Predicting future time-to-event outcomes is a foundational task in statistical learning. While various methods exist for generating point predictions, quantifying the associated uncertainties poses a more substantial challenge. In this study, we introduce an innovative approach specifically designed to address this challenge, accommodating dynamic predictors that may manifest as stochastic processes. Our investigation harnesses the forward intensity function in a novel way, providing a fresh perspective on this intricate problem. The framework we propose demonstrates remarkable computational efficiency, enabling efficient analyses of large-scale investigations. We validate its soundness with theoretical guarantees, and our in-depth analysis establishes the weak convergence of function-valued parameter estimations. We illustrate the effectiveness of our framework with two comprehensive real examples and extensive simulation studies.

Domain generalization (DG) in time series poses significant challenges due to domain shift, particularly under the strict DG setting, where no target domain data are available during training. To address this, we propose AFM-CIR, a unified framework that integrates semantic-similarity-guided Adaptive Fourier Mixing (AFM) with Causality-Inspired Regression (CIR). Specifically, we construct a domain-invariant order-preserving guidance embedding that drives a similarity-based adaptive modulation of amplitude mixing and a bounded shortest-angle phase perturbation, thereby generating label-consistent and causally coherent augmented samples. CIR then enforces invariance and inter-dimensional independence through correlation factorization, while causal sufficiency is encouraged via adversarial masking. We further provide theoretical guarantees of the controllability of phase interventions, supported by mutual information analysis and Lipschitz-spectral norm bounds. Extensive experiments on four widely used benchmark industrial data sets demonstrate that AFM-CIR consistently achieves state-of-the-art performance, outperforming strong ERM, general DG, and task-specific DG baselines.

Rotating machinery often operates under time-varying conditions. This can result in nonstationary behavior that violates the stationarity assumption underlying many fault monitoring methods. Cointegration analysis can address nonstationarity but assumes that all monitored variables are linearly related and integrated of order one. To overcome these limitations, this study reformulates the cointegration model in a functional-coefficient form. The coefficients therein are parameterized using neural networks to capture nonlinear relationships and accommodate variables with arbitrary integration orders. An iterative Bayesian inference algorithm is developed to estimate model parameters, with a stationarity constraint imposed on the cointegration error during estimation. This constraint mitigates overfitting to noise and enforces a consistent cointegration structure across varying noise levels. A heuristic fault isolation strategy is further introduced to eliminate the need for manual regularization. The effectiveness of the proposed method is validated through numerical simulations and two real-world cases involving large-scale rotating machinery.

In engineering practice, it is common to observe simultaneous degradation of multiple performance characteristics in a system, in which these characteristics are correlated and exhibit differing degradation behaviors. This poses significant challenges to reliability modeling and analysis of multivariate degradation data. In this study, we propose a novel bivariate degradation model to meet the challenge. We employ the Wiener and inverse Gaussian processes to model the marginal processes, allowing for differing degradation patterns in the two dimensions. A shared frailty is then incorporated into the two marginal processes to capture their dependence structure. We derive the closed form of the reliability function for the proposed bivariate degradation model, and we develop an efficient Bayesian procedure for parameter estimation by combining the Gibbs sampler with the Metropolis-Hastings algorithm for posterior sampling. The performance of the Bayesian estimation method, along with the derived reliability formulas, is validated through comprehensive numerical simulations and a practical example involving a permanent magnet brake.

Bearing skidding is the primary factor restricting the development of aeroengines toward ultrahigh speed, low friction, and lightweight. Compared to typical bearing faults, analysis of bearing skidding presents greater challenges due to the weak signal properties, significant time-varying characteristics and coupling influence of multiple factors. It is crucial to fully utilize multisource signals to enhance skidding features and capture time-varying characteristics. This article proposes a prior knowledge-embedded dual feedback spatial-temporal graph convolutional network (DFSTGCN) for skidding assessment. Unlike existing adjacency matrix construction strategies, the correlation between multisource signals is described based on multiple prior knowledge, which includes dynamic model, structural dynamics, and expert experience. Furthermore, a DFSTGCN is designed to simultaneously focus on the spatial and temporal dependencies of time-varying skidding data. Specifically, a dual feedback mechanism that includes prediction error ratio and uncertainty loss function is employed to improve the generalization performance of skidding prediction model. The effectiveness of the proposed strategy is validated under different working conditions.

