ill‐sized and poorly performing in the presence of heteroscedasticity, while the proposed test continues to perform well in heteroscedastic environments. These results are further demonstrated in a study of the linear connection between the price of crude oil and the U.S. dollar, and in detecting changes points in asset pricing models surrounding the COVID‐19 pandemic. [ABSTRACT FROM AUTHOR]

Accelerated degradation test (ADT) is generally used to accelerate degradation processes in products to estimate their lifespan and to assess their reliability in a short period of time. How to perform the failure mechanism consistency test is crucial in the application of the ADT method. Existing failure mechanism consistency test methods assume that degradation rates among individual products are the same. However, these methods do not take degradation dispersions caused by manufacturing technologies into consideration. To address this issue, a failure mechanism consistency test method for ADT based on the activation energy invariant method and the likelihood ratio test is proposed. First, a degradation modeling method for ADT is introduced. Then, the logarithmic maximum likelihood function values of the degradation models are estimated based on the two‐step maximum likelihood estimation (MLE) method. Finally, the decision rule is proposed based on the likelihood ratio test. The method mentioned above is, then, used on the real degradation data of carbon‐film resistors and bullet O‐rings, and its effectiveness is verified. Furthermore, based on the failure mechanism change point in RTV5370 siloxane rubbers, the simulated degradation data are degenerated to compare the proposed method with the method not considering individual differences in different ADT programs and degradation dispersions. [ABSTRACT FROM AUTHOR]

Considering the large‐scale development of renewable energy resources globally, control optimization of coal‐fired power plants is becoming increasingly crucial. The dynamics of the coordinated control system (CCS) must be studied prior to designing a controller. These dynamics of the subcritical units have been expressed through various modeling methods. However, in previous studies, ordinary differential equations (ODEs) have been primarily employed, which cannot reflect the uncertainties in the system. Therefore, a model with a greater accuracy should be observed to comprise uncorrelated residuals. In this study, the uncertainties in the calorific value of fired coal and combustion process were analyzed first. A normal distribution of disturbance was assumed in this process. The dynamics of the CCS were then described with stochastic differential equations (SDEs). Furthermore, a parameter estimation procedure was designed. The residual evaluation is employed to improve the model evaluation. After simulations, the SDE‐based model‐3 in this study elucidates the dynamics of the subcritical boiler‐turbine system better than the ODE‐based model and other SDE‐based models. The measured values can be regarded as a possible result of this model, rendering it a potential platform to employ stochastic model predictive control in CCS. [ABSTRACT FROM AUTHOR]

A single component nonrepairable system suffering from both an internal stochastic degradation process and external random shocks is investigated in this paper. More specifically, the Wiener process with a positive drift coefficient is introduced to describe the gradual deterioration and the arrival number of external shocks is counted with a nonhomogeneous Poisson process (NHPP). Meanwhile, fault tolerant design is incorporated into the stochastically deterioration system so as to protect it from shock failures to some extent and is consummately addressed via a generalized m − δ shock model. From the actual engineering point of view, external shocks are typically classified into two distinct categories in this current research, that is, a minor shock (Type I shock) increasing the damage load on current degradation level and a traumatic shock (Type II shock) resulting in system catastrophic failure immediately. The closed‐form expression of system survival function is derived analytically and is viewed as the generalization of existing reliability function for systems subject to dependent and competing failure processes. Based on which, two time‐based maintenance (TBM) policies including an age replacement model and a block replacement model are scheduled, where the expected long‐run cost rate (ELRCR) in each model is, respectively, optimized to seek the optimal replacement interval. In the illustrative example part, a subsea blowout preventer (BOP) control system is arranged to validate the theoretical results numerically. To compare which policy is more profitable under different conditions, the relative gain on optimal maintenance cost rate of the two TBM policies is presented. [ABSTRACT FROM AUTHOR]

A degradation model is used to analyze degradation data and product reliability. Owing to model uncertainty, the assumed degradation model may be improper, which can create a difference between the evaluated and actual product reliabilities. Thus, model misspecification analysis is essential. Recent studies on misspecification analysis have mainly considered single‐phase degradation models; two‐phase degradation models have not been investigated intensively. In this study, an approach to model misspecification analysis was developed for a two‐phase gamma‐Wiener process, where the change point was assumed to be known. The gamma and Wiener processes in a two‐phase degradation model may be incorrectly assumed, so five misspecified degradation models were considered: the two‐phase Wiener process, two‐phase gamma process, two‐phase Wiener‐gamma process, one‐phase Wiener process, and one‐phase gamma process. A Monte Carlo simulation was performed to examine the effects of model misspecification on the relative bias and relative variability. A case study was performed to examine the effects of model misspecification on the evaluated mean time to failure and median lifetime of a product for different sample sizes, termination time, and change points. The results clearly demonstrated the effects of model misspecification on the evaluated reliability of a product. [ABSTRACT FROM AUTHOR]

