Nonparametric Estimation In The Stree-strength Model Based On Type ⅠInterval-Censored Data

When doing research in actuarial science, reliability theory and many clinical tests, we often need to deal with time’s estimation and forecasting, for example, the estimation of distribution of human life, distribution of machine service life and regular follow-ups of a cancer patient. Thinking such problems in the abstract, we can find them have a common character-we only know these random variables would occur in a certain interval, however, we haven’t a clue about the exact time on which they would fall. We call this type of data as interval-censored data, and the random variable we mentioned above means the occurrence time of an event (such as death or disease). Interval-censored data frequently appear in medical research related to regular follow-up.In this thesis, based on previous research, we do a further analysis and re-search of nonparametric estimate on survival function of Ⅰ-type interval censored data according to their characteristics. We summarize several kinds of nonparamet-ric methods for estimating Ⅰ-type interval censored data, which are Maximin formula based on isotonic regression, Maximin formula based on Ⅰ-type interval censored data and NPBAI algorithm, build simulations based on these classic algorithms, and do an analysis of and comparison between them.Stress-strength model is an approach widely applied to engineering reliability theory, however, it mainly focuses on processing complete data. Therefore, it is nec-essary to do research on stress-strength models in case of Ⅰ-type interval censored da-ta. In this thesis, we solve the nonparametric estimation problem of stress-strength model according to nonparametric method for estimating the survival function of Ⅰ-type interval censored data. Besides, we develop several simulation stress-strength models based on different algorithms, make a comparison between the analysis re-sults, and then do a further analysis of the consistency and asymptotic normality property of estimator R in stress-strength model.The structure of this thesis is as follows:the chapter 1 is introduction, which briefly describes the research background of interval censored data and the definition of Ⅰ-type interval censored data; the chapter 2 gives several methods for estimating distribution function of Ⅰ-type interval censored data, which are Maximin formula based on isotonic regression, Maximin formula based on Ⅰ-type interval censored data and NPBAI algorithm; in chapter 3, we first briefly describe the research back- ground of stress-strength model and its definition, then give a general expression for stress-strength model in case of Ⅰ-type interval censored data and do a nonparamet-ric estimation of stress-strength model in case of Ⅰ-type interval censored data, and finally make an analysis of consistency and asymptotic normality property of distri-bution functions of different algorithms; the chapter 4 is the stress-strength model simulation using nonparametric estimation of Ⅰ-type interval censored data and the comparative analysis; in chapter 5, we point out the inadequacy of our thesis, and make a conclusion and prospect.