Optimal control-limit maintenance policy for a production system with multiple process states

Highlights

• Take process states and spare parts as part of maintenance decisions.

• Include virtual age to help the indication of machine state.

• Consider the randomness of imperfect maintenance effect and spares lead time.

• Consider the impact of process state and virtual age on production cost.

• Propose an effective modified policy-iterative algorithm for cost optimization.

Abstract

In this paper, a new control limit maintenance policy is proposed for a production system with multiple process states. The process state can be obtained by quality information or other measurable indicators from the production process, when the process state by itself provides an insufficient indication or measure of the actual machine state. This can make the maintenance activities difficult to implement. Alternatively, machine virtual age can indicate the actual machine state and the maintenance effect on the machine state. Therefore, machine virtual age is used to compensate for the possible weakness of process state as an indication of machine state, and it is also used as part of maintenance decisions for more effective maintenance activities. At each inspection time, maintenance decisions are made for spare parts ordering and maintenance activities. The maintenance activities which are considered in this paper are replacement and two types of imperfect maintenance. The new maintenance planning model considers the different maintenance levels and their effects on system performance. Moreover, different maintenance cost and durations are considered. The system and associated maintenance policy are modeled by a discrete-time Markov decision process, and the long-term expected cost rate is investigated. A modified policy-iterative algorithm is then proposed to accelerate the search speed effectively during cost optimization. Compared to a traditional algorithm, the modified algorithm checks the effects of some possible parameters, rather than all parameters during the policy-iteration process. Simultaneously, it assures that the checked parameters are better than those unchecked. Finally, a numerical example is presented to illustrate the proposed method, and sensitivity analyses of important parameters are also implemented.

Introduction

Most industries require effective production systems. In production systems, maintenance activity is necessary and very important for sustaining the normal work and efficient operation of production machines (Barata, Soares, Marseguerra, & Zio, 2002). Most production machines deteriorate over time, which can affect the production levels and costs, and eventually cause machine failure. Maintenance activities can prevent system failures and improve the production process by restoring the system to a better functioning state. However, implementing a maintenance action has certain costs and time based on its frequency and type. And it can be influenced by some non-punctual factors, for example, Wang et al., 2020, Wang, Zhou, Parlikad, & Xie, 2020 studied preventive maintenance with unpunctual execution. In fact, production and maintenance plans are often not optimal with respect to the objective of minimizing the combined maintenance and production cost (Nourelfath, Nahas, & Ben-Daya, 2016).

The maintenance frequency can be controlled by some time-based or condition-based thresholds (Huynh, 2020, Wang et al., 2019, Yousefi et al., 2020). Considering a balance between maintenance action frequency and production state of the machine would lead us to have a more cost-effective maintenance policy. Spare parts planning is one of the factors involved in production systems that should be considered as part of maintenance optimization. At any time that maintenance actions are implemented, spare parts are needed for some actions, and the maintenance activities will be delayed if there are not enough spare parts available. Delay in maintenance may cause sudden failure due to the system deterioration, and consequently, an expensive penalty cost due to loss of production. On the other hand, holding too many spare parts has inventory costs, and spare parts may become obsolete due to chemical interaction with the environment and on-shelf deterioration during long-term storage.

In this paper, a new control-limit maintenance policy is proposed considering the spare parts and their stochastic arrival time. In the control-limit maintenance policy, different thresholds are suggested for various maintenance actions such as replacement, minimal maintenance, and middle maintenance. The required time, cost and the uncertain effects of maintenance actions are considered in modeling of the maintenance optimization problem. Additionally, the production cost depends on the process state and the virtual age. The maintenance problem is formulated as a discrete-time Markov decision process. The system states in the Markov decision process involve the process state, the virtual age, and the state of spare parts. The process state can be obtained by quality information or other measurable indicators from the production process. In this case, the process state by itself provides an insufficient indication or measure of the actual machine state. Machine virtual age can indicate the actual machine state and the maintenance effect on the machine state. Therefore, machine virtual age is used to compensate for the possible weakness of process state as an indication of machine state. This can provide for more effective maintenance.

Due to the model complexity and optimization difficulty, a modified policy-iterative algorithm is also proposed to accelerate the search speed of the optimal policy. It differs from the traditional method in evaluating only parts of possible parameters, rather than all parameters during the policy-iteration process, on the premise that the checked parameters are better than those unchecked.