Parameter estimation for a repairable system under imperfect maintenance

Estimation of reliability and maintainability parameters is essential in modeling repairable systems and determining maintenance policies. However, because of the aging of repairable systems under imperfect maintenance, failure times are neither identically nor independently distributed, which makes parameter estimation difficult. In this paper, we apply Bayesian methods for estimation of reliability and maintainability parameters based on historical reliability and maintainability (RAM) data. We assume the first failure of the repairable system follows a Weibull probability distribution. The repairable system experiences Kijima Type I imperfect corrective maintenance and Kijima Type I imperfect preventive maintenance. Using a Bayesian perspective, we estimate four parameters for this repairable system: the shape parameter of the Weibull probability distribution (beta), the scale parameter of the Weibull distribution (eta), the imperfect maintenance factor for corrective maintenance (alpha_r) and the imperfect maintenance factor for preventive maintenance (alpha_p). The proposed method is illustrated with simulated RAM data.