一些寿命分布和寿命试验截尾方案的扩展研究

The lifetime distributions are used for reliability analysis of high-performance products and sophisticated systems. However, the existing lifetime distributions exhibit many defects. For example, the single shaped hazard rate function, poor flexibility of data fitting, low precision of statistical inference, incomplete statistical inference theory under the progressive censoring samples, and flawed progressively censoring test scheme. Thus we propose this project with following objectives to solve some of the listed defects...A new progressively censoring scheme will be proposed. The continuous inverse Gaussian distribution will be extended. The mathematical properties of the new distribution and its statistical inference under the progressive censoring sample will be studied. The discrete extended inverse Gaussian model will be proposed, and its statistical inference theory under the progressive censoring sample will be established. Statistical inference of some classical distributions and their extended models under the progressive censoring sample as well as several equations of characteristic parameter and stress will be investigated in the accelerated life test. The stress-strength reliability, P(X<Y), of general exponential and general inverse exponential distributions based on new progressively censoring sample will be discussed. ..In each proposed objectives, the maximum likelihood estimations (MLEs) of parameters, algorithms of MLEs, and the corresponding assessment methods of precision will be established. The procedures and algorithms to solve Bayesian parameter estimation and prediction will be studied. Real-life or simulated data sets will be used to compare the proposed maximum likelihood estimation and Bayesian approach. A unified parameter estimation and prediction method of the extended inverse Gaussian, general exponential, and general inverse exponential distribution under progressive censoring will be built in the proposed project. Moreover, the proposed project will improve reliability statistics, which can be used as theoretical and technical supports for engineering applications.

寿命分布用于分析高性能产品和复杂系统的可靠性问题。但已有寿命分布存在危险率函数形状单一、拟合数据不灵活、统计推断精度低和逐次截尾数据下统计推断理论及其逐次截尾试验方案不完善等缺憾。为此开展：挖掘新逐次截尾方案; 扩展连续逆高斯分布，研究其数学性质、逐次截尾数据下统计推断；建立离散扩展逆高斯模型及其截尾数据下统计推断理论；在加速寿命试验中，基于逐次截尾样本和几种应力与寿命特征参数方程下，研究一些经典分布及其扩展的统计推断；基于新方案样本讨论一般指数和逆指数模型的应力-强度可靠性P(X<Y)估计问题。在各项内容中，讨论参数似然估计及算法实现，建立评价估计精度方法；建立求解参数贝叶斯估计方法及算法；选择实际或模拟数据对极大似然估计、贝叶斯估计进行比较研究。项目实施将建立扩展逆高斯模型、一般指数和逆指数模型统一的逐次截尾数据下参数估计和预测方法，完善可靠性统计理论，为工程应用提供理论和技术支撑。

高性能产品和复杂系统可靠性分析技术是设备安全可靠运行的保障，寿命分布和寿命数据试验方案的选择是高精度可靠性推断的两个关键方面。本项目围绕拓展新分布和新试验方案，研究扩展新分布及其统计理论和应用案例，构建了样本数据试验新方案及其可靠性理论和应用。.主要研究内容有：连续、离散寿命分布扩展及其在截尾数据下的统计推断；加速寿命试验中逐次截尾方案的应用；建立首次失效逐次混合截尾方案；基于内蒙古、新疆地区风速数据新分布挖掘和风能资源评估。.项目组针对若干前沿问题，瞄准扩展分布和数据驱动建模目标开展研究，主要研究成果有：.（1）扩展了若干连续寿命分布，如，基于T-X族方法，利用逆高斯分布和威布尔分布, 提出广义逆高斯分布；通过增加额外参数，扩展了伽马分布得到Alpha Power伽马分布。将Lindley分布和Weibull分布结合，构建了Lindley-Weibull分布;.（2）构建了若干离散寿命分布：如，通过离散化引入了扩展离散威布尔分布。新模型具有递减、递增、恒定和倒浴盆形状危险率函数；离散了Weibull-pareto分布；.（3）加速寿命试验可靠性:在逐次截尾样本下，常应力、步进应力加速竞争失效模型统计分析;.（4）基于不同分布不同类型样本研究应力-强度干涉模型：如，当应力和强度有独立和相依情形的Birnbaum–Saunders分布，估计可靠性R=P(Y<X)；在广义混合截尾样本下，讨论多分量应力-强度模型可靠性问题;.（5）基于多种截尾样本开展了可靠性统计热点问题研究；例如，逐次II型截尾、逐次I型截尾、改进的逐次混合截尾、自适应混合截尾、广义逐次混合截尾、首次失效逐次混合截尾方案;.（6）内蒙古新疆地区风速数据分布建模和风能资源评估：构造了Topp-Leone Lindley (TLL)分布，能很好地拟合内蒙古10个地区风速，研究了TLL分布的数学性质。构建了α对数变换对数正态分布，拟合新疆地区风速分布具有很好的适用性。该研究是对传统采用Weibulle风速分布的挑战。.本项目研究丰富了可靠性理论，有推动可靠性发展的作用。具有重要理论意义和潜在应用价值。