경쟁적 위험모형에 대한 고장률의 베이지안 추정

Abstract

This research deals with the failure rate of the components of a complex system. The failure of a complex system is caused by the failure of one or more components. The exact estimating the failure rate of a component is important for efficient maintenance of a complex system. The lifetime data that can be obtained during the operation of the system is an important information representing the environment of system operation. Therefore, it is desirable to estimate the failure rate of components using the lifetime data. This research suggests the Bayesian estimation for the failure rate using lifetime data in competing risks model. We derive a likelihood function in both cases of which failures of components are independent and dependent. And then, Bayesian estimation process using the lifetime data is proposed with natural conjugate prior distribution. In case of independent components, the exponential distribution is used as a lifetime distribution of each components. In case of dependent components, Marshall and Olkin's bivariate exponential distribution is used as a lifetime distribution of the components. This research shows that it is possible to make use of a few of real-time lifetime data in estimating of the failure rate. Hence the result of this research can be used in determining relevant system maintenance policy. A basic complex system combined with series and parallel structure is studied in this research. Since the structure of this system is a basic one for a real complex system, the result of this research can be extended to the real complex system which consists of many components in a complex structure.