Reliability Inference and Degradation Modeling based on a Class of Nonhomogeneous Levy Processes

本文研究退化数据的非齐次Levy过程的半参数似然估计。在一些研究中，受试者在零时间进行测试，这些受试者随着时间的推移而退化。失效定义为降解量达到预定临界水平的时间。这种类型的数据称为退化数据。观测数据的设置是一个n个独立的单元，每个单元都有一个非齐次Levy过程，具有共同的形状函数和尺度参数，在研究过程中，在几个可能不同的时间观察。困难在于这些过程的未知参数包括单调函数和有限维参数，并且数据本身是相关的。研究者研究了未知参数的极大似然估计（MLE）和极大伪似然估计（MPLE），并开发了计算MLE和MPLE的有效算法。建立了估计量的渐近性质，包括相合性、收敛速度和渐近分布。本文还研究了相关问题，包括随机效应和/或时间无关协变量模型的半参数推断、失效时间数据和退化数据的联合建模以及方差估计的Neyman-Scott问题的一种变形。这在几乎没有故障的高可靠性应用中造成了困难。传感技术的进步使得收集与系统和组件相关的大量退化数据成为可能。退化建模允许制造商以及时的方式获得所需的可靠性信息，使得他们可以做出关于保修期的有效商业决策或证明产品满足客户的可靠性规范。本文的工作建立了一类灵活的模型来分析退化数据，并在工业工程和艾滋病患者的免疫系统研究中有直接的应用，因为它制定了真实的退化数据。调查员开发R和/或MATLAB形式的数值软件，用于通过互联网进行公众使用的退化分析。

This proposal aims to study semiparametric likelihood inference of some nonhomogeneous Levy processes for degradation data. In some studies where the subjects are put on test at time zero, these subjects degrade over time. Failure is defined as the time when the amount of degradation reaches a pre-specified critical level. Data of this type are called degradation data. The setting for observed data is one on which n independent units, each with a nonhomogeneous Levy process with common shape function and scale parameter, are observed at several possibly different times during the study. The difficulty is that unknown parameters of these processes include a monotone function and a finite dimensional parameter and also the data themselves are correlated. The investigator studies the maximum likelihood estimator (MLE) and maximum pseudo-likelihood estimator (MPLE) of the unknown parameters and develops efficient algorithms to compute both the MLE and the MPLE. Asymptotic properties of these estimators including consistency, convergence rate and asymptotic distribution are established. Related problems, including semiparametric inference of models with random effects and/or time-independent covariates, joint modeling of failure time data and degradation data, and a variation of the Neyman-Scott problem on variance estimation are also investigated.Traditional analysis in reliability focuses on collecting and modeling failure time data. This poses difficulties in high-reliability applications where there are few failures. Advances in sensing technologies are making it possible to collect extensive amount of data on degradation associated with systems and components. The degradation modeling allows the manufactures to obtain the reliability information required in a timely manner such that they can make effective business decisions regarding warranty periods or demonstrate that the product meets the customer's reliability specifications. The proposed work develops a class of flexible models to analyze the degradation data and has direct applications in industrial engineering and AIDS patients' immune system study, as it formulates real degradation data. The investigator develops numerical software in the forms of R and/or MATLAB for degradation analysis for public use through the internet.