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50 (+) Ways to break your Westgard Rules

There may be 50 ways to leave your lover, but how many ways can you break the "Westgard Rules"? Can you guess? You may be surprised by the possibilities.

 50 ways (+) to Break your Westgard Rules

Sten Westgard,MS
September 2019

Years ago, we explored different ways to "Break all the Rules" (Part 1, Part 2, Part 3) of the "Westgard Rules".

While waiting at an airport recently, I started working on a list. I have been authoring a “basic basic” QC workbook. I suppose I should change the terminology, now that "Basic" is a pejorative in younger circles.

(A digression: we seem to be in an era of increasing complexity combined with increasing confusion – things that we took for granted as comprehensible for students and staff in past decades is now too hard, too long, and too advanced. We must distill our lessons down until they can be Facebooked, Instagrammed, Twittered and Snapchatted (Vimeo’d? Tiktok’d? I fear I’m betraying the obsolescence of my social media awareness) . Paragraphs like the one you’re reading now are considered too long for today’s youth. If it’s not in a 3 minute YouTube video, the topic is too complicated, and the youth seem incapable of devoting enough attention and concentration to learn. Oh, the complaints of being older, how I wish they would get off my lawn…)

In any case, while I was constructing some examples and data sets, I began to realize we have never fully cataloged the number of ways you can break the “Westgard Rules.” In principle, of courses the rules explain how they can be broken, and we have listed those ways in general terms in earlier articles, as well as the very popular Basic QC Practices textbook, but we haven’t reached down to the minutia of exactly which control, exactly in what direction, positive or negative, a control outlier could be.

But no more, this is now remedied. And for those who wish to subject themselves to a spurious test of knowledge, read on…

The "Classic Westgard Rules" for 2 controls, using the 1:2s warning rule: 
1:2s/1:3s/2:2s/R:4s/4:1s/10:x

Rule

Interpretations of Rule Violations

1:2s

Level 1: -2s, current run
Level 1: +2s, current run
Level 2: -2s, current run
Level 2: +2s, current run

1:3s

Level 1: -3s, current run
Level 1: +3s, current run
Level 2: -3s, current run
Level 2: +3s, current run

2:2s

Level 1: +2s, current run and previous run
Level 1: -2s, current run and previous run
Level 2: +2s, current run and previous run
Level 2: -2s, current run and previous run
Levels 1 and 2: both +2s, current run
Levels 1 and 2: both -2s, current run

R:4s

Level 1: +2s and Level 2: -2s, current run
Level 1: -2s and Level 2: +2s, current run
[Optional: Difference between Level 1 and Level 2 >4s]

4:1s

Level 1: +1s, current run and 3 previous runs
Level 1: -1s, current run and 3 previous runs
Level 2: +1s, current run and 3 previous runs
Level 2: -1s, current run and 3 previous runs
Levels 1 and 2: both +1s, current run and previous run
Levels 1 and 2: both -1s, current run and previous run

10:x

Level 1: above mean, current run and 9 previous runs
Level 1: below mean, current run and 9 previous runs
Level 2: above mean, current run and 9 previous runs
Level 2: below mean, current run and 9 previous runs
Levels 1 and 2: above mean, current run and 4 previous run
Levels 1 and 2: below mean, current run and 4 previous runs

 

Total: 29 ways to break the classic “Westgard Rules”
(30 with optional R:4s calculation approach)

 more than you expected? Just wait...

The "Modern Westgard Rules"  for 2 controls (no 1:2s warning rule): 
1:2s/1:3s/2:2s/R:4s/4:1s/10:x

It should be no surprise that this the same table as shown above, just with one less rule/row.