We study various decision problems regarding short‐term investments in risky assets whose returns evolve continuously in time. We show that in each problem, all risk‐averse decision makers have the same (problem‐dependent) ranking over short‐term risky assets. Moreover, in each problem, the ranking is represented by the same risk index as in the case of constant absolute risk aversion utility agents and normally distributed risky assets. [ABSTRACT FROM AUTHOR]

For degradation data in reliability analysis, estimation of the first‐passage time (FPT) distribution to a threshold provides valuable information on reliability characteristics. Recently, Balakrishnan and Qin (2019; Applied Stochastic Models in Business and Industry, 35:571–590) studied a nonparametric method to approximate the FPT distribution of such degradation processes if the underlying process type is unknown. In this article, we propose some improved techniques based on saddlepoint approximation, which enhance those existing methods. Numerical examples and Monte Carlo simulation studies are used to illustrate the advantages of the proposed techniques. Limitations of the improved techniques are discussed and some possible solutions to such are proposed. Some concluding remarks and practical recommendations are provided based on the results. [ABSTRACT FROM AUTHOR]

A new age‐ and state‐dependent degradation process is proposed, which can be used in the case the degradation phenomenon under study is not necessarily monotonic increasing. In particular, the degradation increments of the proposed model are assumed to be possibly dependent on each other and negative. The model is obtained by generalizing the well‐known and largely applied Wiener process and partially preserves the mathematically tractability of the Wiener process. In the paper, the main features and properties of the proposed model are first discussed and the maximum likelihood estimators of its parameters are derived. An applicative example is finally developed, which shows the feasibility and the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The analysis of residual life prediction of batteries for electric vehicles under driving conditions was performed based on the degradation data. This article, characteristics of lithium iron phosphate battery performance degradation as the object, mainly considers two factors about the charge–discharge rate and vibration stress, first, the lithium battery performance degradation test simulating a car in a real driving environment is designed, which provides the lithium battery performance test reference. Then, the model parameters were obtained based on the test data. Finally, the performance degradation model and residual life prediction model of the lithium battery based on the Wiener process are established. This method not only has a high prediction accuracy, but also avoids the construction of a complex battery mechanism degradation model. What is more, this article provides a good perspective for residual life prediction in simplified experiments saving cost. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

We consider a Wiener process with linear drift for degradation modeling. Regularly, maintenance actions are carried out which produce a reduction of the degradation level. In this paper, we consider the influence of such maintenance actions to the further development of the degradation process and the resulting lifetime distribution. A connection between virtual age in Kijima‐type models and degradation level in the underlying degradation process is developed. Furthermore, estimators for the process parameters as well as for the degree of repair are developed. [ABSTRACT FROM AUTHOR]

For reliability assessment based on accelerated degradation tests (ADTs), an appropriate parameter estimation method is very important because it affects the extrapolation and prediction accuracy. The well‐adopted maximum likelihood estimation (MLE) method focuses on interpolation fitting and obtains results via maximizing the likelihood of the observations. However, a best interpolation fitting does not necessarily yield a best extrapolation. In this paper, therefore, a pseudo‐MLE (P‐MLE) method is proposed to improve the prediction accuracy of constant‐stress ADTs by considering the degradation mechanism equivalence under Wiener process. In particular, the degradation mechanism equivalence is characterized by a mechanism equivalence factor which presents the proportional relationship between degradation rate and variation. Then, the mechanism equivalence factor is determined via a two‐step method. The other model parameters can be estimated by the general MLE method. The asymptotic variances of acceleration factors and the p‐quantile of product failure time under normal condition are adopted to compare the statistical properties of the proposed method and the general MLE approach. Numerical examples show that the novel P‐MLE method may not achieve a maximum likelihood but can provide more benefits regarding prediction accuracy enhancement especially when the sample size is limited. [ABSTRACT FROM AUTHOR]

