In the capability algorithm a trapezoidal membership function is
The piece thickness often requires or restricts the use of a particular process. For example if a 2 mm thick iron sheet needs to be cut, oxifuel cutting would not be acceptable if a minimum quality cut is needed, since the heat input that this Embelin process transfers to the sheet produces significant deformations, creates mechanical stress and therefore the loss of uniformity. This piece would be perfectly cut with laser or plasma, but how ideal the laser (plasma) would be? The capability algorithm is designed to be an initial filter of process elimination. Considering that not all processes can cut all materials and not all processes can cut all thicknesses, the algorithm shows the capability that a process i has to cut a material m with a thickness t . For most machine tools the materials and thicknesses that these can cut are previously defined by specification charts from the manufacturers or experts in their use, in which the process capability is fixed by means of a m-tm-t relation. On this premise, smog is possible to define a fuzzy set representing the m-tm-t relation for each process.