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The accelerated degradation testing (ADT) has been widely applied as an efficient strategy to obtain the reliability (life) information of the assets in a shorter-than-normal period of time by exposing the assets to higher-than-normal stresses. Recently, with advances in the sensor technology, it has been revealed that the degradation of some assets demonstrates a long-term memory effect, which implies that the future degradation process not only depends on the current degradation state but also strongly correlates with the past degradation history across a long period of time, and the degradation increments are correlated for nonoverlapping time intervals. The existing ADT methods do not consider the long-term memories, which could lead to biased life testing results. In this article, we propose a novel ADT model by integrating the long-term degradation memory effect based on a utilization of the fractional Brownian motion. A maximum likelihood approach is developed to estimate the model parameters. A likelihood-ratio hypothesis test is designed to test the existence of long-term memories. Simulation studies are implemented to illustrate the developed methods. Physical experiments on accelerated testing of a photocatalyst are designed and conducted to demonstrate the proposed model and its advantage over benchmark approaches. The results show that the traditional ADT paradigm, which ignores the long-term memories, significantly underestimates asset lifetime uncertainties.

In credit scoring, survival analysis models have been widely applied to answer the question as to whether and when an applicant would default. In this paper, we propose a novel mixture cure proport...

Reliability analysis of repairable systems has been widely conducted based on collected information such as the systems’ failure counting processes. In many real-life situations, the failure counting processes may not be completely observed when some failure times are not recorded or missing due to various practical reasons. In the literature, only a limited number of reliability studies focus on missing failure time data for repairable systems with an assumption that the system repair is either perfect or minimal. When the repair effect is general as in many real-world situations, challenges arise for reliability analysis in that the observed and unobserved failure times are statistically dependent in a complex manner, and the time censoring problem becomes unconventional. In this paper, to overcome these challenges, we propose a reliability model for repairable systems with incomplete failure time data under general repair. The proposed model is suitable for modeling both a single system and multiple systems subject to failure heterogeneity. A maximum likelihood estimation method is developed to estimate the model parameters. Based on the proposed model, statistical inference of the missing times is developed. Simulation and real-life case studies are conducted to verify the developed methods.

Material deformation is one of the major causes of material failure. In a dynamic deformation process, local deformation—defined as the displacement of various local points on a material—essentially determines the failure. Most existing studies on material reliability are conducted based on either the failure time or the degradation data. The studies do not consider the dynamic local deformation of materials and often are not efficient enough to model the failure mechanism. In this article, we develop reliability analysis by using information contained in the dynamic local deformation of materials in a tensile process. Specifically, a new multivariate general-path model is proposed to describe the deformation process. A two-stage method is developed to estimate the model parameters and overcome the computational complexity. Based on the proposed model, reliability analyses are conducted for various cases of material deformation paths. A simulation study is implemented to verify and validate the de...

Optimal maintenance planning for repairable systems plays a critical role in ensuring an appropriate level of system reliability and availability. An important class of optimal maintenance planning decisions are those in which one must determine whether to implement a repair or a renewal (replacement) upon system failure. Most existing models within this class are based on a single-state framework, wherein the system age is utilized as the unique measure to determine whether to repair or renew. Extended models have also appeared in the literature which utilize both the system age and the number of failures/repairs since last replacement to provide a two-dimensional characterization of the system state thereby providing more flexibility and improving the quality of maintenance planning. The existing two-state optimal maintenance planning models, however, only work for a single system. They cannot handle situations where multiple systems are involved, especially when multiple systems operate in different environments (treated as covariate effects) leading to heterogeneity in failure processes of those systems. Ignoring the covariate effects can result in a non-optimal (i.e., more costly) maintenance planning. In this article, we propose a two-state covariate-dependent optimal maintenance planning model for multiple systems. Specifically, we develop a covariate-dependent trend renewal process model to formulate the heterogeneous failure processes of multiple systems. A maximum likelihood estimation method is developed for model parameter estimation. Based on the proposed model, we develop a two-state covariate-dependent optimal maintenance planning by utilizing a discrete semi-Markov decision process. The optimal covariate-dependent control-limit maintenance policy is derived based on a numerical search algorithm. A simulation study and a real-world case study are conducted to illustrate the proposed approach.

Accelerated life testing has been widely applied to obtain the reliability information of an asset (component) at use conditions when the component is highly reliable. In accelerated life testing, tested components are exposed to stress levels more severe than usual so that more component failures can be observed in a short period of time. Most existing statistical models assume a known parametric relationship between the lifetime (or lifetime characteristic) and accelerating stresses. In this paper, we propose semiparametric modeling for the relationship between the lifetime characteristic and accelerating stresses. The proposed model is suitable for both single and multiple accelerating stress cases. A maximum penalized likelihood estimation method is developed to estimate the model parameters. A simulation study is implemented to illustrate the performance of the proposed model, and a real-world case study is conducted to demonstrate the proposed model.

