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pzajkowski

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Posts: 46
Reply with quote  #16 

Stacey -- your post is hardly a waste of time -- I'm glad you've contributed to the discussion. Many of your comments affirm what I've begun to understand about Wheeler's message about using process behavior charts. Indeed, he does indicate that it's hard to go wrong with plotting any type of data on an XmR, especially as a first step towards understanding the nature of a given process. And, that's essentially where I'm at -- a first step to understanding control charts, their uses, and whether these charts can be applied to the tasks that gets carried out at the company I work for.

I agree that the chart I posted certainly could use a few more data points. Even if the current chart did have a data point outside of the limits, I wouldn't necessarily feel inclined to investigate the driving forces behind this extreme data point just yet. The data plotted isn't based on an actual process, but rather the rate of compliance for patients to get a certain type of blood test done with test results falling within a desired range. So, we don't control a process, but rather influence whether patients get their appropriate blood tests done. (A lot of factors impact the outcomes of patient health care. A doctor can do all the right things, but if a patient doesn't get a test performed or doesn't get a prescription filled or doesn't change their lifestyle, then unpredictable or undesirable outcomes may likely prevail.)

As I mentioned in my previous post, many of our clinical measures (like blood test compliance) show a visible, desirable, upward shift from baseline -- i.e., once our care management team began to engage a client's patients directly or indirectly by providing consultation with physicians, the vast majority of clinical measures (both process and outcomes oriented measures) reveal an impact that is essentially evident immediately after baseline. Even with such positive results, I feel we need more data before we can presume that the positive outcomes we're witnessing early on are actually sustainable and attributable to our efforts. 

Again, my purpose in initiating this discussion thread was to expose my newness to process behavior charts (SPC) and collect feedback. Hopefully along the way, other fellow readers who may be dabbling with control charts can benefit from this discussion, too. I am certainly learning quite a bit from everyone that has contributed to the discussion.

Speaking of learning, does Wheeler ever reveal how to calculate other control limits besides the upper/lower natural control limits on an XmR chart? These natural control limits reflect 3-sigma, right? So what about 2 sigma or 1 sigma limits? Perhaps Wheeler doesn't find these inner limits all that necessary or perhaps it's inappropriate to have other limits plotted on an XmR chart?

staceybarr

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Reply with quote  #17 
My understanding is that Wheeler, and others including myself, don't use 2 or 1 sigma limits because all we need the limits to do is help us interpret signals. I don't want 1 sigma limits because then I would be trying to find the reasons for the 32% of performance measure values that would likely fall outside those 1 sigma limits.

As long as you know the rules for interpreting the signals in XmR charts, using a mean line and 3 sigma limits, your attention should be on those signals:

-- a point falling outside the 3 sigma limits (outlier)
-- 7 or more points in a row on the same side of the mean line
-- 2 out of 3 points in a row beyond 2 sigma
-- 4 out of 5 points in a row beyond 1 sigma
-- 3 points in a row closer to 3 sigma than to the mean line
-- 7 points in a row consecutively decreasing (or increasing)

To help identify those signals that depend on 1 and 2 sigma comparisons, it probably wouldn't hurt to have those limits also on the XmR chart. But I think we need to adopt some of Steve Few's ideas about keeping the chart as simple and visually uncluttered as possible. (Steve, do you have suggestions for how to do this? I know when we spoke of these charts once we made the upper and lower limits a shaded background rather than dotted lines as is the normal convention. What else could work?)

To me, XmR charts are about highlighting signals of change in performance. For most performance measures, we WANT change, and more specifically we want that change to indicate improvement in performance. So we're wanting to see signals that indicate improvement.

Smiles, Stacey.

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Smiles, Stacey.

http://www.staceybarr.com
pzajkowski

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Posts: 46
Reply with quote  #18 
Stacey -- your reply provides clarity. It seems, though, that I've misspoke about 1 and 2 sigma "limits". What I meant to inquire is not about setting tighter "limits", but how to determine 1 and 2 sigma. Your list of signals mention "2 out of 3 points in a row beyond 2 sigma" and "4 out of 5 points in a row beyond 1 sigma". So, I find myself asking how to compute 1 sigma and 2 sigma? Is 1 sigma merely 1/3 of 3 sigma; is 2 sigma merely 2/3 of 3 sigma? I suppose one could eye-ball whether "2 out of 3..." or "4 out of 5..." signaling something, but I'd prefer to know the calculations for 1 and 2 sigma.

As for keeping things visually simple, yet effective, I agree that it may not be necessary to have the various 1 & 2 sigma slices visually represented. Certainly in Wheeler's book "Understanding Variation", his XmR charts keep to just 3 sigma.
jlbriggs

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Posts: 194
Reply with quote  #19 
Sigma is just the symbol used for standard deviation.  So 1 sigma = 1 standard deviation (so yes, 1 sigma is 1/3 the value of 3 sigma).
pzajkowski

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Posts: 46
Reply with quote  #20 

jlbriggs -- "Sigma is just the symbol used for standard deviation"

That's what I thought.

But, when I stumbled across Wheeler's article "The Right and Wrong Way of Computing Limits" (http://www.spcpress.com/pdf/DJW205.pdf), he states "A very common, and yet completely erroneous, method for computing the limits for a process behavior chart is to use the global standard deviation statistic."

When I read this statement, I found myself asking "is sigma different from standard deviation?"... 'cause I thought they were the same.

As I take another look at the fore mentioned article, I think my initial confusion rests not with sigma representing standard deviation, but from what data to compute a standard deviation for a process control chart. As such, I think the pieces are finally falling into place. 

Hopefully I haven't diverted this entire discussion thread from understanding a XmR chart (and other process control charts) to a course in basic statistics.

staceybarr

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Posts: 3
Reply with quote  #21 
This has been a great discussion, actually. If you take the time to answer some of these very common questions, the answers aren't that complex, and then we can all use these XmR charts with confidence (and enjoy the power they give!!).

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Smiles, Stacey.

http://www.staceybarr.com
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