Due to the continuous development in society and the multiplicity of customers' desires and their keeping pace with this development and their search for the quality and durability of the commodity that provides them with the best performance and that meets their needs and desires, all this has led to the consideration of quality as one of the competitive advantages that many industrial companies compete for and which are of interest to customers and are looking for. The research problem showed that the Diyala State Company for Electrical Industries relies on some simple methods and personal experience to monitor the quality of products and does not adopt scientific methods and modern programs. The aim of this research is to design a system to monitor the production quality of the transformer (400/11 KVA) through the use of a method that helps to make decisions of a quantitative multi-objective nature, which is the method of lexicographic goal programming that the researcher used to integrate the preferences of the decision-maker in monitoring the quality of the production of the transformer (400/11 KVA). Using the two programs (Excel and Lingo) in constructing and solving the mathematical model that was applied in the sections (outer and inner iron core, winding and isolating, final assembly and quality control). The results obtained were efficient, as they achieved the least possible deviations from all the target values for all goals
