Optimization of Metal Refinement Process by Selecting the Optimal Threshold Value

The purpose of study is to find the optimal threshold value for metal refinement processes based on Taguchi loss function. Taguchi method is a widely employed methodology in many different industries for improving the performance of product/process. In Taguchi’s dynamic systems, if both input and output have only two digital values (0 and 1) with the possibility of committing two types of errors (judging 0 as 1 and 1 as 0), such a problem is called the digital system. Metal refinement processes can be viewed as a digital dynamic problem when the goal is to separate the metal molecules from the impurities. Molten metal stays at the bottom and the impurities float as slag on the top of molten metal. For this purpose, a threshold value R is required to discriminate molten metal from slag. A material is assessed as valuable metal or slag depending on the corresponding the output, which is affected by control factors and noise factors. If output is less than this threshold value R then may be considered slag and if value comes greater than or equal to threshold value R then considered valuable metal. Two types of error rate are occurred, p percent of metal molecules go into slag and q percent of a particular impurity go into the molten metal. This paper views the error rates as random variables with normal distributions and find the setting value of threshold R for the cases of loss coefficients are unequal.