Process Capability – What is It?
Process capability indices can be misleading. For instance, let’s consider the Cp Index. This process capability index compares the process spread to the tolerance spread. It provides a measure of how well the process can meet a tolerance expectation under certain conditions. Let’s review this in greater detail.
Process Capability Index, Cp:
I show the the Process Capability Index, Cp below.
In this expression one must know the upper and lower specification limits to compute the tolerance spread. We must also know the standard deviation which is then multiplied by 6 to compute the process spread. But this is where the confusion comes into play. That is, how is the standard deviation estimated? This estimate is a function of the sampling program used to collect specimens for measure.
Process Capability Index for Xbar and Range Charts
One common approach to sampling is to collect n=5 samples to form a subgroup. This is shown in the figure below.
Such a subgroup contains samples made under homogeneous conditions. This just means the samples were made under like conditions, also called common cause conditions. By computing the range for each subgroup we can then compute the average range and divide this by a d2 correction factor (read more about d2 here). Dividing by d2 allows us to estimate the subgroup standard deviation. I show the Cp index for this type of subgroup sampling program below.
Process Capability Index for Individual and Moving Range Charts
Another common approach to sampling is to collect 1 sample at equally spaced intervals. I show this in the following figure.
In this case, we would compute the absolute value of the difference between two consecutive points. We call this a moving range. As an example, assume we have 8 points. The first moving range is the absolute value of the difference between points 2 and 1 and we call this MR1. The second moving range is the absolute value of the difference between points 3 and 2 and we call this MR2. And the third moving range is the absolute value of the difference between points 4 and 3 and we call this MR3. Once we compute the moving range values for the entire string of data we can calculate the average moving range. We then divide this by a d2 correction factor (read more about d2 here) to estimate the standard deviation based on a moving range of n=2. In this case, I show the Cp index for this type of sampling program in the expression below.
The Process Capability Index, Cp, Measures the Best Capability of a Process
By now I trust you recognize the problem. Collecting n=5 consecutive samples or a moving range of n=2 consecutive points is a SHORT PERIOD OF TIME! The standard deviation used to compute Cp is thus based on a short-term standard deviation estimate. Such an estimate is usually free of special cause variation. It thus measures the best capability the process can hope to achieve versus a tolerance specification.
What Does this All Mean?
If the Cp Index is less than 1 it suggests the process spread is larger than the tolerance spread. In this case we need a smaller short-term standard deviation to meet the tolerance specification. This usually means we need a technological leap to improve the process. This is not to say we can’t do it. It just means it’s going to take time, brain power, and we may need to spend some money on incremental capital.
If the Cp Index is greater than 1 it suggests the process has the capability to meet a tolerance specification; but only based on a short-term standard deviation estimate. If special cause variation is present the Cp index is not a true measure of the actual performance of the process. Quality Engineers should compute two standard deviation estimates: short-term and long-term. We estimate the long-term standard deviation using the following expression.
Once you have a long-term and short-term standard deviation estimate then compute the following ratio:
If this ratio substantially exceeds 1 then you know you’ve got special cause variation. Special cause variation show up as patterns and trends in the data. Identifying the type of special cause variation and tracing it to a root cause can help reduce special cause variation.
In a nut shell, I don’t spend a lot of time computing Capability Indices. I feel it takes focus away from the real issue. I want to know what type of variation is affecting my process. Do I need to reduce special cause variation or common cause variation? The best way to answer that question is to compute the standard deviation ratio of long-term to short-term and apply these rules.
Why Is This So Improvement?
These rules are helpful if your organization tracks critical product or process features. Given the state of IT today, many companies check hundreds of product and process features using SPC. But that’s as far as it goes. They have nice charts but no way to filter which process or product features to improve. One quick and easy way to rank which features to improve is to compute,
and rank from largest to smallest. This way you won’t be spending a lot of time reviewing each control chart. You’ll be looking only at those SPC charts that show the most special cause variation. Once you review these charts make sure there isn’t a problem with measurement discrimination (read more about measurement system discrimination here). If you do this, you’ll spend more time identifying a root cause and driving continuous improvement. I can’t stress this enough! A root cause is usually a problem with one or a few isolated subsets of a process. Fixing these often does not need a lot of capital investment. And this is where you get your BIGGEST BANG FOR BUCK. I often see continuous improvement practitioners trying to reduce common cause variation. They soon get frustrated because they can’t identify a root cause. And this doesn’t surprise me because that’s why they call is common cause variation. All the causes are common across all the sources of variation! You would need to reduce each one to have a major impact and that often means a technological leap. Such leap takes time, money and effort. It can be done, just be clear about the effort its going to take.