Rule

Interpretation of Rule Violations

1:3s

Level 1: -3s, current run
Level 1: +3s, current run
Level 2: -3s, current run
Level 2: +3s, current run

2:2s

Level 1: +2s, current run and previous run
Level 1: -2s, current run and previous run
Level 2: +2s, current run and previous run
Level 2: -2s, current run and previous run
Levels 1 and 2: both +2s, current run
Levels 1 and 2: both -2s, current run

R:4s

Level 1: +2s  and Level 2: -2s, current run
Level 1: -2s  and Level 2: +2s, current run
[Optional: Difference between Level 1 and Level 2 >4s]

4:1s

Level 1: +1s, current run and 3 previous runs
Level 1: -1s, current run and 3 previous runs
Level 2: +1s, current run and 3 previous runs
Level 2: -1s, current run and 3 previous runs
Levels 1 and 2: both +1s, current run and previous run
Levels 1 and 2: both -1s, current run and previous run

8:x

Level 1: above mean, current run and 7 previous runs
Level 1: below mean, current run and 7 previous runs
Level 2: above mean, current run and 7 previous runs
Level 2: below mean, current run and 7 previous runs
Levels 1 and 2: above mean, current run and 3 previous run
Levels 1 and 2: below mean, current run and 3 previous runs

 

Total: 25 ways to break modern “Westgard Rules”
(26 with optional R:4s calculation approach)

But for those of you following closely, you know there are two more possibilities: "Westgard Rules" formulated for 3 controls instead of 2.

The "Classic Westgard Rules" for 3 controls, using the 1:2s warning rule: 
1:2s/1:3s/2of3:2s/R:4s/3:1s/6:x

Rule

Interpretation of Rule Violations

1:2s

Level 1: -2s, current run
Level 1: +2s, current run
Level 2: -2s, current run
Level 2: +2s, current run
Level 3: -2s, current run
Level 3: +2s, current run

1:3s

Level 1: -3s, current run
Level 1: +3s, current run
Level 2: -3s, current run
Level 2: +3s, current run
Level 3: -3s, current run
Level 3: +3s, current run

2of3:2s

Level 1: +2s, current run and previous run
Level 1: -2s, current run and previous run
Level 2: +2s, current run and previous run
Level 2: -2s, current run and previous run
Level 3: +2s, current run and previous run
Level 3: -2s, current run and previous run
Levels 1 and 2: both +2s, current run
Levels 1 and 2: both -2s, current run
Levels 1 and 3: both +2s, current run
Levels 1 and 3: both -2s, current run
Levels 2 and 3: both +2s, current run
Levels 2 and 3: both -2s, current run
[below, more optional than most interpretations…]
Level 1: +2s, current run, not previous run, but 2nd previous run
Level 1: -2s, current run, not previous run, but 2nd previous run
Level 2: +2s, current run, not previous run, but 2nd previous run
Level 2: -2s, current run, not previous run, but 2nd previous run
Level 3: +2s, current run, not previous run, but 2nd previous run
Level 3: -2s, current run, not previous run, but 2nd previous run

R:4s

Level 1: +2s and Level 2: -2s, current run
Level 1: -2s and Level 2: +2s, current run
Level 1: +2s and Level 3: -2s, current run
Level 1: -2s and Level 3: +2s, current run
Level 2: +2s and Level 3: -2s, current run
Level 2: -2s and Level 3: +2s, current run
[Optional: Difference between Level 1 and Level 2 >4s]
[Optional: Difference between Level 1 and Level 3 >4s]
[Optional: Difference between Level 2 and Level 3 >4s]

3:1s

Level 1: +1s, current run and 2 previous runs
Level 1: -1s, current run and 2 previous runs
Level 2: +1s, current run and 2 previous runs
Level 2: -1s, current run and 2 previous runs
Level 3: +1s, current run and 2 previous runs
Level 3: -1s, current run and 2 previous runs
Levels 1, 2, and 3: all +1s, current run
Levels 1, 2, and 3: all -1s, current run

6:x

Level 1: above mean, current run and 5 previous runs
Level 1: below mean, current run and 5 previous runs
Level 2: above mean, current run and 5 previous runs
Level 2: below mean, current run and 5 previous runs
Level 3: above mean, current run and 5 previous runs
Level 3: below mean, current run and 5 previous runs
Levels 1, 2, and 3: above mean, current run and previous run
Levels 1, 2, and 3: below mean, current run and previous run

 

Total: 46 ways to break the classic “Westgard Rules” with 3 controls
(55 with optional R:4s calculation approach and 2of3 across level interpretation)

That extra control level really multiples the possibilities, doesn't it?

