We’ve all had that feeling before that something just isn’t right, but can’t quite put our finger on what that something is. The same phenomenon can occur when using control charts. The control limits appear too wide; you know something must be up and are itching to determine just what it is.
Welcome to a little something called stratification.
If you have multiple stream processes, you’ve likely met stratification before—maybe without realizing it. This state occurs in processes that may have two or more streams of parallel outputs that are systematically (statistically significantly) different.
Let’s take a look at a classic example for a clearer understanding:
Take a liquid filling process with an industrial beverage filler. Any liquid, from beer to soft drinks, will have multiple filling heads from two to 100+. The valve of each filling head is adjustable, meaning the output may vary.
They are adjustable as some may naturally give systematic differences, or it may be due to maintenance related factors. Regardless, they’re quite susceptible to being different. When working with a typical Xbar / R chart sampling scheme, you may end up taking a subgroup with samples coming from multiple filling heads.
The trouble lies in large systematic differences between the filling heads as compared to the overall process variation for the average output (the Xbar). When this takes place, the estimate of the standard deviation for constructing the control limits becomes inflated. Why? The estimates of the standard deviation for calculating the statistical control limits are based on the ranges within the sample group (in this case, between the filling heads).
Solutions for Stratification
So, what can you do about it? One option is to select parts for the subgroups from only one filling head each time. Then, rotate randomly through the different streams as you continue to collect subgroups for the control chart over time. By doing so, you’ll ensure that the only variation reflected in the calculation of the ranges used for estimating the standard deviation for the control limits is purely a process variation as it should be.
It is not “adulterated” with the systematic variation that exists between the filling heads. In fact, it will make any systematic differences between filling heads readily apparent so that the process engineer can recognize an opportunity to better synchronize the filling valves and reduce overall process variation.
There’s also the possibility of adjusting the filling head outputs by adjusting the valves. However, in some cases, like with a multi-cavity injection mold, you’re limited in your ability to do that. The systematic differences are inevitable given the state of the technology today and you’ll need a different control chart strategy. In this case, you can attempt to normalize the data by charting the outputs as a difference from the expected output that accounts for those differences.
The other less desirable solution, but sometimes necessary, is to treat the average of multiple streams (injection cavities) as if it were an individual value. Then, use the moving range between those averages to estimate the standard deviation used for the statistical control limits. That strategy allows the systematic differences to remain (since they are inevitable) while avoiding the problem of too wide control limits, which are useless. In that case, you could also employ an additional tolerance chart using specification limits instead of statistical control limits to monitor individual streams (cavities) for compliance with specifications.
Sound like a lot to master? Start by building the right foundation and register for NWCPE’s Statistical Process Control (SS503) course. You’ll learn how to solve stratification and manage processes for control and improvement.