This article investigates the reliability and optimal replacement policy of a multistate system under the Markov renewal shock model, which has broad applications in engineering practice. The successive arrivals of shocks follow a continuous-time renewal process, and the system's state (damage) evolution is depicted as a homogeneous, irreducible Markov renewal process. In this context, the system incurs dual damages over time as follows: 1) one comes from the previous shocks' damage evolutions and 2) the other comes from the damage of successive arrivals of shocks. The reliability and optimal replacement time of the developed system are provided and the asymptotic evolution results for each shock, that is, the probabilities for each shock finally dissipating or causing the system's failure, are deduced. The optimal replacement policy for the developed shock model is discussed through minimizing the average cost rate function. Finally, numerical studies are given for the Markov renewal shock model, with interarrival times between adjacent shocks assumed to follow an exponential distribution.

Health prognostics within the Internet of Things (IoT) paradigm face several challenges, including data privacy, client drift, and prediction accuracy. Federated learning (FL), as an emerging decentralized machine learning paradigm, has the potential to address these challenges by integrating multiple data silos in a distributed and privacy-preserved fashion. This article develops a novel personalized federated transfer learning (PFTL) framework for customized health prognosis of multiple heterogeneous clients. The framework starts with a powerful initial global prognostic model that is pretrained using a publicly available data set in a central server. The pretrained global model is then distributed to the local clients and fine-tuned separately on their respective private data sets. The fine-tuned local prognostic models are uploaded to the central server for dynamic weighted model aggregation. The aggregated model is then distributed to each client for implementing domain adversarial training to obtain a fine-grained local prognostic model. The proposed PFTL framework embeds a multiscale attention module and a multihead self-attention module parallelly into the deep learning-based prognostic model, which is shared between the central server and each local client. Through experimental verifications from lab testing-based and open-source fast-charging lithium-ion batteries data sets, we demonstrate that the proposed method can achieve accurate cycle-life prediction without compromising data privacy.

Degradation analysis is essential in system health management and remaining useful life prediction. Since the observed degradation data are inevitably contaminated by measurement error, degradation state estimation is hence important for a more accurate evaluation of the health status. There are two challenges for estimating the degradation state. The first is the uncertainty associated with the estimated parameters for the model, and the other is the measurement outlier. Current models usually assume Gaussian measurement errors and they are sensitive to the measurement outlier. To deal with these two challenges, we develop a framework for degradation state estimation under the context of the distributionally robust optimization, which is robust to the parameter uncertainty. We further incorporate the Huber loss into this framework to make it robust to the measurement outlier. A procedure for estimation of the model parameters as well as setting the parameters of the ambiguity set is provided. The effectiveness of the model is validated using numerical and real case studies.

By using in situ health information, many existing studies for online remaining useful life (RUL) prediction adopt a stochastic process-based degradation model and a computation-intensive parameter estimation method for RUL prediction of a single operating asset. Nevertheless, it is common that there are multiple assets under operation, and it would be more statistically efficient to jointly update their RULs by allowing information sharing among them for model parameter estimation. To this end, we propose a collaborative RUL prediction framework with closed-form online update. The framework is a hybrid algorithm that combines the conjugate prior for part of the model parameters and a stochastic approximation to the rest parameters. With this framework, a recursive online Bayesian algorithm is developed to jointly update the model parameters and RUL prediction using data from multiple operating assets. The effectiveness of the proposed method is demonstrated through a simulation study and two real cases.

