Atkinson and Riani's forward search approach has been proposed as a robust procedure for the detection of multiple outliers in fitting statistical models. However, problems appear when it is applied to certain data sets. This thesis identifies the probable reason to be their method of initial subset choice. The degree of alias- . ing, inadequate representation of the range of values in the predictor set, and the' robust estimation can all lead to a poor choice of subset, which will lead to erroneous conclusions. This motivat.~s the concept of model coverage. Three coverage measure are proposed to consider model coverage in the search. A starting set with good coverage was found to improve the forward search procedure on a wide ' range of data sets. These ideas 'are implemented in Lisp-Stat and illustrated using many real-life and simulated data sets. Several methodologies, using these ideas in the forward search, were investiga~ed and observed improvements to the search were recorded. Vve called the best such methodology,' the UCA forward search algorithm. This new algorithm was applied to many data sets and substantial improvements in the' diagnostic plots were observed proving better results when the outlier structure is known. The DCA forward search algorithm is shown to give good improvement over the Atkinson and Riani methodology, and produces accurate results with data sets containing high leverage outliers. The DCA forward search algorithm is simple to use and produces results quickly and efficiently.