Statistical Infenence On Censored Data In Survival Analysis And Its Applications

It has been observed that censored data has aroused wide concern in survival anal-ysis. In recent years, many authors considered the progressively censored scheme and hybrid censored scheme in the literature. In this thesis, we discuss the statistical inference with the exponential model, Weibull model, exponentiated Pareto model and generalized exponential model in survival analysis with consideration of censored scheme. Because of censoring of data, statistical information is missing. We have studied the optimal cen-soring scheme based on the Fisher information matrix and budget constraint of a life experiment. We also discussed the acceptance sampling plan in life testing. We develop the life test plan such that the producer and consumer risks are satisfied. In reliability, R=P(Y< X), where X is the strength of a system and Y is the stress acting on it has aroused wide concern. It can be used for reliability design of mechanical component. R is a measure of the system performance. We discuss the reliability of a system, when the strength of the system and the stress imposed on it are independent, non identical exponentiated Pareto distributed random variables. Different point estimations and inter-val estimations are proposed. We also present an approximation computation of renewal function when the inter arrival time follows generalized exponentiated distribution.This thesis contains 6 chapters. Chapter 1 reviews the history of censored data and depicts the present situation and development. The main work of the thesis is concluded.In chapter 2, we discuss the statistical inference of exponential distribution and Weibull distribution which are widely considered in survival analysis with progressively type-I censored scheme. Based on the equivalent quantity and exponential distribution to Weibull distribution translation technique, we propose a new method to estimate the unknown parameter. This method is an alterative to other method in the literature.In chapter 3, we discuss the statistical inference with hybrid censored scheme of Weibull distribution. We derive the exact distribution of maximum likelihood estimator as well as exact confidence interval for the scale parameter of Weibull distribution. For the complexity of exact conditional survival function, we also provide approximate method and bootstrap method for constructing confidence interval. Acceptance sampling with censoring is an important topic in life testing. Life test plan are developed such that the the producer and consumer risks are satisfied. Using the exact conditional survival function of the scale parameter, we establish an acceptance sampling procedure.The generalized Pareto distribution is proposed by Pickands (1975). Since then, the generalized Pareto distribution has been widely studied in the literature; for example, see Hosking and Wallis (1987), Smith (1985) and Wu (2009) et.al.. In chapter 4, we study the generalized Pereto modeling which is widely considered in reliability. We discuss the sta-tistical inference problem with progressively type-I censored scheme. Using the missing information principle, the observed Fisher information can be obtained. We discuss the optimal censored scheme with consideration of the budget constraint in an experiment.The exponentiated Pareto distribution has been discussed by Gupta et.al.(1998). The exponentiated Pareto distribution can be used quite effectively in analysing many lifetime data because it can have decreasing and upside-down bathtub shape failure rate function. In chapter 5, the reliability R= P(Y