Tools, Technologies and Training for Healthcare Laboratories

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