P and U Charts and Limburger Cheese: A Smelly Combination
The art of cheese-making has been around for thousands of years. By that measure, Limburger cheese is a relative newcomer. It was first produced in the 1800s in the Duchy of Limburg (now split by the borders of Germany, Belgium, and the Netherlands). Limburger cheese is notorious for its distinct smell…which resembles body odor!
Given the most common reaction to Limburger – “P.U.!” – I thought it made a perfect topic for discussing how to decide between using the P or U control charts for attribute data.
When to Use P Charts
Let’s suppose we work for Stinky Cheese Company inspecting Limburger cheese. One of our duties is to monitor the packaging process. The plastic wrapping around the cheese must be airtight or the cheese will spoil. We randomly pull several blocks of cheese every hour to check the package integrity. We count how many blocks of cheese we had to reject for poor packaging and record the number in Minitab. Since we are simply accepting or rejecting the block of cheese based on package integrity, we can run a P Chart from the Assistant menu with the following results:
Because we had an unusually high number of poorly wrapped cheeses in the eighth hour of inspection, we stopped the packaging line briefly to find the cause of the problem. The line operator quickly identified a misaligned roller, fixed it, and got the line moving again. Our inspection the next hour was back on track.
When to Use U Charts
In addition to inspecting the packaging, we also need to make sure the cheese is of a very high (i.e., stinky) quality. Every hour we randomly select one brick of cheese for stink inspection. Imperfect Limburger includes cheeses that are too salty, chalky, crumbly, or not stinky enough. We tally up the number of imperfections we count on each cheese block and record the number in Minitab. A U Chart is the best option when trying to analyze the number of defects.
From the U Chart, we can see that the fifth block of cheese we inspected had an unusual number of defects. There were several cracks apparent on the surface of the cheese and it crumbled when cut in half.
After some discussion with the head cheese master, we discovered that the lot of cheese that this sample came from had to go back to the aging room. It needed more time to ripen -- so it could reach its full stink potential.
A Built-In Guide to Choosing Control Charts
I created the P and U charts for this article using the Assistant menu in Minitab Statistical Software. The Assistant makes it easier to identify the right analysis and even helps you interpret results.
If you like this article, you might want to check out Eston's article on "What Control Chart Should I Use?"