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

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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.