Interpretation & Calculations
All SPC control charts may be defined as having the following properties
1. The x-axis is sequential, usually a unit denoting the evolution of time.
2. The y-axis is the statistic that is being charted for each point in time.
3. Limits are defined for the statistic that is being plotted. These upper and lower Control Limits are statistically determined by observing process behavior, providing an indication of the bounds of expected process behavior. They are never determined using customer specifications or goals. See also: Tampering and Defining Control Limits .
4. We recognize that we will see variation in any process (providing we have adequate measurement equipment to detect the variation), and the fluctuation of the points between the control limits is due to the variation that is intrinsic (built in) to the process. We can say that this variation is due to "common causes." Although we do not know what these causes are, their effect on the process seems to be consistent over time. Thus, if the process is in control, the location (or measured value) of any of the points that lie between the control limits is not useful information. We do not care if one data point is 4.5 and the next is 5.2, so long as the process is stable. We do not react to this variation within the control limits. If we want to reduce this variation, or re-locate the process center line to a new location, we will need to fundamentally change (or re-design) the process, rather than looking for a single "cause" for a given point variation from its neighboring point.
5. When points exceed the control limits, we assert that the process must have shifted, since the chance of this happening is so small. See also Tampering. Any points outside the upper and lower control limits can be attributed to a "special cause." A key value of SPC charts is to identify the occurrence of special causes so that they can be removed, leading to a reduction in overall process variation.
6. The limits are determined by estimating the "short-term" variation in the process, and defining process stability (or process control) as when the short-term variation provides a good model (or estimate, or prediction) of the longer-term variation. This is perhaps the most critical component to effective use of these SPC charts, yet unfortunately one of the most overlooked. See: Rational Subgroups
Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).