Interpretation & Calculations
by Paul A. Keller, CQE, CQA, CQM
A question that arises periodically concerns the use of pre-defined control limits, and their impact on Process Capability Indices. A client recently inquired about this, saying that they had previously determined that the process was "capable", but had not yet established statistical control on the process. When they attempt to use the control limits based on the Capability study data, the process is continuously out of control, even though the Cpk index well exceeds 1.33.
In understanding this dilemma, it is important to realize the relationship between control limits and Capability indices. Their relationship is simple: they both use Process Sigma in their calculations, which is based on the Range (or Moving Range , or Sigma) control chart.
Thus, it is a statistical requirement that statistical control be established before process capability levels be determined. The statistical estimates of process sigma are meaningless unless the process is stable. Another way to say this is that when a process is out-of-control, you cannot estimate its variation using a control chart.
Likewise. when you create a control chart using pre-determined control limits, the premise is that these control limits were based on past data, obtained when the process was proven to be in statistical control.
In the case of this client, the frequent out of control signals are likely due to their estimate of capability and the resulting control limits based on a small sample, over a relatively short period of time. Over longer periods, the process is subject to increased causes of variability, which appear as out of control points when the control limits are based on the initial (short-term) control limits.
In this case, there are a couple choices:
1. Establish the control limits and capability indices based on longer term estimates of process variation. If you can establish control, and the resulting capability index is satisfactory, your work is done.
2. If the short term estimates used for your capability index is the desired level of process performance, use these on your control chart. Look for patterns, and search for causes of data stratification. This option has some risk to it, especially if there are large number of out of control groups. It is best to use these “hunches” as input to a more detailed designed experiment before making significant changes to your process.
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).