Censoring Methodologies and Censored Data Analysis with Applications in the Engineering and Environmental Sciences

当观测信息缺失或只有部分可用时，就会进行审查。审查有各种各样的类型，其中一些是纳入研究设计的，有些是自然发生的，人们无法控制。经过审查的数据出现在各个领域，从制药业的临床试验到工程科学的寿命试验，再到环境科学中森林火灾蔓延的建模。因此，至关重要的是要有必要的工具来分析这些数据并作出有用的推论。在可靠性分析中，寿命试验是一种有效的技术，即工程师对部件进行测试，并试图对部件的寿命分布做出有用的推断。在这些测试中，通常采用某种类型的审查来节省时间和金钱等资源。一种特殊的审查类型是渐进式审查，这是本研究项目的重点。在渐进式审查试验中，幸存单元在整个寿命试验过程中按照预先规定的方案被随机移除。这种类型的审查可以作为寿命测试设计的一部分，比传统类型的审查更通用，因此特别有用。在这个主题上，我介绍了有限的渐进审查方案，并研究了一步计划，这是一种特殊的计划，需要在一次故障时间随机移除幸存的单元。尽管这两种审查具有限制性，但从实际的角度来看，这些计划有特别的好处。庞巴迪公司（Bombardier Inc.）等公司的研究部门将能够从这项工作中受益，这些部门对零部件的可靠性至关重要，需要进行审查。

Censoring occurs when information about observations is either missing or only partially available. There are various types of censoring, some of which are incorporated into the design of a study, some of which occur naturally and one has no control over. Censored data arise in various fields, ranging from clinical trials in the pharmaceutical industry, to life-tests in the engineering sciences, to the modelling of the spread of a forest fire in the environmental sciences. It is therefore crucial to have the necessary tools to analyze such data and make useful inferences. A life-test, wherein an engineer puts units on test and attempts to make useful inferences about the units' lifetime distribution, is an effective technique employed in reliability analysis. In these tests, some type of censoring is often employed to save resources like time and money. One particular type of censoring is progressive censoring, which is a focus of this research program. In a progressive censoring experiment, surviving units are randomly removed throughout the life-test according to a prespecified scheme.  This type of censoring can be part of the design of a life-test and is more versatile than the traditional types of censoring, and hence is particularly useful.  On this topic, I introduce restricted progressive censoring schemes as well as investigate one-step plans, which are special plans entailing surviving units being randomly removed at one failure time. Despite the restrictive nature of these two types of censoring, these plans have particular benefits from practical points of view. Research departments in companies like Bombardier Inc., where reliability of components is critical and censoring is needed, will be able to benefit from this work. Alongside censoring methodologies is censored data analysis. Here, I focus on various non-parametric methods, that is, methods wherein little is assumed about the underlying distribution of the data. A particular class of tests are rank-based tests, i.e., some ordering of the data points is utilized. While such tests are well established in the literature, they have only recently been explored in the case of multi-dimensional data. My work thus investigates the use of such tests in the case of multivariate censored data where censoring occurs according to different mechanisms. This is especially important in the environmental sciences where many naturally occurring processes can be modelled as multi-dimensional point processes where oftentimes, some sort of censoring has occurred. For this reason, agencies addressing environmental concerns, such as Manitoba Hydro or Environment Canada, will find my work useful. This research program makes significant contributions to the areas of censoring methodologies and censored data analysis. Spanning inference, experimental design and data analysis, this work provides ideal problems to work on with students.