Break all the rules, part 3 - answers

The answers to the most complex control situation - how to interpret "Westgard Rules" when there are 3 controls at different levels.

Break All the Rules, Part Three: The Answers!

Sten Westgard, MS
August 2017

Here we finally reveal the interpretation of using 3 levels of "Westgard Rules". It's the trickiest set of control data yet, looking at the 1:3s/2of3:2s/R:4s/3:1s/6:x across all levels and all runs. After run 77, apply the 9:x rule. After run 103, apply the 12:x rule.

The tables and graphs

The following data set is going to have a low control with a mean of 47 and an SD of 3 and a middle control with a mean of 71 and an SD of 8 and a high control of 256 with an SD of 18. I'm not going to tell you which test or what units are involved. They're irrelevant to this exercise. We're also not going to look at the total allowable error or CV or bias. All of that becomes important after we know the basics of QC and charting.

To make it a little easier to understand this data, here are the Levey-Jennings charts for these first 29 values (notice for each control, not only is the raw value given, but the z-score is shown as well - that's really useful):

Runs 1 through 29:

2017 Break All the Rules answers 1 through 30

Values	Control 1	1 z	Control 2	2-z	Control 3	3 -z	RULE
Run 1	51.5	1.5	82.2	1.4	272.2	0.9
Run 2	38.9	-2.7	51	-2.5	288.4	1.8	2of3:2s
Run 3	47.6	0.2	74.2	0.4	245.2	-0.6
Run 4	46	-0.33333	91.8	2.6	212.8	-2.4	R:4s
Run 5	50.9	1.3	74.2	0.4	239.8	-0.9
Run 6	53.9	2.3	69	-0.25	211	-2.5	R:4s
Run 7	52.7	1.9	58.2	-1.6	263.2	0.4
Run 8	49.1	0.7	83.3	1.54	324.4	3.8	1:3s
Run 9	48.5	0.5	65.4	-0.7	286.6	1.7
Run 10	37	-3.33	90	2.375	230.8	-1.4	1:3s
Run 11	47	0	63	-1	261.0	0.28
Run 12	54	2.333333	82.2	1.4	239.8	-0.9
Run 13	50.3	1.1	65.4	-0.7	259.6	0.2
Run 14	40	-2.33333	86.2	1.9	223.6	-1.8
Run 15	55.4	2.8	70.2	-0.1	254.2	-0.1	2of3:2s
Run 16	49.4	0.8	88.6	2.2	290.2	1.9
Run 17	46.7	-0.1	87.8	2.1	261.4	0.3
Run 18	45.8	-0.4	78	0.875	256	0.0
Run 19	52.7	1.9	76.6	0.7	293.8	2.1	2of3:2s
Run 20	51.2	1.4	65.4	-0.7	261.4	0.3
Run 21	49	0.667	86.2	1.9	304.6	2.7
Run 22	53	2	71	0	248.8	-0.4
Run 23	49.7	0.9	81.4	1.3	241.6	-0.8
Run 24	48.2	0.4	90.2	2.4	308.2	2.9	2of3:2s
Run 25	46.4	-0.2	80.6	1.2	221.8	-1.9
Run 26	54.2	2.4	90	2.375	243.4	-0.7	2of3:2s
Run 27	51.2	1.4	53	-2.25	266.8	0.6
Run 28	53.9	2.3	76.6	0.7	308.2	2.9	2of3:2s
Run 29	44.3	-0.9	72.6	0.2	263.2	0.4

Runs 30 through 59:

Break all the Rules, 3 controls, runs 30 - 59 answers

Values	Control 1	1 z	Control 2	2 z	Control 3	3 z	Rule
30	48.5	0.5	84.6	1.7	279.4	1.3	3:1s
31	48.8	0.6	79.8	1.1	254.2	-0.1
32	46.7	-0.1	82.2	1.4	250.6	-0.3
33	46.1	-0.3	83.8	1.6	265	0.5
34	49.7	0.9	72.6	0.2	279.4	1.3	3:1s
35	53.9	2.3	63.8	-0.9	286.6	1.7
36	52.1	1.7	60.6	-1.3	284.8	1.6
37	48.2	0.4	62.2	-1.1	245.8	-0.6
38	52.1	1.7	71	0	286.6	1.7	3:1s
39	50.6	1.2	69.4	-0.2	261.4	0.3
40	50.3	1.1	64.6	-0.8	245.2	-0.6
41	44.3	-0.9	87.8	2.1	263.2	0.4
42	51.8	1.6	79.8	1.1	281.2	1.4	3:1s
43	41.9	-1.7	64.6	-0.8	284.8	1.6
44	49.4	0.8	63.8	-0.9	261.4	0.3	6:x
45	48.8	0.6	75.8	0.6	241.6	-0.8
46	49.9	0.97	66.2	-0.6	263.2	0.4
47	52.4	1.8	71	0	293.8	2.1
48	52.7	1.9	82.2	1.4	248.8	-0.4
49	49.1	0.7	56.6	-1.8	223.6	-1.8
50	44	-1	66.2	-0.6	229	-1.5
51	48.8	0.6	82.2	1.4	247	-0.5	6:x
52	50.6	1.2	77.4	0.8	266.8	0.6
53	43.7	-1.1	78.2	0.9	290.2	1.9
54	47.6	0.2	75	0.5	281.2	1.4
55	45.5	-0.5	85.4	1.8	245.2	-0.6
56	44.3	-0.9	86.2	1.9	261.4	0.3
57	52.4	1.8	55.8	-1.9	221.8	-1.9
58	53.9	2.3	65.4	-0.7	277.6	1.2
59	45.2	-0.6	83.8	1.6	284.8	1.6

Runs 60 through 89:

Break all the rules, 3 controls, runs 60 through 89, answers

Values	Control 1	z 1	Control 2	Z 2	Control 3	z 3	Rule
60	45.8	-0.4	74.2	0.4	277.6	1.2
61	50.6	1.2	64.6	-0.8	284.8	1.6
62	48	0.3	83	1.5	266.8	0.6	6:x
63	49	0.7	83	1.5	259.6	0.2
64	46	-0.3	67.1	-0.49	260.1	0.23
65	53	2.0	74.2	0.4	281.2	1.4
66	48	0.3	80.6	1.2	241.6	-0.8
67	45.8	-0.4	71.8	0.1	272.2	0.9
68	48.2	0.4	69.4	-0.2	288.4	1.8	9:x
69	50.9	1.3	81.4	1.3	250.6	-0.3
70	50.3	1.1	65.4	-0.7	277.6	1.2
71	51.2	1.4	70	-0.125	221.8	-1.9
72	49.1	0.7	69	-0.25	263.2	0.4
73	51.5	1.5	66	-0.625	247	-0.5
74	47.9	0.3	68.6	-0.3	254.2	-0.1
75	48.5	0.5	86.2	1.9	261.4	0.3
76	50.9	1.3	59.8	-1.4	266.8	0.6
77	46.7	-0.1	67.8	-0.4	252.4	-0.2
78	47.8	0.3	86.2	1.9	236.2	-1.1	9:x
79	45.5	-0.5	72.6	0.2	250.6	-0.3
80	52	1.7	81.4	1.3	259.6	0.2
81	52	1.7	74.2	0.4	243.4	-0.7
82	48.5	0.5	80.6	1.2	275.8	1.1
83	44.3	-0.9	79.8	1.1	281.2	1.4
84	49.4	0.8	75	0.5	252.4	-0.2
85	46.7	-0.1	76.6	0.7	272.2	0.9
86	52.7	1.9	72.6	0.2	281.2	1.4
87	45.2	-0.6	55.8	-1.9	275.8	1.1
88	48.8	0.6	79	1	256	0
89	46.4	-0.2	70.2	-0.1	236.2	-1.1

Runs 90 through 119:

break all the rules, 3 controls, 90 - 119, answers

Values	Control 1	Z 1	Control 2	Z 2	Control 3	Z 3	Rules
90	49.7	0.9	82.2	1.4	275.8	1.1	9:x
91	47	0	68.6	-0.3	265	0.5
92	45.5	-0.5	60.6	-1.3	272.2	0.9
93	46.4	-0.2	79	1	283	1.5
94	51.5	1.5	59.8	-1.4	288.4	1.8
95	48.8	0.6	66.2	-0.6	259.6	0.2
96	44.9	-0.7	77.4	0.8	274	1
97	50.3	1.1	74.2	0.4	281.2	1.4
98	44.3	-0.9	65.4	-0.7	265	0.5
99	46.7	-0.1	63	-1	245.2	-0.6
100	50.6	1.2	74.2	0.4	268.6	0.7	9:x
101	49.4	0.8	85.4	1.8	279.4	1.3
102	47.6	0.2	80.6	1.2	288.4	1.8
103	46.7	-0.1	60.6	-1.3	234.4	-1.2
104	50	1	71	0	275.8	1.1	12:x
105	51.8	1.6	72.6	0.2	275.8	1.1
106	47.6	0.2	70.2	-0.1	250.6	-0.3
107	50	1	68.6	-0.3	261.4	0.3
108	49.1	0.7	81.4	1.3	230.8	-1.4
109	50.3	1.1	78.2	0.9	232.6	-1.3
110	48.8	0.6	69.4	-0.2	265	0.5
111	51.8	1.6	63	-1	256	0
112	50.6	1.2	82.2	1.4	252.4	-0.2
113	47.3	0.1	80.6	1.2	238	-1
114	48.8	0.6	76.6	0.7	230.8	-1.4
115	47.8	0.3	62.2	-1.1	239.8	-0.9
116	47	0	75	0.5	234.4	-1.2
117	47.6	0.2	81.4	1.3	275.8	1.1
118	46.7	-0.1	83.8	1.6	268.6	0.7
119	44.9	-0.7	72.6	0.2	236.2	-1.1

Runs 120 through 150:

Break all the rules, 3 controls, runs 120 through 150, answers

Values	Control 1	Z 1	Control 2	Z 2	Control 3	Z 3	Rules
120	46.7	-0.1	62.2	-1.1	239.8	-0.9
121	47	0	75	0.5	234.4	-1.2	12:x
122	47.6	0.2	81.4	1.3	275.8	1.1
123	46.7	-0.1	83.8	1.6	268.6	0.7
124	44.9	-0.7	72.6	0.2	236.2	-1.1
125	50.9	1.3	79	1	263.2	0.4
126	52.7	1.9	76.6	0.7	230.8	-1.4
127	46.4	-0.2	80.6	1.2	232.6	-1.3
128	44	-1	75.8	0.6	270.4	0.8
129	51.2	1.4	86.2	1.9	268.6	0.7
130	48.5	0.5	80.6	1.2	252.4	-0.2
131	49.1	0.7	75.8	0.6	238	-1
132	51.8	1.6	75.8	0.6	248.8	-0.4
133	42.2	-1.6	58.2	-1.6	254.2	-0.1
134	43.4	-1.2	70.2	-0.1	265	0.5	12:x
135	50.3	1.1	69.4	-0.2	279.4	1.3
136	49.1	0.7	72.6	0.2	284.8	1.6
137	43.7	-1.1	70.2	-0.1	259.6	0.2
138	48.2	0.4	65.4	-0.7	274	1
139	42.8	-1.4	81.4	1.3	268.6	0.7
140	43.1	-1.3	78.2	0.9	277.6	1.2
141	48.8	0.6	69.4	-0.2	266.8	0.6
142	49.1	0.7	63	-1	290.2	1.9
143	46.4	-0.2	82.2	1.4	277.6	1.2
144	44	-1	75	0.5	266.8	0.6
145	45.8	-0.4	76.6	0.7	266.8	0.6
146	45.5	-0.5	59	-1.5	243.4	-0.7
147	51.2	1.4	81.4	1.3	266.8	0.6
148	48.5	0.5	78.2	0.9	277.6	1.2	12:x
149	49.1	0.7	73.4	0.3	266.8	0.6
150	50.3	1.1	75	0.5	270.4	0.8

Summary of Rules Violated

1:3s is violated 2 times
2of3:2s is violated 6 times
R:4s is violated 2 times
3:1s is violated 4 times
6:x is violated 3 times
9:x is violated 4 times
12:x is violated 4 times

If there were any differences between your interpretations and ours, they were probably for the following reasons

We were looking ACROSS-levels as well as WITHIN-levels, as well as ACROSS-runs. If you missed that step, you miss out on a lot of errors
We are applying the rules in the order, as specified with the designated "Westgard Rules" sequence: 1:3s/2of3:2s/R:4s/3:1s/6:x. with 9:x and 12:x being used later. If a 2of3:2s violation occurs, then a 3:1s violation in the same data set doesn't matter, nor would a 6:x, etc.
We interpreted control violations in numerical order, starting with run 1, then proceeding sequentially. If you just look at the charts and just look for the most visually outstanding errors, you may miss an error. Also, if an error is found in a previous run, then that data isn't allowed to be used in other rule interpretations. So an error found earlier in the sequence will mean that all data from that point and earlier cannot be used in the interpretations.
there are probably more rule violations in this example than a lab would see in a whole year (I hope), so having these errors occur so quickly one after another is undoubtedly a strange situation

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