The multicategory support vector machine (MSVM) has been widely used for multicategory classification. Despite its widespread popularity, regular MSVM cannot provide direct probabilistic results and suffers from excessive computational cost, as it is formulated on the hinge loss function and it solves a sum-to-zero constrained quadratic programming problem. In this study, we propose a general refinement of regular MSVM, termed as the simplex-based proximal MSVM (SPMSVM). Our SPMSVM uses a novel family of squared error loss functions in place of the hinge loss and it removes the explicit sum-to-zero constraint by the simplex structure. Consequently, the SPMSVM only requires solving an unconstrained linear system, leading to closed-form solutions. In addition, the SPMSVM can be cast into a weighted regression problem so that it is scalable for large-scale applications. Moreover, the SPMSVM naturally yields an estimate of the conditional category probability, which is more informative than regular MSVM. Theoretically, the SPMSVM is shown to include many existing MSVMs as its special cases, and its asymptotic and finite-sample statistical properties are well established. Simulations and real examples show that the proposed SPMSVM is a stable, scalable and competitive classifier.

It is common to encounter large-scale monotone inclusion problems where the objective has a finite sum structure. We develop a general framework for variance-reduced forward-backward splitting algorithms for this problem. This framework includes a number of existing deterministic and variance-reduced algorithms for function minimization as special cases, and it is also applicable to more general problems such as saddle-point problems and variational inequalities. With a carefully constructed Lyapunov function, we show that the algorithms covered by our framework enjoy a linear convergence rate in expectation under mild assumptions. We further consider Catalyst acceleration and asynchronous implementation to reduce the algorithmic complexity and computation time. We apply our proposed framework to a policy evaluation problem and a strongly monotone two-player game, both of which fall outside the realm of function minimization.

Condition monitoring of the wind turbine based on supervisory control and data acquisition (SCADA) data has attracted much attention in recent years. Nevertheless, there are some inherent challenges in SCADA data analysis, including the low sampling rate, time-varying working conditions of the wind turbine, and a lack of historical fault data. To solve these problems, this article develops a novel condition monitoring and fault isolation system. First, a covariate-adjusted preprocessing procedure is proposed to account for the various working conditions of the wind turbine. Next, we construct a global monitoring statistic based on all temperature variables contained in the SCADA data, with a view to monitoring the overall health status of the wind turbine. If an alarm is raised, we isolate the fault through a variable selection method without relying on expert knowledge or historical fault data. Simulation and real cases are provided to demonstrate the effectiveness of this system.

This study considers a repairable production system operated under an age-based preventive replacement policy that is subject to independent random production waits and failures. In addition to the age-based replacement policy, we propose a maintenance model that uses production waits to schedule preventive replacement. That is, a decision maker can preventively replace the system either during a production wait or at the age threshold, whereas if a failure occurs during production, the decision maker must decide whether to perform a minimal repair or a corrective replacement to restore the system. Under the above setting, we develop a semi-Markov decision process (SMDP) to obtain the optimal maintenance policy that minimizes the long-run average maintenance cost rate. We establish the existence of the optimal maintenance policy and provide an algorithm to numerically obtain the optimal action for each state. We further generalize the model to incorporate imperfect maintenance and the nonhomogeneous arrival of production waits. In the latter case, it is computationally intractable to optimize the SMDP using a value iteration algorithm due to the curse of dimensionality. To address this challenge, we further develop an approximate dynamic programming framework to generate high-quality solutions. An attractive feature of our model is its generality, such that the model includes many existing maintenance models as special cases. A real-world example from a steel factory is used to demonstrate the proposed model.

Contamination in the water distribution network poses a serious threat to this critical infrastructure. Detecting contamination sources promptly and accurately, so that remedial action can be taken, is highly desirable. Traditional methods mainly address the source detection problem by brute-force forward simulations, followed by applying statistical or optimization techniques to massive simulation results. Backtracking water parcels from downstream to upstream is more efficient, but it fails in the face of random water demand because tracking requires deterministic hydraulic conditions. To solve this problem, we propose a Bayesian framework that integrates a physical model of forward and backward tracking of contaminant movement into a statistical model to update the probability of contamination events that report the location and time. In the framework, we first impute an ensemble of realizations of water demand. In each demand realization, contaminants are backtracked, and a collection of contamination events is identified. Then, every contamination event is simulated to obtain artificial sensor data. By comparing simulated and incoming field sensor data, the probability of each contamination event is iteratively updated, with high updated probability implying strong suspicion. The efficiency and effectiveness of the framework are demonstrated using a well-studied network and compared with existing methods.