: Burn‐in tests help manufacturers detect defective items and remove them before being sold to customers. In a competitive marketplace, cost is a major consideration and not employing a burn‐in test may result in higher and needless expenses. With this in mind, we consider degradation‐based burn‐in tests in which the degradation path follows a Wiener process and weak items are identified when the process crosses a piecewise linear function. We also study linear functions as a special case of such a piecewise linear barrier. Within this setup, we apply a cost model to determine the optimal burn‐in test. Finally, we discuss an illustrative example using GaAs laser degradation data and present an optimal burn‐in test for it. [ABSTRACT FROM AUTHOR]

Abstract: We consider the stochastic Allen–Cahn equation perturbed by smooth additive Gaussian noise in a bounded spatial domain with smooth boundary in dimension d ≤ 3, and study the semidiscretisation in time of the equation by an Euler type split‐step method with step size k > 0. We show that the method converges strongly with a rate O ( k 1 2 ). By means of a perturbation argument, we also establish the strong convergence of the standard backward Euler scheme with the same rate. [ABSTRACT FROM AUTHOR]

For newly developed, highly reliable, and long-lifespan products, it is quite difficult to implement effective remaining useful life (RUL) prediction in the early usage under limited time cost. However, accelerated degradation testing (ADT) is generally used for lifetime evaluation for such products with harsher test conditions and shorter test time in the late research and development phase. Thus, in this paper, we propose a life prediction framework to integrate the information from ADT to conduct field RUL prediction for highly reliable products. Because ADT belongs to reliability testing used for inferring the population information from the selected test samples, we at first present the modified Wiener process (MWP) model. Different from traditional methods that embody both the random variability and unit-to-unit variability into the diffusion coefficient, the proposed method describes them separately in ADT analysis. Then, the MWP model from ADT is used as a prior for field RUL prediction of the target product during which the strong tracking filtering algorithm is introduced for updating the hidden state and computing the RUL prediction results when the new monitoring data are available. Because of the complexity of the MWP model, the Markov chain Monte Carlo method is provided to estimate the unknown parameters. Finally, the simulation study and the light-emitting diode application verify the effectiveness of the proposed framework that can achieve reasonable life prediction results for highly reliable products for both linear and nonlinear scenarios. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Accelerated degradation test (ADT) has become an efficient approach to evaluate the reliability for highly reliable products. However, when modeling accelerated degradation data with degradation models, it is difficult to exactly figure out the changing rules of parameters with stress variables varying. At present, the changing rules are mainly assumed according to engineering experience or subjective judgements, which probably results in inaccurately extrapolating the reliability. To figure out the changing rules of parameters with stress variables varying, the acceleration factor constant principle and its application under ADT are studied in the paper. It is well known that the acceleration factor between any two different stress levels should be a constant under an effective ADT. For each degradation model, its parameters should obey special changing rules to satisfy that the acceleration factor maintains a constant throughout an ADT. Taking three extensively used stochastic process models as examples, including Wiener process model, gamma process model, and inverse Gaussian process model, the method of deducing the changing rules of the parameters according to the acceleration factor constant principle was demonstrated. A simulation test was conducted to validate the deduced changing rules of the parameters for the three stochastic process models. An illustrative example involving self-regulating heating cables was used to illustrate the application of the acceleration factor constant principle under ADT. Results indicate that the acceleration factor constant principle offers an appealing and credible approach to help model accelerated degradation data. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Cusum charts are widely used for detecting deviations of a process about a target value and also for finding evidence of change in the mean of a process. The testing theory approximates the process by a Wiener process or a Brownian bridge, respectively. For quality control, it is important that other aspects are monitored in addition to or instead of the mean. Here, we show that cusum theory is easily adapted when the target is not the mean but some other aspect of the distribution. [ABSTRACT FROM AUTHOR]

Precisely predicting the remaining life for an individual plays an important role in condition-based maintenance, so Bayesian inference method, which can integrate useful data from several sources to improve the prediction accuracy, has became a research hot. Aiming at the situation that accelerated degradation tests have been widely applied to assess the reliability of products, a remaining life prediction method based on Bayesian inference by taking accelerated degradation data as prior information is proposed. A Wiener process with random drift, diffusion parameters is used to model degradation data, and conjugate prior distributions of random parameters are adopted. To solve the problem that it is hard to estimate the hyper parameters from accelerated degradation data using an Expectation Maximization algorithm, a data extrapolation method is developed. With acceleration factors, degradation data are extrapolated from accelerated stress levels to the normal use stress level. Acceleration factor constant hypothesis is used to deduce the expression of acceleration factor for a Wiener degradation model. Besides, simulation tests are designed to validate the proposed method. The method of constructing the confidence levels for the remaining life predictions is also provided. Finally, a case study is used to illustrate the application of our developed method. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Stochastic optimal control problems in which two-dimensional diffusion processes are controlled until they enter a given set are solved explicitly. When symmetry can be used, exact solutions are obtained. The same arguments are valid for one-dimensional processes. In the general case, it is shown how to obtain good approximate solutions. Various examples are presented. [ABSTRACT FROM AUTHOR]

