A Structural Property of Optimal Policies for Multi-Component Maintenance Problems

作者：Jia Qing Shan^*

来源：IEEE Transactions on Automation Science and Engineering, 2010, 7(3): 677-680.

DOI：10.1109/TASE.2009.2036375

• Action space reduction
• joint replacement
• Markov decision processes
• multicomponent maintenance

In this paper, we focus on the opportunistic maintenance of an asset which is composed of multiple nonidentical life-limited components with both economic and structural dependence. Besides the random asset failure, each component also has independent failure with constant rate. Both finite and infinite horizons are considered. We first prove the optimality of the Generalized Strict Shortest-Remaining-Lifetime-First (GSSRLF) rule to efficiently reduce the size of the action space from O(2(n)) to O(Pi(m)(i=1) n(i)), where is the number of components, is the number of modules, and is the number of components in module. Then, we show that the GSSRLF rule is more general than the existing SRLF rule, and has close relationship with several other rules and properties known in literature. Finally, we discuss the limitations of the GSSRLF rule and use numerical results to show that even when the rule is not optimal, it helps to identify good policies.
Note to Practitioners-Motivated by a practical problem, we study a structural property of optimal policies for opportunistic maintenance of an asset with multiple nonidentical life-limited components. Both economic and structural dependence among the components are considered. During the optimization of joint replacement policies, the action space grows exponentially with respect to the number of components. We identify the GSSRLF rule, which reduces the size of the action space and makes the action selection efficient. We prove that the GSSRLF rule preserves the optimal actions when each component has independent failure with constant rate. The rule has close relationship with several other rules and properties known in literature. Numerical results show that even when the rule is not optimal, it helps to identify good policies. Practitioners can combine the GSSRLF rule with neurodynamic programming to address both large action space and large state space. However, the choice of basis functions is usually problem dependent and experience-based.

• 出版日期2010-7
• 单位清华大学