Degradation is one of the major root causes of system failure. In some applications, the degradation levels are different upon failure, in which the fixed failure threshold assumption commonly adopted in the degradation literature may not hold. This article tackles the difficulty by jointly analyzing the system degradation and the lifetime data, which enables the corresponding remaining useful life (RUL) prediction. We treat the degradation level as a multiplicative time-varying covariate of the system hazard rate, where a random-effects Wiener process is adopted to model the degradation process. The model parameters are estimated under a Bayesian framework, and we also develop a particle filter method to update the estimates when new data are available. This makes the proposed model be able to realize online RUL prediction based on the in-situ system health state signals. Through case studies on lead-acid batteries and digital communication systems, the proposed model is shown to outperform existing methods in terms of the RUL prediction accuracy.

The optimal plan of a time-censored accelerated life test (ALT) depends on unknown parameters in the ALT model. The general strategy for coping with this problem is to replace the unknown parameters with their a priori estimated values, after which we can design test plans that are robust to deviations of the estimated values. In an ALT with log-location-scale lifetime distribution and linear acceleration relation function, the slope parameter of the acceleration relation function usually has the highest uncertainty. Instead of prespecifying the slope parameter in the ALT design, in this article, we propose a new design criterion that minimizes the risk of misclassifying whether the product's pth quantile meets the design specification. Through a case study of a circular electric connector, we illustrate the proposed method, and compare it with other test criteria. The comparison result shows that the proposed plan exhibits good performance in both estimating and s-testing the product's pth quantile.

Most systems can fail in multiple ways, and the failure modes are usually positively correlated. This phenomenon complicates the reliability analysis and makes the corresponding maintenance planning challenging. This article proposes a condition-based maintenance policy for systems that are subject to both degradation-induced soft failure and sudden hard failure, where a higher degradation level leads to a higher hazard rate of the hard failure. The Wiener process is adopted for the degradation process, and the Weibull model is used to describe the baseline hazard rate of the hard failure. The degradation level is then treated as a time-varying covariate that affects the hazard rate of the hard failure, and the closed-form of the reliability function is derived by using the Brownian bridge theory. An inspection/replacement maintenance policy is employed, and the long-run cost rate is formulated based on the semiregenerative property of the system state. The optimal inspection interval and the preventive replacement threshold are then jointly determined by minimizing the long-run cost rate. A numerical study on a hydraulic sliding spool system is conducted to validate the derived reliability function and the maintenance policy.

The mission abort is an effective action to reduce the risk of casualties and enhance the survivability of mission-based systems such as aircrafts, submarines, and unmanned aerial vehicles (UAVs). A main task in real operations is to strive for balance between the mission reliability and the system survivability via elaborate mission abort plans. In this paper, we design the optimal mission abort policies based on the information of early-warning signals, which indicates the possible forthcoming fatal malfunction. Depending on the acquisition time of such information, the operator may immediately abort the mission, or ignore the information and continue the task. Within the framework of a constant mission duration, we carry out an economic analysis for the above problem. The optimal abort decision that minimizes the expected total economic loss is investigated. We further extend the proposed model to the scenario of a random mission duration and derive the corresponding optimal abort decisions. A case study on a UAV executing power-grid inspection missions is used to illustrate the applicability of the abort policies.

Stochastic processes and filtering methods are popular tools for degradation modeling and online remaining useful life (RUL) prediction. However, most models are for one-dimensional degradation and various filtering methods can only handle observations from a single system. This paper studies joint online RUL prediction of multideteriorating systems with multisystem observations and measurement errors. A multivariate degradation model equipped with a batch particle filter is developed and built for characterizing multiple dependent performance deteriorations with measurement errors in each system. The batch particle filter is developed for simultaneous online parameter estimation and degradation state identification by leveraging multisystem observations. A numerical example and a case study are provided to demonstrate the proposed method. The results show that homogeneous multisystem observations from a population of multideteriorating systems can be jointly processed on-the-fly. Individualized online RUL prediction with improved precision for each system can be achieved through the joint online inference.

