## 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, MSAugust 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:

 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:

 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:

 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:

 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:

 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