Availability Analysis and Preventive Maintenance Planning for Systems with General Time Distributions

System failures can be pre-empted by ensuring timely maintenance during the operating life of the system. Ideally, it is vital to implement an effective maintenance strategy to ensure a system’s availability uninterrupted. The simplest maintenance plans involve only corrective maintenance; i.e., maintenance is only performed upon an unexpected failure. In contrast, many preventive maintenance models have been studied to reduce the significant loss experienced during system failures. Of these, the steady-state availability is one of the most important performance measures for repairable systems. To further improve the steady-state availability approach, preventive maintenance models have been extensively studied. However, these models assume that the distributions of the system lifetime and maintenance duration are exponential. In practice, the probabilistic characteristics of different systems and maintenance actions are so broad making the exponential distribution an inappropriate model. A review of existing literature reveals that majority of existing preventive maintenance studies assume that preventive maintenance actions are carried out precisely at scheduled preventive maintenance times. However, in practice, preventive maintenance actions are usually carried out flexibly during a time window around scheduled preventive maintenance times due to practical reasons. To this end, various functions have been developed to evaluate the effectiveness of preventive maintenance polices. Most of them are based on cost-related and availability related criteria.

Generally, in real applications, both lifetime and maintenance durations can have different distribution types. It is therefore necessary to develop a steady-state availability model for systems with general distributions so that the optimal preventive maintenance plan can be determined to match the stochastic nature of such systems. Motivated by this, Beihang University researchers: Dr. Naichao Wang, Dr. Lin Ma and Dr. Boping Xiao, together with Professor Jiawen Hu from University of Electronic Science and Technology of China, and Professor Haitao Liao from University of Arkansas, investigated a preventive maintenance model that maximizes the steady-state availability of a system with general distributions, where preventive maintenance actions are carried out flexibly during a time window around scheduled preventive maintenance times. The researchers sought to determine the optimal preventive maintenance strategy that maximizes the steady-state availability of a system involving general probability distributions. Their work is currently published in the research journal, Reliability Engineering and System Safety.

In their approach, the preventive maintenance actions were scheduled periodically, and a replacement was carried out to restore the system back to its good as-new state after a certain number of imperfect maintenance actions or upon a failure. The researchers developed a state-transition equation using the supplementary variable method, and the steady-state availability was obtained based on the stationary distribution.

Remarkably, numerical examples demonstrated that a flexible preventive maintenance time could influence the optimal decision variables, which were determined by the specific transition rate function and duration of the time window. Moreover, they proved the existence of the optimal combination of the number of imperfect maintenance actions before each replacement and scheduled preventive maintenance interval, in addition to presenting an algorithm for solving the optimization problem.

In summary, the study presented an in-depth assessment of a preventive maintenance planning model that maximizes the steady-state availability of a system with general lifetime and maintenance duration distributions. In the presented model, preventive maintenance actions were carried out flexibly during a time window around scheduled epochs, where several imperfect maintenance actions were carried out before each replacement. The proposed model has many applications in practice because it is capable of dealing with different types of transition rate functions. In a statement to Advances in Engineering, Professor Jiawen Hu explained their work offers useful insights for maintenance engineers to calculate the steady-state availability of a system under proposed preventive maintenance policy, in addition to assisting in making an effective preventive maintenance plan to increase the steady-state availability of a system.