But the Limits Are Too Wide!

When the XmR Chart Doesn’t Seem to Work

Last month I described what makes the XmR chart work. This month I will describe some common failure modes for the XmR chart and show how they come from a failure to follow the two fundamental principles behind the XmR chart.

When administrative and managerial data are placed on an XmR chart, the first reaction will frequently be that the limits are far too wide: “We have to react before we get to that limit.” So what are we to do when this happens? Are the limits really too wide? There are three cases to consider: the data are full of noise; the data are full of signals; and the data, in turn, represent different processes.

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Comments

Very interesting!

Hello!,

There are countless opportunities to apply the XmR chart...., either on Manufacturing or Services industries.

The Engineering services Industry, has a lot of potential for applying this tool.

Rgeards,

Roberto

Chart-istics

Hi, Mr. Wheeler, thank you for your efforts. While XmR statistics charts seem to be very fashionable nowadays, due to the ever smaller production lots, be they administrative or manufacturing, your analysis of Signal versus Noise is really a "signal versus noise" to me. I still consider Statistics quite a "noise-ance", in the sense that it makes us look at the tree but ignore the forest - of our inherently human capabilities of observation and understanding. Your signal that a statistical tool like XmR charting can lead to error is very wisdom-oriented - yet it's a noise to my cynical mind. Mankind's history is made by humans, not by numbers, though some of Mankind's best minds think that our brains work by numbers. But wasn't Cybernetics born from and grown on EMOTIONAL fields?

The Importance of Context

Umberto wisely reminds us of the human component. I always emphasize that the analysis of data begins with context, must be guided by context, and the results of any analysis have to be interpreted in context. This is where we bring our experience and understanding to the table. This is also why some things cannot be meaningfully reduced to numbers. But many other things can be and will be quantified, and when they are, it is important to filter out the noise of routine variation before we begin to interpret every little change as a signal. There are two mistakes we can make when interpreting data: We can interpret noise as a signal, or we can miss a signal thinking that it is noise. The trick is to balance the economic effects of these two errors, and this is precisely what the process behavior chart does.

Question about Manager One

Another enlightening article! I recently had occasion to look at a very similar situation to the medical case; a friend gave me data on his blood sugar readings. The data displayed a similar pattern, because he took one reading in the morning as soon as he woke up, and another in the evening, after dinner. Two very different situations. I split the data and made two charts, so he could get an idea of what to expect in the morning and what to expect in the evening.

I have a question about this statement: "Manager One’s adjustments were so frequent (over 80% of the time) that the impact of those changes looked exactly like routine variation to the computations. Manager One had 150 percent of the variation displayed by Manager Two, along with a lower average daily output, yet his data appear to come from a predictable process." Would it be accurate to say that Manager One's data do come from a predictable process? Granted, it's not as good a process, but as long as he continues to tamper daily, won't he continue to get this level of variation and this mean? Is this just someone using rule one with the funnel (but consistently using rule one)?

Rip's Question

Yes, Manager One's adjustments have become routine and so the variation of the adjustment process is added to the variation of the production process and the result is a reasonably predictable process with increased variation. Since his use of Rule One of the Funnel is triggered by misinterpreting the process variation, and since the process is fairly predictable, Manager One's tampering will also be fairly predictable. With an unpredictable production process Manager One's tampering could also be unpredictable.