M. Ebrahimi, R. Farnoosh,
Volume 20, Issue 4 (4-2010)
Abstract
This paper is intended to provide a numerical algorithm based on random sampling for solving the linear Volterra integral equations of the second kind. This method is a Monte Carlo (MC) method based on the simulation of a continuous Markov chain. To illustrate the usefulness of this technique we apply it to a test problem. Numerical results are performed in order to show the efficiency and accuracy of the present method.
Khamiss Cheikh, El Mostapha Boudi, Hamza Mokhliss, Rabi Rabi,
Volume 35, Issue 3 (9-2024)
Abstract
Maintenance plan efficacy traditionally prioritizes long-term predicted maintenance cost rates, emphasizing performance-centric approaches. However, such criteria often neglect the fluctuation in maintenance costs over renewal cycles, posing challenges from a risk management perspective. This study challenges conventional solutions by integrating both performance and robustness considerations to offer more suitable maintenance options.
The study evaluates two representative maintenance approaches: a block replacement strategy and a periodic inspection and replacement strategy. It introduces novel metrics to assess these approaches, including long-term expected maintenance cost rate as a performance metric and variance of maintenance cost per renewal cycle as a robustness metric.
Mathematical models based on the homogeneous Gamma degradation process and probability theory are employed to quantify these strategies. Comparative analysis reveals that while higher-performing strategies may demonstrate cost efficiency over the long term, they also entail greater risk due to potential cost variability across renewal cycles.
The study underscores the necessity for a comprehensive evaluation that balances performance and resilience in maintenance decision-making. By leveraging the Monte Carlo Method, this research offers a critical appraisal of maintenance strategies, aiming to enhance decision-making frameworks with insights that integrate performance and robustness considerations.
