Bill Levinson
Industrial Statistician and Trainer
Process Capability (Cp, Cpk) and Process Performance (Pp, Ppk) - What is the Difference? - iSixSigma agrees with you: "“Cpk tells you what the process is CAPABLE of doing in future, assuming it remains in a state of statistical control. Ppk tells you how the process has performed in the past. You cannot use it predict the future, like with Cpk, because the process is not in a state of control. The values for Cpk and Ppk will converge to almost the same value when the process is in statistical control. "
The process capability is how the process would perform if no long-term variation sources were present, and the sample range or standard deviation reflected all the variation sources present. The process performance index reflects long-term variation sources as well.
I can see, however, where the perception that special causes affect Ppk comes from. Here is a batch process I simulated for an SPC presentation. The control limits are based on the sample ranges and they reflect the short-term (within batch) variation. They do not reflect the long-term variation because there is also between-batch variation. The between-batch variation is however not a special or assignable cause, it is common cause variation that exists because of differences between setups and so on. It is true that the means of the batches are different, so the process mean changes from batch to batch, but this is an expected part of the job so we cannot call it a special or assignable cause. It is however why single-unit flow is preferable to batch processes.
Another example would be an autoregressive process that involves, for example, successive fluid elements in a pipe. The moving range will reflect the variation between fluid elements, which we expect however to be very similar to one another. It will not reflect long-term variation that is inherent to the process so Cpk >> Ppk in this case. I suppose the long-term variation would indicate a lack of ability to control the process to such an extent that the mean remains absolutely constant (typical automatic process control systems do not even pretend to be able to do this) but this does not mean a special or assignable cause is present that requires intervention.
The process capability is how the process would perform if no long-term variation sources were present, and the sample range or standard deviation reflected all the variation sources present. The process performance index reflects long-term variation sources as well.
I can see, however, where the perception that special causes affect Ppk comes from. Here is a batch process I simulated for an SPC presentation. The control limits are based on the sample ranges and they reflect the short-term (within batch) variation. They do not reflect the long-term variation because there is also between-batch variation. The between-batch variation is however not a special or assignable cause, it is common cause variation that exists because of differences between setups and so on. It is true that the means of the batches are different, so the process mean changes from batch to batch, but this is an expected part of the job so we cannot call it a special or assignable cause. It is however why single-unit flow is preferable to batch processes.
Another example would be an autoregressive process that involves, for example, successive fluid elements in a pipe. The moving range will reflect the variation between fluid elements, which we expect however to be very similar to one another. It will not reflect long-term variation that is inherent to the process so Cpk >> Ppk in this case. I suppose the long-term variation would indicate a lack of ability to control the process to such an extent that the mean remains absolutely constant (typical automatic process control systems do not even pretend to be able to do this) but this does not mean a special or assignable cause is present that requires intervention.