Components in a system work under the same dynamic operating conditions, and their lifetimes are generally positively correlated. Ignorance of the correlation may lead to a significant bias in the evaluation of system reliability. Using the cumulative exposure principle, we model the equivalent operating time of the components, resulting from the cumulative effects of the dynamic environments, as a monotone increasing stochastic time scale. Commonly-used models, such as the compound Poisson, gamma, and the inverse Gaussian processes, are adopted for the stochastic time scale. Based on the above settings, reliability models for multicomponent systems are developed. We investigate how the stochastic time scale influences the system reliability and the correlations between component lifetimes. Under the stochastic time scale, the component lifetimes are shown to be positively quadrant dependent. Overlook of the correlation would overestimate the reliability of a parallel system but underestimate the reliability of a series system. When the stochastic time scale degenerates to a deterministic function of the calendar time, on the other hand, the system reliability becomes the reliability of the system where components work independently. The proposed models are successfully applied to lifetime data of brake pads in the automobile braking system.

During the useful life period of a costly system, it has been a common practice to perform imperfect preventive maintenances (PMs) with the purpose of failure prevention and useful life extension. Nevertheless, a system cannot be restored to an as-good-as-new state even though the imperfect PM actions are performed with a high frequency. This is known as the saturation effect and it is commonly overlooked in the existing literature. Motivated by a PM problem in a manufacturing company, this study proposes two PM models to capture the dynamics of the saturation effect. The first model divides the system deterioration into recoverable damage and irreversible intrinsic fatigue. The PMs are assumed to be effective only in healing the first type of damage. When the intrinsic fatigue for some complex systems cannot be well defined, we propose another model that generalizes the existing virtual age models by allowing the proportion of virtual age reduction to depend on the PM frequency. The long-run average costs of the two models are derived, and optimization of the cost models is investigated. The proposed PM models are then applied to two types of mechanical systems in the manufacturing company. The case study shows that ignorance of the saturation effect will make inferior maintenance policy that incurs substantial losses. The proposed models are also shown to be robust in the sense that the parameter estimation errors cannot significantly increase the system operational cost rate.

Motivated by the need to support effective asset management of infrastructure systems, this paper presents a novel reliability model for a load-sharing system where the operator can adjust component work load to balance system degradation. The operator-intervention effect, combined with other system complexities, makes modeling reliability interesting and challenging. We first develop cost modeling for a load-sharing system that has experienced operational service at the time of analysis. The system replacement process is modeled as a delayed renewal process for which the expected operational cost of the system is derived. A numerical algorithm is proposed to compute the cost, and the error bound is shown to be of order O(n-1). Next, we extend modeling to consider multiple heterogeneous systems located at different sites within the infrastructure network. Heterogeneities here refer to possible cross-site differences in the operating environments and the operators' actions. When the heterogeneities are observable, we model as covariates; otherwise, we model as random effects. Statistical inference methods are developed for the proposed models. An example using real data from a water utility illustrates the logical model behavior given parameter choices as well as showing how analysis might inform asset management.

Condition-based maintenance (CBM) is proved to be effective in reducing the long-run operational cost for a system subject to degradation failure. Most existing research on CBM focuses on single-unit systems where the whole system is treated as a black box. However, a system usually consists of a number of components and each component has its failure behavior. When degradation of the components is observable, CBM can be applied to the component level to improve the maintenance efficiency. This paper aims to study the optimal inspection/replacement CBM strategy for a multi-unit system. Degradation of each component is assumed to follow a Wiener process and periodic inspection is considered. We cast the problem into a Markov decision framework and derive the optimal maintenance decisions that minimize the maintenance cost. To better illustrate the optimal maintenance strategy, we start from a 1-out-of-2: G system and show that the optimal maintenance policy is a two-dimensional control limit policy. The argument used in the 1-out-of-2: G system can be readily extended to general cases in a similar way. The value iteration algorithm is used to find the optimal control limits, and the optimal inspection interval is subsequently determined through a one-dimensional search. A numerical study and a comprehensive sensitivity analysis are provided to illustrate the optimal maintenance strategy.

