Taking measurements and using measuring devices are ubiquitous in commerce and scientific activities today. Inter-laboratory studies (especially so-called Key-Comparisons) are conducted to ensure measurement capability for commerce, evaluate national and international equivalence of measure, and validate measurement devices and measurement methods or standard materials. A common protocol employed in many inter-laboratory studies is for a pilot lab to prepare materials or objects to be measured and deliver them to participating labs. The labs proceed to take measurements and report the results to the pilot lab which performs a statistical analysis. An overarching goal of many inter-laboratory studies is to establish a reference value for some measurand (the underlying quantity subject to measurement).

In these studies, it is not unusual for one or more labs to report measurements that are unlike the majority. There is no consensus on how to handle these unusual measurements in a statistical analysis. Most methods, in one way or another, attempt to determine if each laboratory should be classified as an ``outlier" and discard measurements from those labs that are so classified. The practice of excluding particular measurement results without substantive reasons is discouraged. In Key-Comparison studies, the concept of outlying laboratories must be treated even more delicately. For these, discarding outlying measurements is often politically untenable.

There is a need to develop methodologies for the analysis of inter-laboratory studies that model the potential existence of laboratory outliers in a way that doesn't let them dominate the estimation of a measurand. The development of such methodologies is the general theme of this dissertation.