Often you want to work out what a competitor's product is made of.  Frequently you have a data sheet showing the chemical analysis.  Frequently the data sheet was made many years ago and no longer applies to the actual materials used currently.  Therefore you can only calculate what it is supposed to be made of.  In the case of a castable you assume that all the calcium oxide comes from the calcium aluminate cement used.  The colour of the castable generally tells you whether it was made with a 70% alumina cement, a 50% alumina cement or ciment fondu.  Calculate the percentage of the calcium aluminate cement and subtract the total composition from the stated chemical analysis.  If you have a sample of the material, wash all the fines out with water and try to identify the aggregate.  Use the silica content to identify the percentage of aggregate used.  Calculate the composition of this aggregate and subtract it from the total on the data sheet.  If there is alumina left over, assume that a calcined alumina has been added.  If it contains zirconia it is probably present in the form of zircon and the percentage zircon can be obtained from the percent zirconia.  This should be the first step in your calculation.  Note that bauxite usually contains some titania and this can help in your calculations.  

If your sample is not a castable, reverse engineering is somewhat more difficult.  When washing a sample look for the fibres.  Use a microscope to distinguish between rft fibres, water dispersable glass fibres and ceramic fibres.  Water dispersible fibres are very straight, ceramic fibres are curved and rft fibres are a bit squiggly.