Yifan Zhou

Maintenance optimisation of a multi-state series–parallel system considering economic dependence and state-dependent inspection intervals

Abstract This paper presents a maintenance optimisation method for a multi-state series–parallel system considering economic dependence and state-dependent inspection intervals. The objective function considered in the paper is the average revenue per unit time calculated based on the semi-regenerative theory and the universal generating function (UGF). A new algorithm using the stochastic ordering is also developed in this paper to reduce the search space of maintenance strategies and to enhance the efficiency of optimisation algorithms. A numerical simulation is presented in the study to evaluate the efficiency of the proposed maintenance strategy and optimisation algorithms. The simulation result reveals that maintenance strategies with opportunistic maintenance and state-dependent inspection intervals are more cost-effective when the influence of economic dependence and inspection cost is significant. The study further demonstrates that the optimisation algorithm proposed in this paper has higher computational efficiency than the commonly employed heuristic algorithms.

An effective approach to reducing strategy space for maintenance optimisation of multistate series–parallel systems

Abstract Maintenance optimisation of series–parallel systems is a research topic of practical significance. Nevertheless, a cost-effective maintenance strategy is difficult to obtain due to the large strategy space for maintenance optimisation of such systems. The heuristic algorithm is often employed to deal with this problem. However, the solution obtained by the heuristic algorithm is not always the global optimum and the algorithm itself can be very time consuming. An alternative method based on linear programming is thus developed in this paper to overcome such difficulties by reducing strategy space of maintenance optimisation. A theoretical proof is provided in the paper to verify that the proposed method is at least as effective as the existing methods for strategy space reduction. Numerical examples for maintenance optimisation of series–parallel systems having multistate components and considering both economic dependence among components and multiple-level imperfect maintenance are also presented. The simulation results confirm that the proposed method is more effective than the existing methods in removing inappropriate maintenance strategies of multistate series–parallel systems.

Maintenance optimisation of a parallel-series system with stochastic and economic dependence under limited maintenance capacity

Maintenance optimisation of a parallel-series system considering both stochastic and economic dependence among components as well as limited maintenance capacity is studied in this paper. The maintenance strategies of the components are jointly optimised, and the degradation process of the system is modelled to address the stochastic dependence and limited maintenance capacity issues. To overcome the “curse of dimensionality” problem where the state space of a parallel-series system increases rapidly with the increased number of components in the system, the factored Markov decision process (FMDP) is employed for maintenance optimisation in this work. An improved approximate linear programming (ALP) algorithm is then developed. The selection of the basis functions and the state relevance weights for ALP is also investigated to enhance the performance of the ALP algorithm. Results from the numerical study show that the current approach can handle the decision optimisation problem for multi-component systems of moderate size, and the error of maintenance decision-making induced by the improved ALP is negligible. The outcome from this research provides a useful reference to overcome the “curse of dimensionality” problem during the maintenance optimisation of multi-component systems.

Maintenance decision-making using a continuous-state partially observable semi-Markov decision process

Due to the limitation of current condition monitoring technologies, the actual health state of an asset may not be revealed accurately by health inspections. A maintenance strategy ignoring this uncertainty of health state can cause additional costs or downtime. The partially observable Markov decision process (POMDP) is a commonly used approach to derive optimal maintenance strategies when the health inspection is imperfect. However, the existing applications of the POMDP to maintenance decision-making largely adopt the discrete time and state assumptions. The discrete-time assumption requires the health state transitions and maintenance activities only happen at discrete epochs, which cannot model the failure time accurately and is not cost-effective. The discrete health states, on the other hand, may not be elaborate enough to improve the effectiveness of maintenance. To address these limitations, this paper proposes a partially observable semi-Markov decision process (POSMDP) which is continuous in time and states. A Monte Carlo-based density projection method is adopted to convert the POSMDP to a complete observable semi-Markov decision process (SMDP). The converted SMDP is then solved by the policy iteration. At the end of this paper, a simulation study is performed to evaluate the performance of the POSMDP. The result shows that the maintenance strategy derived by the POSMDP is more cost-effective than another two maintenance strategies derived by approximate methods, when regular inspection intervals are adopted. The simulation study also shows that the maintenance cost can be further reduced by developing maintenance strategies with state-dependent maintenance intervals using the POSMDP.

A study of ribbing effect on the vibration response and transmission of an L-shaped plate.

