Bayesian Estimation of Parameters of Reliability and Maintainability of a Component under Imperfect Repair and Maintenance

The determination of maintenance policies in companies depend on the reliability and maintainability (RAM) parameters. This work estimates the RAM parameters of a component under the condition of imperfect maintenance. Exact mathematical expressions using virtual age model of Kijima type I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{I}$$\end{document} are derived for the evaluation of probability distributions of these parameters. The mathematical derivations are based on Bayes formula of posterior probabilities. Bayes formula is applied directly without the need of application of approximate sampling techniques. Computations of probability distribution of parameters of reliability and maintainability have been elaborated using Visual Basic. The application of Bayes formula of posterior probabilities to estimate the parameters shows satisfactory results.