Interpretation & Calculations
In several places in your Six Sigma Demystified book, you mention to never put
specifications on an X-bar chart. Please explain.
The specifications indicate the desirable values of the process observations, not their actual values. The process itself may be quite different from these recommended levels, so we measure from the process and use the statistics of the measurements to estimate the true process conditions. When we plot values on an X-bar chart, we are not plotting individual measurements: we plot the average of a sample of measurements. For example, the measurements from a process might be 6, 8, 12, and 14. The average of this sample is 10. If the process specification is LSL = 8 and USL = 12 (i.e., desired value is 10, with allowable deviation of plus or minus 2), then the average tells me I am doing pretty well. Unfortunately, none of the individual measurements satisfy the requirements.
The point is: the specifications apply to the individual measurements, not the average. Think of that the next time your plane is trying to land on the runway: we care if this individual landing is well-centered within the traffic lanes, not whether the average of many flights is within the traffic lanes.
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).