This paper presents an analytical solution for the vibration response of a ribbed L-shaped plate using a modal expansion solution approach. The analytical model is then employed to study the ribbing effect on vibration reduction and transmission between the two plate components of the L-shaped plate. It is found that for the system considered in the study, a rib inserted between the excitation force and the source plate can lead to a large vibration reduction for both source and receiving plates except at a frequency band near the fundamental resonant frequency of the rib where the ribs flexural stiffness is negligible. A reduced vibration transmission to the receiving plate can also be achieved by placing a rib near the plate/plate junction, attributed to the increased moment impedance at the coupling after the rib insertion. Increasing the ribs flexural stiffness under this condition can further reduce vibration transmission in the low frequency bands while increasing the ribs mass can lead to a reduced vibration transmission in the higher frequency bands. The insights obtained from this study are relevant to vibration control of structures such as transformer tanks and machine covers.

Asset life prediction using multiple degradation indicators and lifetime data: A gamma-based state space model approach

This paper proposes a Gamma-based state space model to predict engineering asset life when multiple degradation indicators are involved and the failure threshold on these indicators are uncertain. Monte Carlo-based parameter estimation and model inference algorithms are developed to deal with the proposed Gamma-based state space model. A case study using real data from industry is conducted to compare the performance of the proposed model with the commonly used proportional hazard model (PHM). The result shows that the Gamma-based state space model is more appropriate to deal with the situation when the failure data is insufficient.

Reliability evaluation of multi-state series systems with performance sharing

In this paper, a new reliability model for a multi-state system (MSS) with performance sharing is proposed. The MSS consists of N multi-state units connected in series. Each unit in the system has a random performance level and a random demand. If the performance of a unit exceeds its demand, the surplus performance can be transmitted to its adjacent units through intermediate transmitters. Each transmitter has a random capacity, through which only a limited amount of performance can be transmitted. The entire system fails if the demand of any unit is not satisfied. An algorithm based on the universal generating function (UGF) is developed to evaluate the reliability of the system. Analytical and numerical examples are provided to validate the proposed method. Examples show that the developed algorithm is efficient in system reliability evaluation.

Maintenance optimization for a system with an implemented interval of replacement activities

Most research on maintenance optimization regarded that a replacement activity is performed as soon as a planned time reaches, some other considered a time delay on replacement schedule when one job is completed or a failure comes. However, there is no existing research taking into account the influence of changes of the replacement schedule and catastrophic failures of a system on the replacement activity. In this paper, Failures of the system are divided into minor and catastrophic ones, and the replacement activity is performed either at the time when a catastrophic failure happens or in the implemented interval of the replacement activity randomly, whichever comes first. The objective of this paper is to find a constraint on the implemented interval length which is determined by engineers and an optimal implemented range of replacement activities for minimize the mean maintenance cost.

An efficient maintenance optimisation method for series-parallel systems using stochastic ordering and revenue difference boundaries

A critical problem during the maintenance optimisation of series-parallel systems is the large strategy space. To address this issue, existing research largely relies on heuristic algorithms, e.g. genetic algorithm (GA) and ant colony optimisation (ACO). These heuristic algorithms can have a low convergence speed, and the obtained strategy are often not global optimal. Instead of searching an optimal strategy in a large space, this paper focuses on the reduction of optimisation space. After investigating the performance dependence among subsystems, this research develops a new strategy space reduction criterion based on the average revenue difference boundaries. By combining the proposed criterion and an earlier method developed by the authors which is based on the stochastic ordering [1], this research develops an efficient maintenance optimisation algorithm. The simulation study shows that the developed maintenance optimisation algorithm can reduce the strategy space more considerably than that proposed in [1].

Maintenance optimisation of a series production system with intermediate buffers using a multi-agent FMDP

Maintenance decision making of a series production system with intermediate buffers is a research topic of practical significance. The Markov decision process (MDP) is an effective tool to undertake maintenance optimisation of a series production system with buffers due to its capacity in dealing with complex structure of maintenance strategies for such systems. However, the MDP has only been employed to analyse small systems due to the “curse of dimensionality”. A multi-agent factored Markov decision process (FMDP) is adopted in this study to remit the “curse of dimensionality”. The series production system considered in the study consists of several subsystems, and each subsystem is managed by an agent. A new method is developed to select maintenance actions in cooperation of different agents. An approximate linear programming algorithm is used to solve the FMDP model efficiently. The numerical study shows that the developed methods can deal with medium-scale series production systems with an insignificant small error in maintenance decision making.