Joint Modeling of Death Times and Number of Failures for Repairable Systems using a Shared Frailty Model

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Journal of Korean Society for Quality Management > Volume 26(4); 1998 > Article

Journal of Korean Society for Quality Management 1998;26(4): 111-.

공유환경효과를 고려한 수리가능한 시스템의 수명과 고장회수의 결합모형 개발

박희창¹, 이석훈²

¹창원대학교 자연과학대학 통계학과
²충남대학교 자연과학대학 통계학과

Joint Modeling of Death Times and Number of Failures for Repairable Systems using a Shared Frailty Model

ABSTRACT

We consider the problem of modeling count data where the observation period is determined by the life time of the system under study. We assume random effects or a frailty model to allow for a possible association between the death times and the counts. We assume that, given a random effect or a frailty, the death times follow a Weibull distribution with a hazard rate. For the counts, given a frailty, a Poisson process is assumed with the intensity depending on time. A gamma distribution is assumed for the frailty model. Maximum likelihood estimators of the model parameters are obtained. A model for the time to death and the number of failures system received is constructed and consequences of the model are examined.