Choosing a Control Chart for Individuals Data

09/21/2010:

I created a control chart using 23 data points for the time in minutes to achieve small bowel intubation on patients. As you can see the lower control limit is 17.18. Could you please explain how the system could calculate a negative lower control limit when time could not be less than 0 minutes? Also, is an x chart the best chart to be used for this type of analysis?

Tammy W., Quality, Accreditation & Risk Management Dept.

The normal distribution, by definition, will place the individual x control limits at plus and minus 3 times the process sigma value from the process mean, without regard to whether your process can logically operate there. Of course, the calculations have no advance knowledge of your process, and in this case assumes that your process approximately follows the conditions of a normal distribution.

Given the physical nature of your process ("time could not be less than 0 minutes"), it is wise to ask what distribution best approximates the process. Keep in mind that a process out of control (by definition) will not be well approximated by a single distribution. Yet, as you saw with your data, we need to understand the distribution to define meaningful control limits for the individual x chart. Since we need to know the distribution to define the control limits for the individual x chart, and we cannot fit a meaningful distribution without verifying that the process is in control, the individual x chart is not the best tool at this point in the analysis.

Instead, I generally recommend the Moving Average, EWMA or Moving Average chart for initial analysis of individuals data. For the EWMA chart, use a lambda value of 0.4. For a Moving Average chart, a cell width of 3 usually works. This chart will allow you to see whether the process is in control. If so, a distribution may be fit to the data for capability analysis or for use in the individual x chart. In this case, there is insufficient data for a complete conclusion, but initial analysis indicates it is not in control (groups 9 and 10 are out of control). For fun, we could omit those groups from the analysis. When we repeat the analysis for this limited data on the individual x chart, we use the Johnson distribution with a lower bound defined at 0. This provides a reasonable initial estimate for your control limits, but it is best to collect quite a bit more data to verify the stability and curve fit (using the EWMA to establish control, then the Johnson curve fitting for predicting the distributional properties) before reaching any broad conclusions on the 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).