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

当有关观测的信息缺失或仅部分可用时，就会进行审查。审查有各种类型，其中一些是纳入研究设计的，有些是自然发生的，一个人无法控制。被审查的数据出现在各个领域，从制药行业的临床试验到工程科学的生命测试，再到环境科学中森林火灾蔓延的模型。因此，拥有必要的工具来分析这些数据并作出有用的推论是至关重要的。寿命测试是可靠性分析中采用的一种有效技术，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，为了节省时间和金钱等资源，通常会采用某种类型的审查。渐进式审查是审查的一种特殊类型，这是本研究计划的重点。在渐进式审查实验中，根据预先指定的方案，在整个寿命试验过程中，存活的单元被随机移除。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具通用性，因此特别有用。在这个主题上，我介绍了受限的渐进审查方案以及研究一步计划，这是一种特殊的计划，需要在一次故障时间随机移除存活的单元。尽管这两类审查具有限制性，但从实际角度来看，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，因为零部件的可靠性至关重要，需要进行审查。 除了审查方法，还有审查数据分析。在这里，我将重点介绍各种非参数方法，也就是几乎不假设数据的基本分布的方法。特定类别的测试是基于排名的测试，即，利用了数据点的某种排序。虽然这样的测试在文献中已经很好地建立了，但它们只是最近才在多维数据的情况下被探索。因此，我的工作调查了在根据不同机制进行审查的多变量删失数据的情况下，这种检验的使用。这在环境科学中尤其重要，在环境科学中，许多自然发生的过程可以被建模为多维的点过程，其中经常发生某种审查。出于这个原因，解决环境问题的机构，如马尼托巴省水电或加拿大环境部，将发现我的工作有用。 这一研究计划在审查方法和审查数据分析领域做出了重大贡献。这项工作跨越了推理、实验设计和数据分析，为学生提供了理想的问题。

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.