The microstructure of a material is known to strongly influence its macroscopic properties, such as strength, hardness, toughness, and wear resistance, which in turn affect material service lifetime. In the reliability literature, most existing research conducts reliability analysis based on either lifetime data or degradation data. However, none of these studies take the information contained in an image of the microstructure of the material into account when conducting reliability analysis. In this article, considering the strong effect on a material's reliability created by its microstructure, we conduct a reliability analysis of an advanced high-strength dual-phase steel by utilizing information about its microstructure. Specifically, the lifetime distribution of the steel, which is assumed to belong to a log-location-scale family, is predicted by utilizing the information contained in images of its microstructure. For the prediction, we propose a novel statistical model called the distributio...

Consider a situation where we measure the strength of two different components that go into a finished product. In order for the product to work well, it is crucial that the strength of component A...

The Kijima model has been widely used in reliability literature to analyze repairable systems with various degrees of repair efficiency including “perfect repair,” “minimal repair,” and situations in between. Most existing studies, however, treat repair efficiency as a fixed value even though repair efficiency can vary among a series of repairs. In this paper, we propose a generalized mixed effect Kijima model to characterize the variation of repair efficiency. In particular, the newly proposed “mixed effect” model incorporates a fixed time-dependent effect and a random effect of repair efficiency, while the term “generalized” refers to the fact that the classic Kijima model is generalized to handle more maintenance situations such as “better than new” and “worse than old” situations after repair. To estimate the model parameters given a series of observed system failure times, we develop a stochastic approximation expectation maximization algorithm which is a type of maximum likelihood estimation method. Further, an optimal periodic maintenance planning is developed based on the proposed reliability model. A simulation study and a real-world case study are conducted to demonstrate the developed methods.

Condition-Based Maintenance (CBM) planning for multi-component systems has been receiving increasing attention in recent years. Most existing research on CBM assumes that preventive maintenances should be conducted when the degradations of system components reach specific threshold levels upon inspection. However, the search of optimal maintenance threshold levels is often efficient for low-dimensional CBM but becomes challenging if the number of components gets large, especially when those components are subject to complex dependencies. To overcome the challenge, in this paper we propose a novel and flexible CBM model based on a customized deep reinforcement learning for multi-component systems with dependent competing risks. Both stochastic and economic dependencies among the components are considered. Specifically, different from the threshold-based decision making paradigm used in traditional CBM, the proposed model directly maps the multi-component degradation measurements at each inspection epoch to the maintenance decision space with a cost minimization objective, and the leverage of deep reinforcement learning enables high computational efficiencies and thus makes the proposed model suitable for both low and high dimensional CBM. Various numerical studies are conducted for model validations.

Degradation data, frequently along with low-dimensional covariate information such as scalar-type covariates, are widely used for asset reliability analysis. Recently, many high-dimensional covariates such as functional and image covariates have emerged with advances in sensor technology, containing richer information that can be used for degradation assessment. In this article, motivated by a physical effect that microstructures of dual-phase advanced high strength steel strongly influence steel degradation, we propose a two-stage material degradation model using the material microstructure image as a covariate. In Stage 1, we show that the microstructure image covariate can be reduced to a functional covariate while statistical properties of the image are preserved up to the second order. In Stage 2, a novel functional covariate degradation model is proposed, based on which the time-to-failure distribution in terms of degradation level passages is derived. A penalized least squares estimation method is developed to obtain the closed-form point estimator of model parameters. Analytical inferences on interval estimation of the model parameters, the mean degradation levels, and the distribution of the time-to-failure are also developed. Simulation studies are implemented to validate the developed methods. Physical experiments on dual-phase advanced high strength steel are designed and conducted to demonstrate the proposed model. The results show that a significant improvement is achieved for material failure prediction by utilizing material microstructure images compared with multiple benchmark models.

Crack propagation subjected to fatigue loading has been widely studied under the assumption that loads are ideally cyclic with a constant amplitude. In the real world, loads are not exactly cyclic, due to either environmental randomness or artificial designs. Loads with amplitudes higher than a threshold limit are referred to as overloads. Researchers have revealed that for some materials, overloads decelerate rather than accelerate the crack propagation process. This effect is called overload retardation. Ignoring overload retardation in reliability analysis can result in a biased estimation of product life. In the literature, however, research on overload retardation mainly focuses on studying its mechanical properties without modeling the effect quantitatively and, therefore, it cannot be incorporated into the reliability analysis of fatigue failures. In this article, we propose a physical–statistical model to quantitatively describe overload retardation considering random errors. A maximum lik...