New State Diagrams for Probabilistic Maintenance Models

Many probabilistic maintenance models developed for maintenance scheduling and optimization are based on state diagrams. Classical maintenance models based on state diagrams provide inaccurate results when inspection rates are nonperiodic. An attempt has been made to rectify some modeling properties through the use of an alternative graph; however, it requires Monte Carlo simulation to accurately calculate reliability. This paper highlights an idealistic property of classical state diagrams and proposes new state diagrams to correct it. The accuracy of Markov models based on proposed state diagrams is verified through a theoretical discussion. Significant differences between the results given by classical and proposed maintenance models are shown through a numerical example for imperfect maintenance. The behavior of mean time between failures is also analyzed to validate the proposed models. With the proposed model, reliability analysis of different maintenance activities can be calculated analytically without the use of Monte Carlo simulation.