可靠性和食品安全中次序统计量的非线性组合理论研究

Many time series data observed in reliability life testing, food safety and environment testing have a natural temporal ordering. These observations naturally ordered according to magnitude are literately considered as observations from order statistics. Therefore, while the world is facing challenging with issues in reliability, food safety and environment, the investigation of order statistics, from theory, method to application has become more and more important nowadays. Many advances have been made on the linear combination of order statistics and applications. Most of the existing methods, however, still lack efficiency for some small sample or high censring rate data or highly skewed life distributions. This project contributes to novel research on nonlinear combinations of order statistics with aiming at new and effective statistical inference methods and tools for progressively censored samples and left censored samples. The main contents include: (1)The general structure of nonlinear combinations of order statistics and their expected statistical properties for progressively censored samples and left censored samples. (2) Nonlinear combinations of order statistics based inference for stress-strength model with application in reliability testing. (3) Nonlinear combinations of order statistics based inference for left censored data and applications in food safety data analysis (4) Nonlinear combinations of order statistics based inference for several independent progressively censored samples and applications.

由于在可靠性寿命试验、食品安全和环境检测中观察到的数据很多都是有序数据，这些数据可以看作是次序统计量的观察值，所以研究次序统计量的相关理论及其在可靠性和食品安全中应用既有理论意义又有重要的实际意义。现有次序统计量的理论与方法大都局限于次序统计量的线性组合或似然方法，这些方法一般基于相应的大样本结果，这些方法对小样本为主的可靠性数据缺乏有效性。本项目以次序统计量的非线性组合为工具，提出了一类非次序统计量的理论、方法以及在逐次右截尾样本和左截尾样本的有效性。主要内容有：(1)在逐次截尾和左截尾情形次序统计量一类非线性组合的构造；(2)在应力强度模型下基于此类非线性组合的参数估计方法和有效性；(3)基于左截尾样本的参数估计方法和假设检验方法(包括分布的拟合优度检验)，并把提出的方法应用于食品安全和环境检测数据；(4)基于逐次截尾样本有关分布参数的比较的检验。

由于在可靠性寿命试验、食品安全和环境检测中观察到的数据很多都是有序数据，这些数据可以看作是次序统计量的观察值，所以研究次序统计量的相关理论及其在可靠性和食品安全中应用既有理论意义又有重要的实际意义。现有次序统计量的理论与方法大都局限于次序统计量的线性组合或似然方法，这些方法一般基于相应的大样本结果，这些方法对小样本为主的可靠性数据缺乏有效性。本项目以次序统计量的非线性组合为工具，首先研究了Weibull分布下基于不同形式的有序数据的统计推断方法，进一步把方法推广到成比例失效模型和成比例倒失效率模型。其次研究了Gamma分布、广义Pareto分布、广义指数分布和Kumaraswamy分布的统计推断方法。第三研究了Weibull分布串联系统下环境因子和Gamma分布下环境因子的点估计和区间估计方法。第四从过程控制角度研究了指数分布、逆Gaussian分布、Pareto分布和正态分布的方差、变异系数的参数比较问题。经过四年的研究较好完成了研究任务。