This study aims to construct an optimal preventive maintenance model for a multi-state degraded system under the condition that individual components or subsystems can be monitored in real time. Given the requirement of minimum system availability, the total maintenance cost is minimized by determining the maintenance activities of components in degraded states. The general non-homogeneous continuous-time Markov model (NHCTMM) and its analogous Markov reward model (NHCTMRM) are used to quantify the intensity of state transitions during the degradation process, allowing the determination of various performance indicators. The bound approximation approach is applied to solve the established NHCTMMs and NHCTMRMs, thus obtaining instantaneous system state probabilities to overcome their inherent computational difficulties. Furthermore, this study utilizes a genetic algorithm to optimize the proposed model. A simulation illustrates the feasibility and practicability of the proposed approach.
Modern equipment is designed to operate under deteriorating performance conditions resulting from internal ageing and/or external environmental impacts influencing downstream maintenance. This study focuses on the development of a multistate system (MSS) that considers a human reliability factor associated with maintenance personnel—a condition-based multiobjective MSS preventive maintenance model (MSSPMM). The study assumes that no more than one maintenance activity is performed to achieve the most appropriate preventive maintenance (PM) strategy and easy implementation and to reduce maintenance error due to human reliability. The MSS performance based on mean system unavailability and total maintenance cost is evaluated using a stochastic model approach, and then, the MSSPMM is used for optimisation. A customised version of the nondominated sorting genetic algorithm III is employed to ensure efficient solution of the PM model with human reliability—which is considered a constrained multiobjective combinatorial optimisation problem. The optimised solutions are determined from the nondominated Pareto frontier comprising the diversified PM alternatives. A helicopter power transmission system is used as an example to illustrate the efficacy and applicability of the proposed approach through sensitivity analyses with relevant parameters.
This study aims for multistate systems (MSSs) with aging multistate components (MSCs) to construct a time-replacement policy and thereby determine the optimal time to replace the entire system. The nonhomogeneous continuous time Markov models (NHCTMMs) quantify the transition intensities among the degradation states of each component. The dynamic system state probabilities are therefore assessed using the established NHCTMMs. Solving NHCTMMs is rather complicated compared to homogeneous continuous time Markov models (HCTMMs) in determining reliability related performance indexes. Often, traditional mathematics cannot acquire accurate explicit expressions, in particular, for multiple components that are involved in designed system configuration. To overcome this difficulty, this study uses Markov reward models and the bound approximation approach to assess rewards of MSSs with MSCs, including such things as total maintenance costs and the benefits of the system staying in acceptable working states. Accordingly, we established a long-run expected benefit (LREB) per unit time, representing overall MSS performance through a lifetime, to determine the optimal time to replace the entire system, at which time the LREB values are maximized. Finally, a simulated case illustrates the practicability of the proposed approach.
Fuzzy multi-state systems (FMSSs) comprise FMS components (FMSCs) aims at analyzing non-probabilistic uncertain circumstances defined by fuzzy state-transition rate and performance numbers. The triangular fuzzy number that features intuitive and algebraic operations is widely used for quantifying fuzziness. This study aims to overcome the drawbacks of the existing FMSS availability index that either does not conform to a normal convex set or is inconsistent with the crisp-circumstance multi-state system (MSS) availability beyond summation over state probabilities that do no equal unity. The proposed method first evaluates the instantaneous state probability (ISP) of FMSCs by establishing the FMSCs Markov model. Subsequently, the FMSSs ISP is evaluated by integrating the FMSCs ISP using the fuzzy universal generating function based on the system-structure function. A "constrained nonlinear parameter programming model" has been developed to evaluate the improved FMSSs availability. The corresponding availability index features the normal convex set whilst fulfilling the MSS theory, which requires state probabilities to equal unity during availability evaluation. The effectiveness of the proposed approach has been verified using an illustrated community-based smart-grid system comprising three FMSCs-solar-and wind-energy systems as well as diesel-generator equipment. Moreover, the results of an independent sensitive analysis provide further insights into the improved FMSSs availability with regard to the time and circumstance fuzziness.
This study aims at the multi-state degraded system with multi-state components to propose a novel approach of performance evaluation and a preventive maintenance model from the perspective of a system's components. The general non-homogeneous continuous-time Markov model (NHCTMM) and its analogous Markov reward model (NHCTMRM) are used to quantify the intensity of state transitions during the degradation process. Accordingly, the bound approximation approach is applied to solve the established NHCTMMs and NHCTM-RMs, thus evaluating system performance including system availability and total maintenance cost to overcome their inherent computational difficulties. Furthermore, this study adopts a genetic algorithm (GA) to optimize a proposed preventive maintenance model. A simulation illustrates the feasibility and practicability of the proposed approach.
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