Abstract : This report is an up-dating of BRL Report No. 867. That report gives a description of the physical model and the random number generators used in this report. The methods of BRL Report No. 867 have become inadequate for the solution of the problem with all the recent modifications and refinements and have been superseded by the methods discussed in this report. The main body of the report is devoted to a mathematical discussion of the problem and appendices are included for the programming. The equations were formulated by Messrs. De Gray and Stubbs. The following assumptions were made: the missile and target are traveling in straight lines, the rear nape of the cone fuze pattern has been omitted, the azimuth and elevation angles are not necessarily standard for all missiles. The discussion has been limited to the fixed-angle (cone-type) guided missile fuze, but another fuze (the proximity fuze) is being analyzed and will be reported upon in the future.