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The modern engineering systems often operate under varying environments and only partial information can be observed at discrete monitoring epochs. For such systems, few works have been done for the prognostics of health status using the available environment and monitoring information. Therefore, the aim of this article is to present a new health prediction method for modern engineering systems whose condition is partially observable under varying environments. A dynamic Gamma process is proposed to model the system degradation observations under changing environments. To describe the relation of system actual status to the observed information, a proportional hazard (PH) model integrating internal aging and external observations is presented for modeling the system hazard rate. To realize prediction of residual life of such systems, a matrix operation-based prognostic method is presented to calculate the closed-form solutions of health characteristics for the system. A case study of partially observable failing systems is demonstrated, and comparisons with other recent developed approaches are also given to show the effectiveness of the model. • Novel environment-varying degradation model. • PH model incorporating failure and environment processes. • Construction of a matrix-based approach for health estimation. • Closed-form expressions for health characteristics. • Comparisons of different published models via case studies. [ABSTRACT FROM AUTHOR]

• Competing risks model with aging and continuous-state degradation. • Development of prognostic approach with dynamic corrective mechanisms. • Development of corrected residual life-based maintenance policy with dynamic control policy. • Development of SMDP approach to optimize the multi-objective maintenance model. • Considerably better MRL and maintenance performance compared with published results. The accurate prediction of residual life in deteriorating systems is a challenging task due to uncertainties and idealized assumptions during data acquisition and model construction. To address this challenge, the paper proposes a bi-level maintenance model that incorporates a corrected residual life (CRL) approach for a deteriorating system under competing risks. Specifically, the degradation failure is modeled using a Gamma process, while the competing sudden failure is described by a proportional hazards (PH) model. To reduce inconsistencies in residual life prediction, a CRL model is presented and continuously updated with a dynamic corrective factor at each monitoring epoch. Based on the updated CRL, a bi-level maintenance model is developed, which considers both system availability and maintenance cost objectives, enabling dynamic monitoring of the system's degradation state and residual life. The optimal decision variables in the maintenance model are determined through a multi-objective optimization algorithm formulated within a semi-Markov decision process (SMDP) framework. The unique aspect of this work lies in the consideration of prediction errors in residual life and the incorporation of multi-attribute optimization for maintenance design. The proposed method is validated through a case study on light-emitting diodes, confirming its effectiveness in improving residual life prediction and optimizing maintenance decisions. [ABSTRACT FROM AUTHOR]

• Development of a multi-attribute Bayesian control scheme for fault prediction. • Multivariate hidden Markov model describes the deterioration process. • Computational algorithm to optimize the multi-attribute Bayesian policy. • Development of a real case study and verification using multivariate data. Although Bayesian approaches have been utilized in engineering systems for health prognostics, very little work has been done using Bayesian methods for fault prediction of systems under multiple attributes. To address this issue, in this paper a novel multi-attribute Bayesian control chart is presented for predicting failures of hidden-state systems by jointly considering two performance measures of system operation. The system actual status is represented by a three-state multivariate hidden stochastic process with a normal state, an abnormal state, and a failure state. The working states are unobservable and failure state is observable. Based on the built hidden-state model, a fault prediction scheme integrating both system availability and cost objectives is constructed via a multi-attribute Bayesian control chart to monitor and predict impending risks of the operational systems. The Bayesian control chart alarms when the probability of impending risks reaches a certain control limit, which is optimized and determined by a computational algorithm developed in a semi-Markov decision process framework. The proposed fault prediction scheme provides an appearing feature to jointly consider multiple attributes for hidden-state systems. A real case study of mechanical generators is presented and a comparison with other Bayesian and non-Bayesian methods is also given, which demonstrates the effectiveness and superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

Generally, the internal states of most engineering systems are inaccessible to sensors under operational conditions, permitting indirect measurements and failures to be observed discretely. For this type of system, a class of proportional hazard (PH) models with multistate process have been proposed for performing prognostics. However, existing studies use a constant degradation mechanism with a very limited number of states, which may fail to model the actual deterioration of the system. Therefore, this article presents a novel PH model that utilizes a nonconstant degradation mechanism with a large number of states to perform health prognostics. A matrix partition-based approximation method is developed to include all the possible state transitions and to estimate important health quantities of the system, such as conditional reliability (CR), mean remaining useful life (MRUL), and remaining useful life distribution (RULD). An online prognostic scheme based on this matrix approach is presented to provide an update with the latest health quantities of the system. The proposed approach provides appealing computational features and avoids difficulties in calculating uncountable transitions for PH model-based prognostics. The effectiveness of the proposed method is demonstrated via a case of helical gearboxes under indirect monitoring and random failure conditions. [ABSTRACT FROM AUTHOR]

Modern engineering components generally work under aging and dynamic cumulative damage processes. To prevent failures of such components, the proportional hazards model (PHM) was proposed to integrate both processes for health prognostics. However, the existing PHMs use constant damage rate within monitoring intervals for machine health estimation and still lack consideration of dynamic operational conditions, which fails to model the practical degradation situations. This article presents a prognostic model using a new PHM to consider aging and environment-varying cumulative damage for engineering machines. A dynamic multistate process with practical transition mechanisms under varying operational conditions is presented to model the cumulative damage progress. To address the difficulties in prognostics with PHMs, a matrix-based approximation method with low computational load is developed to compute important health measures such as conditional reliability, mean residual life (MRL) and residual life distribution. A prognostic scheme featuring online prediction and dynamic updating is presented. The particularity of the proposed model is that it considers dynamic environments and can be applied to a large number of deteriorating states. The proposed approach is illustrated using a case of pump under different operating environments, and comparison with other advanced PHM is given to validate the applicability and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

• New, two-level Bayesian fault detection scheme is developed. • Realistic failure modeling considering two dependent failure modes. • Mean residual life formula is derived considering two failure modes in a new HMM framework. • The proposed two-level Bayesian control scheme outperforms previously published Bayesian control scheme. • Considerably lower average cost, reduced number of failures and more precise residual life estimates. A two-level Bayesian control approach is presented to detect early fault for mechanical equipment subject to dependent degradation and catastrophic failures. The system degradation process is modeled using a continuous time stochastic process with three states. To model the dependence of two failure modes, we assume that the joint distribution of the time to catastrophic failure and sojourn time in the healthy state follows Marshall-Olkin bivariate exponential distribution. To avoid unnecessary sampling cost and to effectively detect impending failure, a two-level control policy, where longer sampling interval is applied for healthier state and shorter sampling interval is used in severe degradation state is proposed in Bayesian control chart framework for a multivariate observation process considering dependent failure modes. The optimization problem is formulated and solved in the semi-Markov decision process (SMDP) framework. A formula for the mean residual life (MRL) is also derived using the Bayesian approach. The validation of the proposed methodologies is carried out using real multivariate degradation data obtained from a milling machine. A comparison with the multivariate Bayesian control chart with a single sampling interval and a single control limit is given, which illustrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]