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R-4s, 10x and finding the cause

14 min

  • Recognize an R-4s violation within one run
  • Recognize a 10x violation in consecutive same-side controls
  • Match a QC shift, trend, or random error to its likely causes

Read the full reference

Try first

Try first

Two glucose control levels are run twice a day. Each result's distance from its own mean: RunLevel 1Level 2Yesterday, 15:00+2.5 SD+0.3 SDToday, 07:00−0.2 SD−2.3 SD Is R-4s met?

The next section explains it.

The next section explains it.

Right. The next section explains why.

The next section explains it.

Get the idea

Two more rules finish the usual Westgard set, and each one points to a different kind of cause.

R-4s within one run

  • The R-4s rule is met when one control is above +2 SD and another in the same run is below −2 SD, a spread of more than 4 SD.
  • Controls measured together share the same reagent and calibration. When they pull apart in opposite directions, the measurement itself was unsteady in that run. That is random error.
  • R-4s never crosses a run boundary. Pairing results from different runs mixes a change between runs into the rule.1,2

The 10x rule along a sequence

  • The 10x rule is met when ten consecutive controls fall on the same side of the mean, even if every one of them is inside ±2 SD.
  • A procedure in control puts about half its results on each side, so ten in a row on one side is a small systematic shift.
  • Some QC plans use 8x or 9x for this check, and the plan sets whether the count runs across levels as well as runs.1,3

Where to look first

Once a rule rejects the run, the rule's error type tells you where to look first.2,3

Error typeRulesCauses to check first
Random1-3s, R-4sBubbles, a clot or short sample in the probe, uneven pipetting, electrical noise
Systematic2-2s, 4-1s, 10x, a shift or trendReagent lot or deterioration, calibration, temperature, a failing lamp or electrode

Fix the cause, then look back

Rerunning the same control until it passes explains nothing, and the fault stays in place. Work in this order:2,4

  1. Correct the cause.
  2. Rerun the controls.
  3. Release patient results only after QC is acceptable.
  4. Review the patient results from the rejected run and every result reported since the last acceptable run. Repeat those the error could have changed.

A sequence rule such as 10x is met only after a shift has lasted several runs, so the review goes back to the run where the shift began.3

References
  1. Westgard JO. Westgard rules and multirules. Westgard QC. Accessed September 23, 2026.
  2. Westgard JO. QC: the multirule interpretation. Westgard QC. Accessed September 23, 2026.
  3. Clinical and Laboratory Standards Institute. Statistical Quality Control for Quantitative Measurement Procedures: Principles and Definitions. 4th ed. CLSI guideline C24Ed4E. Clinical and Laboratory Standards Institute; 2016.
  4. Centers for Medicare & Medicaid Services. 42 CFR §§493.1256 and 493.1282. Electronic Code of Federal Regulations. Accessed September 23, 2026.

Watch one

A BUN level 2 control has a mean of 50 mg/dL and an SD of 2 mg/dL. Its last ten runs, oldest first:

Run12345678910
Result50.8 mg/dL51.5 mg/dL50.4 mg/dL52.2 mg/dL51.0 mg/dL51.8 mg/dL50.6 mg/dL52.4 mg/dL51.2 mg/dL51.6 mg/dL

A new calibrator lot was put into use before run 1. What do you decide, and where do you look?

  1. Check 1-2s: the +2 SD limit is 54 mg/dL and the highest result is 52.4 mg/dL, so there is no warning.

    A warning would send you to the other rules, so it is checked first.

  2. Check 4-1s: only runs 4 and 8 are beyond the +1 SD limit of 52 mg/dL, and they are not consecutive, so 4-1s is not met.

    A value inside ±2 SD does not excuse the run from the sequence rules.

  3. Check 10x: all ten results are above 50 mg/dL, so 10x is met and the run is rejected.

    Ten results in a row on one side of the mean is the sign of a small shift.

  4. Name the error type: systematic, so bubbles and pipetting are not the first place to look.

    Every sequence rule signals systematic error, which pushes every result the same way.

  5. Check the calibration first: the new calibrator lot arrived just before run 1, when the results moved above the mean.

    The shift began when something shared by every result changed.

Reject the run for 10x and investigate the calibration made with the new calibrator lot. Once QC is acceptable, review the patient BUN results reported since the new lot went into use, just before run 1.

Your turn

Problem 1 of 3

Two controls in the same run are +2.4 SD and −2.3 SD from their respective means. Which rejection rule is met?

Incorrect. 2₂s requires consecutive results beyond the same 2 SD limit. These deviations point in opposite directions.

Correct. One result is above +2 SD and the other below −2 SD in the same run. Their separation is 4.7 SD.

Incorrect. Neither result exceeds a 3 SD limit. Their within-run separation meets R₄s.

Hint
  1. Both results come from the same run.
  2. One result is above +2 SD and the other is below −2 SD.
  3. Look for the rule that compares two controls pulling in opposite directions within one run.

Review Multirule interpretation

Problem 2 of 3

A calcium level 2 control has a mean of 11.6 mg/dL and an SD of 0.2 mg/dL. Its last ten runs: Run12345678910Result11.7 mg/dL11.8 mg/dL11.7 mg/dL11.9 mg/dL11.7 mg/dL11.8 mg/dL11.7 mg/dL11.8 mg/dL11.9 mg/dL11.7 mg/dL Which rule, if any, is met?

4-1s needs four consecutive results beyond +1 SD, which is 11.8 mg/dL. Only runs 4 and 9 are beyond it.

All ten results are above the 11.6 mg/dL mean. Ten in a row on one side meets 10x and points to a small systematic shift, though every result is inside ±2 SD.

A stable procedure puts about half its results below the mean. Ten in a row above it meets 10x, however small each difference looks.

Ignored ten controls on the same side of the mean

Ten consecutive results on one side of the mean meet 10x even when all lie within ±2 SD, as with glucose controls from 122 to 127 mg/dL against a mean of 120 mg/dL and an SD of 4 mg/dL. Passing the run because no single value looks extreme lets a shift reach patient results.

No result goes beyond +2 SD, 12.0 mg/dL, so there is no warning. The sequence meets a rule without one.

Hint
  1. No result goes beyond 12.0 mg/dL, the +2 SD limit.
  2. Count how many results fall above the mean.

Review Multirule interpretation

Problem 3 of 3

An ALT level 2 control drifts upward over six days: +0.3, +0.8, +1.2, +1.6, +1.9 and +2.3 SD. Level 1 drifts the same way. The reagent cartridge was loaded on day 1, and its onboard stability ends tomorrow. The run is rejected for 4-1s. What do you check first?

Those are random causes, which scatter results both ways. A steady climb on both levels is systematic, and a cartridge near the end of its onboard stability fits it.

Looked for random causes behind a shift

A shift or trend moves results in one direction, which points to systematic causes such as reagent deterioration, a calibration problem, or a temperature change. Checking only for bubbles or pipetting slips, the random causes, leaves the fault in place, and the next run fails the same way.

Both levels rise a little each day since the cartridge was loaded, a trend that points to a systematic cause. Reagent deterioration near the end of onboard stability, and the calibration made with it, are the first things to check.

A passing rerun does not explain the trend, and the cause would still be there for the next run. The cause is found and corrected first.

Review Levey-Jennings charts

Use it

Try this at the QC workstationPendingQC run due07:00READY TO REVIEWCase 04Review QC

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