Finally, though we can round out our set with the above view, minus the 1:2s warning rule.

The "Modern Westgard Rules" for 3 controls (no 1:2s warning rule):
1:3s/2of3:2s/R:4s/3:1s/6:x

Rule

Interpretation of Rule Violations

1:3s

Level 1: -3s, current run
Level 1: +3s, current run
Level 2: -3s, current run
Level 2: +3s, current run
Level 3: -3s, current run
Level 3: +3s, current run

2of3:2s

Level 1: +2s, current run and previous run
Level 1: -2s, current run and previous run
Level 2: +2s, current run and previous run
Level 2: -2s, current run and previous run
Level 3: +2s, current run and previous run
Level 3: -2s, current run and previous run
Levels 1 and 2: both +2s, current run
Levels 1 and 2: both -2s, current run
Levels 1 and 3: both +2s, current run
Levels 1 and 3: both -2s, current run
Levels 2 and 3: both +2s, current run
Levels 2 and 3: both -2s, current run
[below, more optional than most interpretations…]
Level 1: +2s, current run, not previous run, but 2nd previous run
Level 1: -2s, current run, not previous run, but 2nd previous run
Level 2: +2s, current run, not previous run, but 2nd previous run
Level 2: -2s, current run, not previous run, but 2nd previous run
Level 3: +2s, current run, not previous run, but 2nd previous run
Level 3: -2s, current run, not previous run, but 2nd previous run

R:4s

Level 1: +2s and Level 2: -2s, current run
Level 1: -2s and Level 2: +2s, current run
Level 1: +2s and Level 3: -2s, current run
Level 1: -2s and Level 3: +2s, current run
Level 2: +2s and Level 3: -2s, current run
Level 2: -2s and Level 3: +2s, current run
[Optional: Difference between Level 1 and Level 2 >4s]
[Optional: Difference between Level 1 and Level 3 >4s]
[Optional: Difference between Level 2 and Level 3 >4s]

3:1s

Level 1: +1s, current run and 2 previous runs
Level 1: -1s, current run and 2 previous runs
Level 2: +1s, current run and 2 previous runs
Level 2: -1s, current run and 2 previous runs
Level 3: +1s, current run and 2 previous runs
Level 3: -1s, current run and 2 previous runs
Levels 1, 2, and 3: all +1s, current run
Levels 1, 2, and 3: all -1s, current run

6:x

Level 1: above mean, current run and 5 previous runs
Level 1: below mean, current run and 5 previous runs
Level 2: above mean, current run and 5 previous runs
Level 2: below mean, current run and 5 previous runs
Level 3: above mean, current run and 5 previous runs
Level 3: below mean, current run and 5 previous runs
Levels 1, 2, and 3: above mean, current run and previous run
Levels 1, 2, and 3: below mean, current run and previous run

 

Total: 40 ways to break the classic “Westgard Rules” with 3 controls
(49 with optional R:4s calculation approach and 2of3 across level interpretation)

The point here is that there are many ways to interpret each rule - and you may not have been interpreting the rule violation in every possible way. That's fine, so long as you are aware of it, and choose and document which interpretations you implement and which you do not. Some interpretations may be impractical, may indeed not be possible if you don't have the correct software.

That's another reason for this list - for manufacturers, software developers, vendors, etc. You can use this list to add the right rules to your QC software and to run tests to verify your rule detection capability.

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