An Optimisation Method of Construction for Warping Copper Plates and Engines Using Complete Block Designs with Some Special Types of Graphs

Abstract

The application of bipartite and regular graphs plays a vital role in the area of engineering, mathematical sciences, design of experiments, and medical fields. This study proposes an optimization method for constriction of randomized block design and Latin square design using bipartite and regular graphs with applications of warping copper plates in specimens and comparing them to burners and engines on different days. The construction methods and analysis are performed as follows: the first method is a construction of randomized block design using bipartite and complete bipartite graphs with applications for the amount of warping copper plates and different laboratories are taken to test any significant difference that exists between the mean number of responses for the labs and copper specimens. The second method is the construction of a Latin square design using regular graphs to test whether there is any significant difference between the burners, engines, and some days in statistical analysis of interaction plots, contour plots, and 3D surface plots.