Degradation modeling plays an important role in system health diagnosis and remaining useful life (RUL) prediction. Recently, a class of Wiener process models with adaptive drift was proposed for degradation-based RUL prediction, which has been proven flexible and effective. However, the existing studies use an autoregressive model of order 1 for the adaptive drift, which can result in difficulties in both model estimation and RUL prediction. This paper proposes a new adaptive Wiener process model that utilizes a Brownian motion for the adaptive drift. The new model shares the flexibility of the existing models, but avoids the difficulties in model estimation and RUL prediction. A model estimation procedure based on maximum likelihood estimation is developed, and the RUL prediction based on the proposed model is formulated. The effectiveness of the model in RUL prediction is validated using simulation and through an application to the lithium-ion battery degradation data.

Field data provide important information about product quality and reliability. Many large organizations have developed ambitious reliability databases to trace field failure data of a variety of components on the systems they operate and maintain. Due to the exponential distribution assumption for the component lifetimes, the data in these databases are often aggregated. Specifically, individual lifetimes of the components are not available. Instead, each recorded data point is the cumulative operating time of one component position from system installation to the last component replacement, and the number of replacements in between. In the literature, the gamma distribution and the inverse Gaussian (IG) distribution have been used to fit the aggregate data, while the operating environment of different systems is often assumed the same. In order to capture possible heterogeneities among the systems, this study proposes the gamma random effects model and the IG random effects model. The expectation-maximization algorithm is used for point estimation of the parameters and an algorithm based on the generalized fiducial inference method is proposed for interval estimation. Simulation studies are conducted to assess the performance of the proposed inference methods. A real aggregate dataset is used for illustration.

We propose a quantile regression framework to model accelerated life tests (ALT) data. The quantile of the failure time distribution at the usage level can be easily estimated using quantile regression. Compared with traditional parametric regression methods, quantile regression is distribution-free, efficient in the presence of censoring, and more flexible in modeling ALT relations. More importantly, we show that it is able to handle ALT data with a failure-free life, which is a great challenge in the ALT literature. We use extensive simulation studies and two real ALT case studies to demonstrate the effectiveness of the proposed method.

In addition to conventional censoring schemes such as Type-I or Type-II censoring, progressively censoring is a useful method to reduce cost and obtain additional reliability information in accelerated life testing. Statistical inference for accelerated life testing (ALT) with Weibull distribution and progressively censoring is found to be difficult. This paper develops generalized fiducial inference techniques for the constant-stress ALT model with Weibull distribution and progressively Type-II censoring. Simulation studies reveal the good performance of the proposed inference methods. An example is given for illustration.

In a load-sharing system, total workloads are shared by all components and failure of one component increases stress of the surviving ones. The time interval between two consecutive component failures reflects component reliability under different stress and is of interest to us. This study develops an iterative algorithm for analysis of such data from load-sharing systems. In each iteration, we first obtain the equivalent operating time of each component under a given stress by capitalizing on the cumulative exposure principle. Then the equivalent operating times, which are simply right-censored, are fitted to update the parameter estimates. The conversion has closed forms for most common distributions such as the log-location-scale family and the gamma distribution, and the subsequent fitting of right-censored data is straightforward. Therefore, the algorithm is easy to implement compared with existing methods such as the maximum likelihood estimation. Convergence properties of the algorithm are investigated theoretically and through extensive simulations. Three examples representing different types of real problems are used to demonstrate the proposed algorithm.

This study investigates modeling, estimation and optimization of destructive degradation tests (DDTs) for highly reliable products with random initial degradation values. It is common to observe that the degradation paths of distinct products start from different values specified by a random variable. The random initial value introduces additional uncertainties to the degradation of the product. In this study, Wiener-process-based degradation models are developed for products with random initial values. We first consider a DDT without stress acceleration. In a DDT, the measurement of the degradation destroys a test unit and, thus, only one measurement is available for each unit. Closed-form maximum likelihood (ML) estimators are derived. Then, an accelerated DDT (ADDT) is considered. Based on these results, we investigate optimal designs of both DDT and ADDT with the objective of minimizing the asymptotic variance of the estimated p th-quantile of the failure time distribution under use conditions. The optimal test plans have to be obtained through a numerical approach. Optimality of the plans is verified by the general equivalence theorem. An adhesive bond example with real degradation data is analyzed to show the performance of the proposed methods.

