Condition-based-maintenance Scheme With Cost-effective Inspection And Discounted Rate

As time goes on, the state of the equipment deteriorates, thus inspections, either periodic or non-periodic, should be scheduled. Equipment maintenance plays an important role in the manufacture. Along with the development of the technology, equipment maintenance strategy significantly changes, from traditional periodic maintenance to condition-based maintenance. Meanwhile, hundreds of different mathematical models have been proposed to solve this problem.Most models that do not consider the inspection cost can only be used in the case where the state of the equipment could be easily fetched. The other models either optimize the replacement limit after fixing the next inspection time, or optimize the next inspection time after fixing the replacement limit based on Proportional Hazards Models. None of them have tried to optimize both the next inspection time and the replacement limit at the same time.To achieve this goal, we proposed a discounted Markov decision process, taking all of the inspection cost, prevention replacement and non-periodic inspection into account, while the deterioration can be modeled as a discrete Markov process and the optimization target is the total discounted cost. In this paper we proved the following properties, 1) the discount cost function satisfies the Bellman equation, 2) the discounted cost function increases with the deterioration, 3) replacement exists in the optimal strategy, indicating that the next inspection and the replacement limit can be optimized together. Besides, the requirement of the special No-Inspection strategy has been discussed. Iteration algorithm aimed to find the optimal cost was also proposed and shown to be exponentially convergent. Properties were verified in numerical experiments and the total discounted cost had been reduced comparing with the periodic inspection policy.Multi-component maintenance that considers all the components as a whole is also a research hotspot in the field of maintenance. In those cases, cost correlation and structure correlation should be considered. Cost correlation suggests that there is a fixed amount of cost in a single maintenance activity, which implies that it would cost less to implement maintenance for multiple components at one time, than to implement maintenance for them separately. Structure correlation means that there are series or parallel connections between the components, hence the failure of one of the components does not necessarily lead to a system failure. While most of the models consider only one of the correlations, the extension of our model to a multi-component maintenance model can consider both cost and structure correlations. After performing calculations for various structures such as parallel connection, series connection, parallel-series connection and series-parallel connection, optimal cost and optimal strategies were obtained.