Comparing risk of defective steel coil data using ROC curves

Although references to the awareness of the importance of predicting failure rates in reliability have existed in the literature for many years, the full power of advanced statistical modelling has only been used for engineering calculations in recent times. The main objective of this paper is to compare and to improve models for evaluating defective risks in the steel coil manufacturing process using real data. This study takes into account which steel coil manufacturing process characteristics affect defective risk and which models fit the data best. Statistical models of differing complexity have been suggested in the literature for estimating the quality of galvanized steel coils on the basis of short time histories. The data, consisting of 48 galvanized steel coils, was divided into sets. Five variables were selected for monitoring the process: steel strip velocity and four bath temperatures. The first data set was 25 conforming coils and the second data set was 23 nonconforming coils. Manufacturing companies can manage these failure risk models for evaluating the development of a proactive approach in the manufacturing process, instead of using a traditional reactive scheme. The present paper reports a comparative evaluation of statistical models for binary data using Receiver Operating Characteristic (ROC) curves. A ROC curve is a graph or a technique for visualizing, organizing and selecting classifiers based on their performance. ROC graphs are commonly used in medical decision making, and in recent years have been increasingly used in machine learning and data mining research. The purpose of this paper is to use them in research to obtain the best model to predict defective steel coil probability. We have compared two different models by choosing the best fits for each one of them. Specifically, we have compared the Generalized linear model (GLM) and Classification Tree (CART). The comparison is carried out by applying the ROC curve, from which we can conclude that the GLM model produces a worse fit than CART. In relation to the work of other authors, we should highlight one distinctive feature of the methodology presented here, which is the possibility of comparing the different models with a simple and objective criterion. ROC graphs can provide a measure of classification performance, complementaring scalar measures such as goodness of fit statistics proposed by other authors.