WP.8.1: PROCESS CAPABILITY
[WP.8.1]
I. GENERAL DEFINITION
Process capability compares the output of an in-control process to the specification limits by using capability indices. The comparison is made by forming the ratio of the spread between the process specifications (the specification "width") to the spread of the process values, as measured by 6 process standard deviation units (the process "width").
II. PROCESS CAPABILITY & VARIATION
Process capability is determined by the variation that comes from common causes. It generally represents the best performance (minimum spread) of the process itself when it is under statistical control. However, we are more concerned with the overall output of the process itself and how it relates to a set of tolerances irrespective of variation.
[Note: If the process is proven capable and we keep it in control, it will continue to produce that same distribution as an outcome.]
III. EVALUATION
Capability Indices: A measure of how well the data distribution fit inside a given set of specifications or control limits.
Measures:
Cp – The tolerance width divided by the process variation, irrespective of centering. Focus: Repeatability.
Cpk - The total capability index that accounts for both process variation and location. Focus: Repeatability and Location.
The larger the capability index, the better. General rules are as follows:
Cpk > 1.33; Process is capable
Cpk= 1.00 – 1.33 Process is capable with tight Controls
Cpk< 1.00 Process is incapable
IV. ADDITIONAL NOTES
Process capability studies focus on how well a process is performing relative to the specification limits of that process. For example, if our process involved filling a 12 ounce bottle with beer, we would hope that each bottle has approximately 12 ounces in it. Notice that we said “approximately” and not “exactly”; we are allowing for a certain amount of variation within our process. Let’s suppose that we would like between 11.8 and 12.2 ounces of beer in each bottle. In other words, our lower specification limit is 11.8 ounces and our upper specification limit is 12.2 ounces. Therefore, the maximum range or spread that we desire for our process is 0.4 ounces (12.2 – 11.8 = 0.4 ounces).
Let’s further suppose that we recorded the amount of beer in a sample of bottles and found the sample standard deviation to be 0.04 ounces. By using the sample standard deviation, we can roughly estimate the actual range or spread of our process by recalling the Empirical Rule. If you recall, almost 100% of the data (99.7%) in a normal distribution will lie within 3 standard deviation of the mean. In other words, almost 100% of the data will lie between a point that is 3 standard deviations below the mean and another point that is 3 standard deviations above the mean. You may then notice that these two points are six standard deviations apart. By taking the sample standard deviation and multiplying it by 6, you will have a decent estimate of the actual range of the process. In this case, we estimate the actual range of our process to be 0.24 ounces (0.04*6= 0.24 ounces).
By comparing our estimate of the actual range of the process (0.24 ounces) against the desired range (0.4 range), we can see that we are meeting our goal for variation. In other words, our process is consistent.
Being consistent, however, does not guarantee that our process is capable of performing within the specification limits. For example, if the mean amount of beer in our sample of bottles was 3 ounces and our goal for the amount of beer in each bottle is 12 ounces, we would have some unhappy customers. For a process to be capable, the sample mean should be close to the desired amount. To determine if the sample mean is close enough to the desired amount, we again borrow from the Empirical Rule and state the sample mean should be more than three standard deviations away from each of the two specification limits. If the sample mean is too close to or outside of a specification limit, we will have an unacceptable number of products that do not meet specifications.