Degradation is a common phenomenon for many products. Because of a variety of reasons, the degradation rates of units from the same population are often heterogeneous. In addition, when the degradation process is monitored using dedicated sensors, the measurements are often inaccurate because of various noisy factors. To account for the heterogeneous degradation rate and the non-negligible measurement errors, we model the degradation observations using a random-effects Wiener process with measurement errors. Under the model, direct estimation of current degradation and prediction of future degradation are difficult. We thus develop a filtering algorithm that recursively estimates the joint distribution of the degradation rate and the current degradation levels. Based on the estimates, the distribution of the remaining useful life can be timely predicted. Our method is both computational efficient and storage efficient. Its effectiveness is demonstrated through simulation and real data. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This work focuses on a semiparametric analysis of a cure rate modelling approach based on a latent failure process. In clinical and epidemiological studies, a Wiener process with drift may represent a patient's health status and a clinical endpoint occurs when the process first reaches an adverse threshold state. The first-hitting-time then follows an inverse-Gaussian distribution. On the basis of the improper inverse-Gaussian distribution, we consider a process-based lifetime model that allows for a positive probability of no event taking place in finite time. Model flexibility is achieved by leaving a transformed time measure for disease progression completely unspecified, and regression structures are incorporated into the model by taking the acceleration factor and the threshold parameter as functions of the covariates. When applied to experiments with a cure fraction, this model is compatible with classical two-mixture or promotion-time cure rate models. We develop an asymptotically efficient likelihood-based estimation and inference procedure and derive the large-sample properties of the estimators. Simulation studies demonstrate that the proposed method performs well in finite samples. A case study of stage-III soft tissue sarcoma data is used as an illustration. The Canadian Journal of Statistics 42: 635-649; 2014 © 2014 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

We study the full-discrete finite element method for the stochastic elastic equation driven by additive noise. To analyze the error estimates, we write the stochastic elastic equation as an abstract stochastic equation. Strong convergence estimates in the root mean square L2 -norm are obtained by using the error estimates for the deterministic problem and the semigroup theory. Numerical experiments are carried out to verify the theoretical results. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 [ABSTRACT FROM AUTHOR]

Many new statistical models may enjoy better interpretability and numerical stability than traditional models in survival data analysis. Specifically, the threshold regression (TR) technique based on the inverse Gaussian distribution is a useful alternative to the Cox proportional hazards model to analyse lifetime data. In this article we consider a semi-parametric modelling approach for TR and contribute implementational and theoretical details for model fitting and statistical inferences. Extensive simulations are carried out to examine the finite sample performance of the parametric and non-parametric estimates. A real example is analysed to illustrate our methods, along with a careful diagnosis of model assumptions. [ABSTRACT FROM AUTHOR]

The course of diapause development is studied for the first time for Anarsia lineatella (Zeller) (Lepidoptera: Gelechiidae) under field and laboratory conditions for three successive years (2005–2007) in northern Greece. Photoperiod has a significant influence on diapause termination and the mean number of days to pupation decreases progressively throughout the winter season. Cold storage, for at least 30 days at 4°C, results in a synchronized reactivation of the larvae, with the developmental time of larvae chilled for 45 and 60 days at 4°C becoming significantly shorter. A theoretical stochastic description of the effect of chilling on diapause termination is attempted. Larvae have discrete ‘physiological stages' with different degrees of diapause intensity, and the insect passes through those stages with a probability distribution S( t) that evolves over time. This pattern of progressive transition is similar to Brownian motion and finally leads to a successfully synchronized diapause break in spring. Hence, A. lineatella overwinters in a weak diapause state and may complete diapause development in late January, although it shows synchronized termination in early February, after the experience of essential chilling. [ABSTRACT FROM AUTHOR]

