A Sampling Question

A Six Sigma Green Belt student asked an interesting question about sampling. Here’s the question and my response.

QUESTION:

Just a question that I thought I would run by you…

I work in the Automation industry, and am currently working on two production lines, and logging data for the parts being produced. One line is producing 60 parts per minute and I can thus log the data for every part. The other line is producing 240 parts per minute, and it is not possible to log the data for every part. I remember reading somewhere that in order to perform SPC you must take n consecutive samples (I think n was 5) every x number of cycles. What I need is definitive guidance on how to calculate n and x. I also need to know the statistical reason that n and x are used in order to explain this to the customer. Any feedback you can give me in relation to this would be greatly appreciated.

Regards,

AT in Ireland

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RESPONSE:

There is no rule that you need to sample n consecutive samples every x number of cycles. You are probably thinking of a technique known as PRE-Control, which is different than SPC. PRE-control also incorporates rules for deciding when to increase or decrease sampling frequency, stopping rules for processes, etc.. Personally, I don’t like PRE-Control for a variety of reasons, but if you have The Six Sigma Handbook, 2nd edition I discuss in starting on p. 661 or the 3rd edition starting on p. 465. My primary reason for disliking PRE-control is that it is a specification-based scheme (which I dislike in principle) and it will allow process variation to increase until it is as wide as the specs allow. SPC is all about reducing process variability to a minimum by identifying special causes of variation. When used in conjunction with Lean Six Sigma, SPC will also address common cause variation.

Instead of PRE-control I suggest that you consider using standard SPC control charts. I don’t know anything about your process so I can only offer general advice. If you’re already logging in metrics for 60 parts-per-minute I would be surprised if you’re not encountering problems like autocorrelation, which requires an adjustment to standard SPC such as using EWMA charts instead of classical control  charts. If you have autocorrelation and are not using the proper chart, then you will be experiencing a lot of “false alarms.” Processes seldom change by any meaningful amount in a matter of seconds, so you can probably extend the sampling interval. If you feel that you can economically sample 60 per minute, and that it is wise to do so, then you could sample this number of parts from the process running 240 parts per minute rather than checking every part. It would be best to choose the sample at random, rather than sampling every 4th part. Samples chosen using a fixed pattern are susceptible to problems if the process exhibits similar patterns. For example, if the process had 4 positions on a workstation then your 1-in-every-4 sample would always be sampling from the same workstation. Sometimes the patterns in the process are quite difficult to spot, and “Murphy’s Law” can strike at any time. Murphy’s Law states that anything that can go wrong, will go wrong.