Black Belt Scientist

If you read enough material on Six Sigma principles you most likely have come across the calculation of defects per unit (DPU) or defects per million of opportunities (DPMO). You have also, most likely, come across the suggested "Euler's formula" for estimating defect rates. Now, as we all know, 1 - defect rate equals yield. In other others, if you are somehow calculating a defect rate of a process you are also consequently easily computing the yield of the process. For example, a process with 10% defect rate has, mathematically, 90% yield. With that out of our way, let's look at how each is calculated and the issue with Euler's formula when applied to a defect rate level over 10%. DPMO is simply stated, the defects (per unit) divided by one million (that is, one million opportunities of finding a defect). Note: this is any unwelcome departure from the standard, not necessarily the entire unit being defective , the distinction here is very important. At a 4.5 si...

Here's a quick example of how helpful comparative boxplots and density curves can be when it comes to visualizing the behaviour of the data set. I used RStudio to create these visualizations but the most important part of this post is the interpretation of these plots. If you do not use RStudio, feel free to skip to the section where I address the plots themselves. However, if you are an RStudio user you might pick up some coding tips starting at the top of this post. These plots can be created with most statistical software/packages available in the market (I also use Minitab, ProcessMA, and Sigma XL). These are the plots that we are going to look at: First things first, I've loaded the following libraries in RStudio: Then I used the rnorm function in R to randomly create three sets of data. These are heights in inches for males, females, and NBA players. I created 100 data points for each variable, and you can see in the screen shot below the mean and standard deviation for e...