Behavioral heterogeneity among individuals is a universal feature of natural populations. Most diffusion-based models of animal dispersal, however, implicitly assume homogeneous movement- parameters within a population. Recent attempts to consider the effect of heterogeneous populations on dispersal distributions have been somewhat limited by the high number of parameters required to subdivide a population into several groups. A solution to this problem is to characterize the value of a movement parameter as continuously distributed within a population. We present several cases in which this method is useful and tractable, applying the framework both to spatial distribution data and closely related first passage times. The resulting models allow ecologists to identify the extent to which the variability in dispersal distributions can be attributed to population-level heterogeneity as opposed to intrinsic randomness. We apply the formulation to two very different cases of dispersal: resident organisms in a stream (freshwater chub Nocomis leptocephalus) and migrating organisms (juvenile salmonids Oncorhynchus spp.). In both cases, the application of heterogeneity-explicit models provides insights into the behavioral mechanisms of movement. [ABSTRACT FROM AUTHOR]

This article studies the estimation of a nonhomogeneous Wiener process model for degradation data. A pseudo-likelihood method is proposed to estimate the unknown parameters. An attractive algorithm is established to compute the estimator under this pseudo-likelihood formulation. We establish the asymptotic properties of the estimator, including consistency, convergence rate and asymptotic distribution. Random effects can be incorporated into the model to represent the heterogeneity of degradation paths by letting the mean function be random. The Wiener process model is extended naturally to a normal inverse Gaussian process model and similar pseudo-likelihood inference is developed. A score test is used to test the presence of the random effects. Simulation studies are conducted to validate the method and we apply our method to a real data set in the area of health structure monitoring. [ABSTRACT FROM AUTHOR]

The article proposes to obtain the first-passage times of the process over certain nonfailure thresholds. It proposes a modified maximum likelihood estimator and a new estimator and prove that, by increasing the sample size of the intermediate data, the estimators and the above-mentioned estimator of the mean lifetime can achieve the same levels of accuracy as the estimators assuming one has failure times.

Our purpose here is to develop the Pearson Type IV distribution as a candidate for modelling the evolution of short period stock index returns. Here, early work by Praetz (1972 and 1978) and Blattberg and Gonedes (1974) has shown that the scaled "t" distribution, which is a particular (symmetric) interpretation of the Pearson Type IV, provides a reasonable description of the way stock index returns evolve over time. Our analysis shows this is certainly not the case for the daily stock index returns on which our empirical analysis is based. There is significant skewness in the data and this cannot be captured by symmetric distributions like the scaled "t" and normal distributions. However, the Pearson Type IV, which is a skewed generalisation of the scaled "t," is capable of modelling the skewness inherent in our data and in such a way that it satisfies asymptotically efficient goodness of fit criteria. Furthermore, the Pearson Type IV can be derived from a stochastic differential equation with standard Markov properties. This enables one to integrate the distributional and time series properties of the returns process and thereby, facilitates both the interpretation and understanding of the role played by the distribution's parameters in the generation of the underlying stock index returns. [ABSTRACT FROM AUTHOR]

We determine optimal investment criteria for a capital project whose cash flows evolve in terms of a‘modified square root’ process. The modified square root process has properties similar to the‘square root’ process but in addition, encompasses the possibility of negative cash flows. Although closed form solutions for the valuation equations implied by the modified square root process are the exception rather than the rule we are able to show that analytic solutions, in the form of infinite power series expansions, will always exist. Furthermore, we also show that when a prescribed set of regularity conditions is satisfied, these power series expansions converge to closed form valuation functions. The optimality criteria for capital investment decisions are then simplified considerably. [ABSTRACT FROM AUTHOR]

Abstract. Recently, proposed a method to detect outliers which explicitly imposes the null hypothesis of a unit root. It works in an iterative fashion to select multiple outlier in a given series. We show, via simulations, that, under the null hypothesis of no outliers, it has the right size in finite samples to detect a single outlier but, when applied in an iterative fashion to select multiple outliers, it exhibits severe size distortions towards finding an excessive number of outliers. We show that his iterative method is incorrect and derive the appropriate limiting distribution of the test at each step of the search. Whether corrected or not, we also show that the outliers need to be very large for the method to have any decent power. We propose an alternative method based on first-differenced data that has considerably more power. We also show that our method to identify outliers leads to unit root tests with more accurate finite sample size and robustness to departures from a unit root. The issues are illustrated using two US/Finland real-exchange rate series. [ABSTRACT FROM AUTHOR]