An Application of Bayes’ Rule in Manufacturing Engineering
In the field of manufacturing engineering, one of the most important aspects that is often not considered is the tool wear. When an assembly is undergoing high volume production, it is not uncommon for the same set of cutting tools to be used to machine hundreds of parts during a single operation out of metal; this of course wears the cutting tools down slightly, and after a while will cause the dimensions of the parts being manufactured to be out of tolerance with their design. In order to counter this, software techniques such as cutter compensation have been implemented, but eventually tool wear reaches a point where the tool should be replaced. The main issue with replacing the cutting tool, however, is that it can take a significant amount of time, and in a high volume environment, downtime for any manufacturing process can significantly affect if an assembly quota is met. The issue then becomes: how do we know how long we should use a cutting tool before we replace it to minimize the chance of incorrect or out-of-tolerance parts?
According to a Master’s degree student at Georgia Tech, one promising solution to this question is to use Bayes’ Rule to estimate the probability that a cutting tool is damaged based on collected data. As we have learned in class, Bayes’ Rule is a formula used to find the probability of an event A occurring given event B occurs based on the separate probabilities of A and B occurring as well as the probability of B occurring given A. The method used started by recording the data for a number of different variables that are often monitored during manufacturing operations of metal removal (spindle power, accelerometer output, dynamometer output) as well as geometric output of a trial cut that was being done for sets of tools of varying diameter that were known to be healthy or damaged tools. From this, they developed a set of trial data through which they would pass their actual tools. Based on these variables, the results would then use a multivariate form of Bayes’ rule to estimate the probability that a tool is damaged given the trial data that was used for calibration. Below is a figure from the paper showing the general process used:
Overall, this method is a powerful tool that could significantly impact the manufacturing techniques used in the industry based on a multivariate probability model. It also shows just how powerful Bayes’ Rule can be in estimating the probability that a cutting tool is damaged given data. While there is no opportunity for cascades like what was mentioned in class (only one cutting tool is analyzed at a time, the tools can be considered independent of each other, and all data points collected are relatively independent of each other), the main application of Bayes’ Rule to solve what seemed at first to be a very difficult and multifaceted problem is a testament to how important and impactful the formula we learned in class is.
Source: https://smartech.gatech.edu/bitstream/handle/1853/55036/LOCKS-THESIS-2016.pdf