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Robustness Criteria for Vulnerability of Block Designs in the Event of Observation Loss.

Thornewell, Helen. (2011) Robustness Criteria for Vulnerability of Block Designs in the Event of Observation Loss. Doctoral thesis, University of Surrey (United Kingdom)..

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Abstract

This PhD thesis investigates into the robustness of incomplete block designs in the event of observation loss. If observations are lost during the course of an experiment, the design properties are changed. In particular, a block design, which is optimal at the start of an experiment may result in a disconnected eventual design, in which case the usual null hypothesis cannot be tested, since not all elementary treatment contrasts are estimable. The loss of whole blocks of observations is investigated and improved results on bounded conditions for the maximal robustness of designs are derived and demonstrated. In order to guard against poor eventual designs, a Vulnerability Measure is introduced to determine the likelihood of a design becoming disconnected as a result of random observation loss. For any general block design, formulae are derived and a computer program is written to calculate and output the vulnerability measures. These can be used: as a pilot procedure to ensure the proposed design is sufficiently robust; as a method of design selection and comparison by ranking the vulnerability measures of a set of competing designs in order to identify the least vulnerable design; or as a tool for design construction. Comparisons are made between the vulnerability and optimality of designs, since high efficiency, in the sense of near-optimality, does not necessarily imply minimal or even low vulnerability to observation loss. Furthermore, the comparison of non-isomorphic Balanced Incomplete Block Designs (BIBDs) shows that designs which are equally efficient are not necessarily equally vulnerable, providing a new method for distinguishing between nonisomorphic BIBDs. By observing combinatorial relationships between concurrences and block intersections of designs, this vulnerability method is compared with other approaches in the literature that consider the effects on the efficiency of BIBDs, by either the loss of two complete blocks, or the loss of up to three random observations. The coincidence of these different robustness rankings and the relative strengths and weaknesses of the criteria are discussed. Results are applied to special design classes, including complement and repeated BIBDs. Specific non-balanced design classes such as Regular Graph Designs and Nearly Balanced Designs are also considered.

Item Type: Thesis (Doctoral)
Divisions : Theses
Authors : Thornewell, Helen.
Date : 2011
Additional Information : Thesis (Ph.D.)--University of Surrey (United Kingdom), 2011.
Depositing User : EPrints Services
Date Deposited : 14 May 2020 14:56
Last Modified : 14 May 2020 15:09
URI: http://epubs.surrey.ac.uk/id/eprint/856821

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