What is the minimum number of values to develop individual chart?

[Steve Prevette]

Interesting, we see the same condition and have two interpretations. For me, I'd rather get the signal that the new point is different than the initial set of points and investigate. One thing I do when I get a signal on such a short baseline is see if it goes away if I rebaseline with the newer data. But, as a matter of policy I let the baseline stand unless there is such a signal.

I suppose it depends on your relative costs of a false alarm versus a failure to detect. Most of the literature appears to support locking in the baseline. But there has not been a lot of formal study of use of small sets of data, most assume you have the 25 points on hand. Many people, I suspect, would not even do SPC on such a small set of data. All I can do is state that empirical use of the MW rule, and locking in the baseline has served me well.

[Tim Folkerts]

I think you are exactly right when you point out the dangers of control charting with so few data points. Once you get to 25 or 30, then any one point won't make much difference - here control charting is mostly a science With 5 to 10 points, the informations is so limited that personal interaction and interpretation is critical - here control charting is more of an art (an a bit of luck).

[artichoke]

In Reply to Parent Post by Tim Folkerts

I think you are exactly right when you point out the dangers of control charting with so few data points. Once you get to 25 or 30, then any one point won't make much difference - here control charting is mostly a science With 5 to 10 points, the informations is so limited that personal interaction and interpretation is critical - here control charting is more of an art (an a bit of luck).

Wheeler, "Advanced Topics in SPC" page 65, shows examples of control charts with just 3 points.
The key is that the purpose it is not to make a "perfect" chart to hang on a wall. The aim is to use the chart to help understand the process.
In a similar vein, Wheeler shows that there is no need to remove outliners to calculate limits.

[Tim Folkerts]

I don't have that book so I can't comment specifically on Wheeler's perspective.

From my perspective, control charts are designed to help decide if the process is in control. Duh! In other words, is the process behaving as well as can be expected?

I could imagine running a control chart with just 3 point ifyou already have a good idea what to expect. For example, you might have a process that has been running well and you know the typical variations in dimensions. If you start making a new part that is similar, then you might expect a similar variations. In a sense, you are treating the new points as a continuation of the old control chart - are the variations in the new part behaving as expected based on the data from the old part. I'd be interested to find out the circumstances that Dr. Wheeler thinks are appropriate for a 3 data point control chart.


I also think that removing the outliers from the calculations is reasonable (but perhaps not necesary), especially if you can identify the special cause that caused the variation. Leaving the outliers in will artificially inflate the control limits compared to "normal operations". Granter, if you have 30+ points and the outlier isn't too far out, then it won't matter much.

I can see the benefit of not erasing outliers completely, thought. The fact that there have been outliers is useful information. Perhaps it would even make sense to chart the occurance of the outliers - do the outliers occur at random, or is there some pattern to the rate of outliers!

Tim F

[artichoke]

In Reply to Parent Post by Tim Folkerts

From my perspective, control charts are designed to help decide if the process is in control. Duh! In other words, is the process behaving as well as can be expected?

Wheeler describes this as a "weak usage" on page 19. I'd strongly recommend reading this book. I have read various sections countless times.

I could imagine running a control chart with just 3 point ifyou already have a good idea what to expect.

That's not what he is doing. In the example he is comparing different estimators of dispersion parameters.

I also think that removing the outliers from the calculations is reasonable (but perhaps not necesary), especially if you can identify the special cause that caused the variation. Leaving the outliers in will artificially inflate the control limits compared to "normal operations". Granter, if you have 30+ points and the outlier isn't too far out, then it won't matter much.

Wheeler describes this as "Control Chart Myth No2" on page 84. He does not specify any minimum number of points. In fact one of his 3 point control charts includes an outliner.

Perhaps it would even make sense to chart the occurance of the outliers - do the outliers occur at random, or is there some pattern to the rate of outliers!

Repeating patterns in data are themselves a special cause, with 8 repetitions being a detection rule. Wheeler recommends just this and Rule 4 (8 successive values on same side of CL) be added with caution and with experience, to Rule 1 (point outside 3 sigma limits). More tests beyond these increase the likelihood of false alarms.

[Tim Folkerts]

Artichoke,

I may have to find a copy. Certainly I've heard of the book before, but your comments and recommendations have pushed it up a bit higher on my list of books to read.

In Reply to Parent Post by artichoke

That's not what he is doing. In the example he is comparing different estimators of dispersion parameters.

For Xbar-R charts with a relatively large subgroup size, I can see this. I was thinking about individual charts (I suppose since that was the original question). For an I chart it would make no sense, because it would be mathematically impossible to spot an outlier with just three individual points!

Repeating patterns in data are themselves a special cause, with 8 repetitions being a detection rule. Wheeler recommends just this and Rule 4 (8 successive values on same side of CL) be added with caution and with experience, to Rule 1 (point outside 3 sigma limits). More tests beyond these increase the likelihood of false alarms.

Actually, I was thinking about even longer term patterns. For example, perhaps you typically find 1 or 2 outlying points per week. Then you start seeing 5 or 6 per week. This would indicate that the "normal" causes of outliers has itself gone out of control. My thought was that you could throw out these OOC points from the calculations of control limits, but still record them to see the rate of OOC points.


Tim F

[artichoke]

In Reply to Parent Post by Tim Folkerts

For Xbar-R charts with a relatively large subgroup size, I can see this. I was thinking about individual charts (I suppose since that was the original question). For an I chart it would make no sense, because it would be mathematically impossible to spot an outlier with just three individual points!

Comparing ARL plots (Wheeler says it's OK to use the probability approach to compare control charts), for a given number of data measurements, an XbarR chart is much more sensitive than an XmR chart. (Read Ch 10 )

Actually, I was thinking about even longer term patterns. For example, perhaps you typically find 1 or 2 outlying points per week. Then you start seeing 5 or 6 per week. This would indicate that the "normal" causes of outliers has itself gone out of control. My thought was that you could throw out these OOC points from the calculations of control limits, but still record them to see the rate of OOC points.

Over a longer term, hopefully you would do something about the special causes rather than let them keep occuring.