Xiujie Zhao

Heuristic hybrid game approach for fleet condition-based maintenance planning

The condition-based maintenance (CBM) method is commonly used to select appropriate maintenance opportunities according to equipment status over a period of time. The CBM of aircraft fleets is a fleet maintenance planning problem. In this problem, mission requirements, resource constraints, and aircraft statuses are considered to find an optimal strategy set. Given that the maintenance strategies for each aircraft are finite, fleet CBM can be treated as a combinatorial optimization problem. In this study, the process of making a decision on the CBM of military fleets is analyzed. The fleet CBM problem is treated as a two-stage dynamic decision-making problem. Aircraft are divided into dispatch and standby sets; thus, the problem scale is significantly reduced. A heuristic hybrid game (HHG) approach comprising a competition game and a cooperative game is proposed on the basis of heuristic rule. In the dispatch set, a competition game approach is proposed to search for a local optimal strategy matrix. A cooperative game method for the two sets is also proposed to ensure global optimization. Finally, a case study regarding a fleet comprising 20 aircraft is conducted, with the results proving that the approach efficiently generates outcomes that meet the mission risk-oriented schedule requirement.

Accelerated Degradation Tests Planning With Competing Failure Modes

Accelerated degradation tests (ADT) have been widely used to assess the reliability of products with long lifetime. For many products, environmental stress not only accelerates their degradation rate but also elevates the probability of traumatic shocks. When random traumatic shocks occur during an ADT, it is possible that the degradation measurements cannot be taken afterward, which brings challenges to reliability assessment. In this paper, we propose an ADT optimization approach for products suffering from both degradation failures and random shock failures. The degradation path is modeled by a Wiener process. Under various stress levels, the arrival process of random shocks is assumed to follow a nonhomogeneous Poisson process. Parameters of acceleration models for both failure modes need to be estimated from the ADT. Three common optimality criteria based on the Fisher information are considered and compared to optimize the ADT plan under a given number of test units and a predetermined test duration. Optimal two- and three-level optimal ADT plans are obtained by numerical methods. We use the general equivalence theorems to verify the global optimality of ADT plans. A numerical example is presented to illustrate the proposed methods. The result shows that the optimal ADT plans in the presence of random shocks differ significantly from the traditional ADT plans. Sensitivity analysis is carried out to study the robustness of optimal ADT plans with respect to the changes in planning input.

Utilizing experimental degradation data for warranty cost optimization under imperfect repair

Manufacturers usually want to predict the warranty cost for new products under affordable maintenance policies. With insufficient reliability information, experimental degradation tests are commonly conducted to predict the field reliability before the products are put on the market. In this paper, we propose a novel warranty cost optimization framework based on degradation data within a finite warranty period under the assumption of imperfect repairs. The expected number of warranty claims is given in the analytical form. Two sources of uncertainty are considered to estimate the field reliability for more realistic warranty cost prediction: the uncertainty in experimental data and the variation in field conditions. Effects of imperfect repairs are assumed to be random. The warranty cost for a single repair is assumed to be associated with the improvement factor of imperfect repairs. Optimal imperfect repair policy is obtained by minimizing the expected warranty cost for each sold product. Further, the proposed framework can facilitate the interval prediction for warranty cost. Numerical results show that the proposed analytical method to evaluate warranty claims significantly outperforms simulation methods from the perspective of computational efforts. Finally, an application example of degradation tests along with sensitivity analysis is presented to illustrate the proposed framework.

Optimal Inspection and Replacement Policy Based on Experimental Degradation Data with Covariates

Abstract In this article, a novel maintenance model is proposed for single-unit systems with an atypical degradation path, whose pattern is influenced by inspections. After each inspection, the system degradation is assumed to instantaneously decrease by a random value. Meanwhile, the degrading rate is elevated due to the inspection. Considering the double effects of inspections, we develop a parameter estimation procedure for such systems from experimental data obtained via accelerated degradation tests with environmental covariates. Next, the inspection and replacement policy is optimized with the objective to minimize the Expected Long-Run Cost Rate (ELRCR). Inspections are assumed to be non-periodically scheduled. A numerical algorithm that combines analytical and simulation methods is presented to evaluate the ELRCR. We then investigate the robustness of maintenance policies for such systems by taking the parameter uncertainty into account with the aid of large-sample approximation and parametric bootstrapping. The application of the proposed method is illustrated by degradation data from the electricity industry.

Parameter estimation for load-sharing systems with degrading components

This paper aims to develop a parameter estimation approach for load-sharing systems subject to continuous degradation. The system consists of multiple components in parallel structure. The components of the system suffer a degradation process, characterized respectively by Wiener process and Inverse Gaussian process. When components fail one by one, the total workload is redistributed among the remaining components, which accelerates the degradation process of the surviving components, which is referred to as a load-sharing system. Maximum likelihood estimation (MLE) is used to estimate the parameters for a load-sharing system. The available data are the failure times of the components and the degradation level of the remaining components at failure time. For Wiener process, a close-form MLE is derived and an analytical solution is achieved. For inverse Gaussian process, however, it is difficult to obtain a close-form MLE and numerical method is adopted instead. Finally, numerical studies are conducted to illustrate the estimation procedure.

Optimal condition-based maintenance policy with delay for systems subject to competing failures under continuous monitoring

Abstract Delay in maintenance operations occurs for many systems in real engineering applications. Random delays increase the variability in maintenance modeling, making the optimization of maintenance policy more complicated. In this paper, a delayed condition-based maintenance (CBM) problem for systems under continuous monitoring is studied. The system is assumed to be affected by competing degradation failures and fatal shocks. The degradation path is modeled by a gamma process, while random fatal shocks are modeled by a non-homogeneous Poisson process, of which the failure intensity has a change point that depends on the degradation level. It is assumed that when the degradation level reaches the alarm threshold, the maintenance operation delays for a random duration of time before its implementation. The main objective here is to choose an appropriate alarm threshold to minimize the expected cost rate. We derive the asymptotic cost rate in the analytical form. The proposed modeling and decision framework are validated and illustrated by numerical examples along with sensitivity analysis. The results show the necessity to determine the distribution for delay time precisely and the framework also helps decision maker to identify the source of the cost that is most worthwhile to be controlled in practice.

Reliability and performance modeling for mission-oriented k-out-of-n system under common cause failures

This paper proposes a reliability and performance analysis and modeling methodology for mission-oriented k-out-of-n systems. The system is assumed to suffer both independent internal failures and external common cause shocks, of which arrivals are both modeled by Poisson processes. Periodic missions are assigned to the system due to a fixed schedule. A performance measure is introduced based on the mission workload and number of components working in the system. By modeling the failure modes on such systems with a Markov chain model, the defined reliability and performance is given in analytical forms. In a following numerical example, we illustrate the reliability and performance for such systems by the proposed approach.