This paper develops two component-level control-limit preventive maintenance (PM) policies for systems subject to the joint effect of partial recovery PM acts (imperfect PM acts) and variable operational conditions, and investigates the properties of the proposed policies. The extended proportional hazards model (EPHM) is used to model the system failure likelihood influenced by both factors. Several numerical experiments are conducted for policy property analysis, using real lifetime and operational condition data and typical characterization of imperfect PM acts and maintenance durations. The experimental results demonstrate the necessity of considering both factors when they do exist, characterize the joint effect of the two factors on the performance of an optimized PM policy, and explore the influence of the loading sequence of time-varying operational conditions on the performance of an optimized PM policy. The proposed policies extend the applicability of PM optimization techniques.
Since 1960s, maintenance optimization has continuously been an interesting and important topic for the researchers for its growing impact on a company's competitiveness [1]. In the recent decades, the maintenance policies have gradually shifted from run-to-failure corrective maintenance (CM), time-based preventive maintenance (PM), to condition-based maintenance (CBM) and predictive maintenance (PdM) [2] and [3].
Essential elements of a maintenance policy include: (1) the objective, such as maximization of average system availability in an infinite time horizon [4], [5] and [6], minimization of the overall production and maintenance losses in a finite time horizon [7], minimization of the average maintenance cost rate per operational time in an infinite time horizon [8] and [9], etc.; (2) the maintenance policy, such as periodic policy, control-limit policy [4] and [5], sequential policy [7], [8] and [9], etc.; (3) the maintenance quality/effect, such as perfect PM act which restores a system to a state “as good as new”, imperfect PM act which restores a system to a better but not “as good as new” state [10] and [11], etc.; (4) the degradation characteristics, such as a batch of systems' lifetime distribution [8], the stochastic, Markov, hidden Markov degradation models [12] and [13]; and (5) the maintenance constraints, such as limited maintenance resources, maintenance conflicts among adjacent components [7], etc.
As imperfect PM acts are very common in industrial practice (e.g. spraying lubricant to a drill bit or replacing a component for a walking robot), many recent studies tend to include the effect of imperfect PM acts in maintenance policies [10], [11], [14], [15] and [16]. On the other hand, efforts in maintenance optimization are targeted towards establishing maintenance policies for systems subject to variable operational conditions based on proportional hazards model (PHM) and similar models [17] and [18], proportional intensity model (PIM) [19], [20] and [21], etc. As systems under various operational conditions (e.g. temperature, humidity and vibration level) may exhibit significantly different degradation rate [22], it is necessary to treat the systems under various operational conditions separately.
Although there are many maintenance policies that consider the effect of imperfect PM acts and variable operational conditions [10], [11], [14], [15], [16], [17] and [18], a maintenance policy which accounts for both of these two factors has not been reported yet. However, it is common to see a batch of systems subject to imperfect PM acts as well as different operational conditions (e.g. a batch of drill bits working with different thrust forces and receiving lubricant oil). As a result, it is necessary to develop practical maintenance policies for such systems, and study the properties of the policies for further insights.
By the above motivation, this paper develops two component-level control-limit PM policies for systems subject to the joint effect of imperfect PM acts and variable operational conditions, and investigates the properties of the proposed policies. Within the PM policies, the extended proportional hazards model (EPHM) is used to model the system failure likelihood influenced by both factors, which is capable of handling the case of time-varying operational conditions. Several numerical experiments are conducted for policy property analysis. The most related work might be [23], which presents an age-dependent reliability model considering effects of maintenance and working conditions. However, the work in [23] does not further establish a PM policy and the model in [23] is generally applicable to the case of constant working condition between two consecutive PM cats.
The rest of the paper is organized as follows: Section 2 provides a concise summary of the EPHM and the recursive algorithm for parameter estimation. Section 3 establishes two component-level control-limit PM policies based on the EPHM. Section 4 conducts several numerical experiments to investigate the properties of the proposed PM policies. Finally, Section 5 concludes the paper.