Most commercial products are sold with a warranty. Product repairs during the warranty period are often free of charge, and contribute significantly to the costs of a manufacturer. Estimation of the warranty costs is important for the manufacturer to prepare sufficient warranty reserves for future claims. Because products are often sold to customers intermittently, the total number of sold units under warranty varies over time, which presents difficulties in forecasting the warranty costs over time. In this study, we consider the stochastic sales process, and derive the expectation and variance of the aggregate discounted warranty costs within a given period of time. By taking the variation of the warranty costs into consideration, the result can be used in the preparation of a conservative warranty reserve for a new product. The discounted life-cycle warranty cost is a special case of our model, and it can also be determined from our result. Numerical results show the applicability of our model in estimating periodic discounted warranty costs, and preparing both short-term and long-term warranty reserves.

The IG process models have been shown to be an important family in degradation analysis. In this paper, we are interested in optimal constant-stress accelerated degradation tests (ADTs) planning when the underlying degradation follows the inverse Gaussian (IG) process. We first consider ADT planning for the IG process without random effects. Asymptotic variance of the estimate of a lower quantile is derived, and the objective of the planning is to minimize this variance by properly choosing the testing stresses, and the number of samples allocated to each stress. Next, ADT planning for a random-effects IG process model is considered. We then applied the IG process to fit the stress relaxation data of a component, and use the developed methods to help with the optimal ADT design.

Motivated by an industrial problem affecting a water utility, we develop a model for a load sharing system where an operator dispatches work load to components in a manner that manages their degradation. We assume degradation is the dominant failure type, and that the system will not be subject to sudden failure due to a shock. By deriving the time to degradation failure of the system, estimates of system probability of failure are generated, and optimal designs can be obtained to minimize the long run average cost of a future system. The model can be used to support asset maintenance and design decisions. Our model is developed under a common set of core assumptions. That is, the operator allocates work to balance the level of the degradation condition of all components to achieve system performance. A system is assumed to be replaced when the cumulative work load reaches some random threshold. We adopt cumulative work load as the measure of total usage because it represents the primary cause of component degradation. We model the cumulative work load of the system as a monotone increasing and stationary stochastic process. The cumulative work load to degradation failure of a component is assumed to be inverse Gaussian distributed. An example, informed by an industry problem, is presented to illustrate the application of the model under different operating scenarios.

Degradation signals that reflect a system's health state are important for diagnostics and health management of complex systems. However, degradation signals are often compounded and contaminated by measurement errors, making data analysis a difficult task. Motivated by the wear problem of magnetic heads used in hard disk drives (HDDs), this paper investigates Wiener processes with measurement errors. We explore the traditional Wiener process with positive drifts compounded with i.i.d. Gaussian noises, and improve its estimation efficiency compared with the existing inference procedure. Furthermore, to capture the possible heterogeneity in a population, we develop a mixed effects model with measurement errors. Statistical inferences of this model are discussed. The mixed effects model subsumes several existing Wiener processes as its limiting cases, and thus it is useful for suggesting an appropriate Wiener process model for a specific dataset. The developed methodologies are then applied to the wear problem of magnetic heads of HDDs, and a light intensity degradation problem of light-emitting diodes.

Degradation, and shock are two common mechanisms accounting for product failures. This paper presents a convenient means of capturing both shock and degradation in a single model when the extent of degradation and the magnitude of shocks are not observable, but only the failure times and the corresponding failure modes are recorded. We assume that the lifetime of a degradation-oriented failure, which is regarded as some initial random resource, belongs to some distribution family. Shocks arrive according to a non-homogeneous Poisson process, and the destructive probability depends on the transformed remaining resource of the system. Under these assumptions, we propose the single failure time model, and the recurrent event model. This study complements the well-known Brown-Proschan model. The single failure time model has successfully been applied to a real time data set. We also conduct a simulation study to examine the accuracy of our model.