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QC: Levey-Jennings: Answers

Answers to the Levey-Jennings Control Chart lesson exercise.

Answers for this exercise

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Levey-Jennings QC Exercise Answers:

Cholesterol example where:
Control 1 has a mean of 200 mg/dL and standard deviation of 4.0 mg/dL.
Control 2 has a mean of 250 mg/dL and standard deviation of 5.0 mg/dL.
Prepare appropriate control charts and interpret the results.

Day Control 1
Value
Control 2
Value
12s Rule
Violation
13s Rule
Violation
Accept(A),
Warning (W),
or Reject(R)?
Comments
1 200 247     A  
2 205 250     A  
3 195 255     A  
4 202 243     A  
5 186 254 -2s - 3s R  
6 207 263 + 2s   W(A)  
7 194 251     A  
8 209 264 + 2s twice   R Both exceed + 2s.
9 200 253     A  
10 196 244     A  
11 190 261 + 2s and - 2s   R both exceed 2s
in opposite directions.
12 204 254     A  
13 196 239 - 2s   W(A)  
14 207 236 - 2s   R 2 days in a row
exceeding - 2s.
15 200 250     A  
16 205 259     A  
17 209 257 + 2s   W(A)  
18 197 256     A  
19 196 249     A  
20 198 257     A  
21 197 241     A  
22 195 255     A  
23 198 250     A  
24 199 259     A  
25 191 247 - 2s   W(A) Negative shift.
26 197 242     A  
27 190 256 - 2s   W(A) Follow to see if
negative shift continues
or worsens.
28 202 246     A  

Interpretation of control results - with 12s and 13s rules

Use of a 12s rule as a strict rejection rule would result in rejecting runs on days 5, 6, 8, 11, 13, 14, 17, 25, and 27, for a total of 9 runs, as shown by the check marks in the column for 12s rule violations.

Use of a 13s rejection rule would lead to rejection of only one run on day 5, as shown by the single check mark in the column for 13s rule violations.

It makes a big difference what control rule is being applied -- 9 rejections vs 1 rejection!

What if different control rules were used?

Given that the 12s rule is known to cause a high level of false alarms or false rejections, it might be better to interpret the data more carefully, in effect applying additional control rules, such as the 22s and R4s rules:

  • 22s indicates a rejection when two consecutive control values exceed the same mean +2s limit or the same mean -2s control limit; this rule is sensitive to shifts in the mean of the distribution, therefore it is a good indicator of increases in systematic error or changes in the accuracy of the method.
  • R4s indicates a rejection when one control measurement in a run exceeds a +2s control limit and another exceeds a -2s control limit. This "range" rule is sensitive to changes in the width of the distribution, therefore it is a good indicate of increases in random error or changes in the precision of the method.

Use of the 13s rule together with the 22s and R4s rules leads to a multirule QC procedure in which multiple decision criteria are applied simultaneously. If any single control rule is violated, the run is rejected. Here's how the 13s/22s/R4s multirule procedure would be interpreted for this example set of control results:

  • Day 5. The value for Control 1 exceeds a -3s control limit, which is a good indication that there is a problem with the method. Stop, reject the run, trouble-shoot the method, fix the cause of the problem, then restart the method and reanalyze the patient specimens.
  • Day 6. The value for Control 2 exceeds a +2s control limit, but doesn't exceed a 3s limit. There might be a problem, but this might also be a false rejection. If a 12s rule were strictly applied, the run would be rejected. However, because the value for Control 1 is okay, it is likely that this is a false rejection. Accept the run.
  • Day 8. Both the values for Control 1 and Control 2 exceed their respective +2s control limits. It is rare to see two values in a row exceed the same +2s limit, therefore this occurrence indicates a problem with the method. Note that this interpretation applies the 22s control rule, i.e., 2 values in a row exceeding the same control limit. Since both controls are out in the same direction, it is likely there is a systematic error (or problem with the accuracy of the method). Stop, reject the run, trouble-shoot the method, fix the cause of the problem, then restart the method and reanalyze the patient specimens.
  • Day 11. Both control values exceed 2s control limits, but one is positive and one is negative. It is a rare occurrence and most likely there is a problem with the method. Since the two controls are out in opposite directions, it is likely that there is a random error (or problem with the precision of the method). Note that this interpretation applies the R4s rule, i.e., the range of the control values exceeds 4s. Stop, reject the run, trouble- shoot the method, fix the cause of the problem, then restart the method and reanalyze the patient specimens.
  • Day 13. The value for Control 2 is outside the low end of the 2s range. There is a warning of a possible problem, but this might also be a false rejection. Accept this run because none of the rejection rules are violated.
  • Day 14. The value for Control 2 is again outside the low end of the 2s range. This makes 2 days or 2 runs in a row, which is unusual. Since both values for Control 2 are out in the same direction, it is likely there is a systematic error (or problem with the accuracy of the method). Stop, reject the run, trouble-shoot the method, fix the cause of the problem, then restart the method and reanalyze the patient specimens.
  • Day 17. Control 1 exceeds the +2s control limit. There might be a problem, but this might also be a false rejection. If a 12s rule were strictly applied, the run would be rejected. However, because the value for Control 2 is okay, it is likely that this is a false rejection. Accept the run.
  • Day 25. Control 1 exceeds the -2s control limit. There might be a problem, but this might also be a false rejection. If a 12s rule were strictly applied, the run would be rejected. However, because the value for Control 2 is okay, it is likely that this is a false rejection. Accept the run.
  • Day 27. Control 1 exceeds the -2s control limit. There might be a problem, but this might also be a false rejection. If a 12s rule were strickly applied, the run would be rejected. However, because the value for Control 2 is okay, it is likely that this is a false rejection. Accept the run.

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