Age replacement model using the parameter estimation of Weibull distribution with censored lifetimes

Weibull distribution is widely used in engineering problems for safety and reliability analysis due to its flexibility in modeling both increasing and decreasing failure rates. This study develops an age replacement model using the approximating parameter estimation methods of the Weibull distribution with censored lifetimes. The parameter estimation methods, applied in the numerical example, are the maximum likelihood estimation and Bayesian estimation based on Markov chain Monte Carlo. The accuracy of estimation methods is computed in the numerical simulation increasing the observation unit time. The results show that maximum likelihood estimation and the Metropolis-Hastings of Markov chain Monte Carlo methods in sequence produce better accuracy of estimation. Gibbs sampling of Markov chain Monte Carlo has a particular pattern in which the accuracy of Gibbs sampling has a tendency to stay within a certain range regardless of decreasing censored observations. In addition, this may be beneficial to develop the age replacement model when the trade-off between the estimated system reliability and cost of replacement exists considering the characteristics of the Weibull distribution with censored lifetimes.