ABSTRACT
In recent years, industrial systems have been more large scaled and more complex, and played a significant role to improve the quality of people's daily life. For utilizing the ability of such systems, it is important to understand the behavior of failure phenomena of the industrial systems. Suppose that more than one failure may occur in each system component of a repairable system. Usually, two kinds of repair actions are performed to return the failed component state to the normal condition after each failure. The maximum likelihood estimation is a commonly used technique to identify the failure time distribution or the minimal repair process. In the failure time data analysis, it is often assumed that not only single but also multiple time-series data on minimal repair processes are observed. In the case where nonparametric estimation methods are used to estimate the optimal periodic replacement time, Gilardoni developed nonparametric estimation techniques for a periodic replacement problem with minimal repair.
