9.2 Quality Control Statistics, Levey-Jennings Charts & Westgard Multirules
Key Takeaways
- Accuracy is closeness to the true value and is tracked by the mean; precision is reproducibility and is tracked by the standard deviation and the coefficient of variation, which is the only fair comparison across analytes.
- In a Gaussian distribution about 68% of values fall within 1s, 95.5% within 2s, and 99.7% within 3s, so roughly 1 control in 20 exceeds 2s by chance, which is why 1_2s is a warning rule rather than a rejection rule.
- Random error is detected by 1_3s and R_4s and raises the standard deviation; systematic error is detected by 2_2s, 4_1s, and 10x and moves the mean, appearing as an abrupt shift or a gradual trend.
- A shift points to a discrete event such as a new reagent lot or recalibration; a trend points to something changing slowly such as reagent deterioration, lamp aging, or deposit buildup.
- Bull's moving average (XB) uses batches of about 20 patient specimens to monitor MCV, MCH, and MCHC for analytical drift, and supplements rather than replaces commercial quality control.
Quality Control Statistics, Levey-Jennings Charts & Westgard Multirules
Quality control answers one question: is the measurement system still performing the way it did when it was validated? The ASCP BOC expects candidates to compute and interpret the descriptive statistics, read a Levey-Jennings chart, apply the Westgard multirules, and distinguish random from systematic error.
Accuracy, Precision, and the Four Measures of Center and Spread
Accuracy is closeness to the true value and is monitored by the mean. Precision is reproducibility and is monitored by the standard deviation and coefficient of variation. A method can be precise but inaccurate (tight cluster, wrong place) or accurate but imprecise (scattered around the correct value).
| Statistic | Definition | Laboratory Use |
|---|---|---|
| Mean | Arithmetic average of all values | Target value of a control; measure of central tendency and accuracy |
| Median | Middle value when data are ranked | Preferred when the distribution is skewed or contains outliers, as in turnaround time data and many reference interval studies |
| Mode | Most frequently occurring value | Describes multi-peaked data, for example a bimodal red cell volume histogram |
| Standard deviation (s) | $s=\sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n-1}}$ | Absolute dispersion; sets the control limits |
| Coefficient of variation | $%CV=\dfrac{s}{\bar{x}}\times 100$ | Relative dispersion; the only fair way to compare precision between analytes or concentration levels |
| Confidence interval | Mean $\pm z\times s$ | Approximately 68% of values fall within $\pm 1s$, 95.5% within $\pm 2s$, and 99.7% within $\pm 3s$ in a Gaussian distribution |
Because 95.5% of results fall within two standard deviations, roughly 1 control value in 20 will exceed $\pm 2s$ by chance alone. That is exactly why $1_{2s}$ is a warning and not a rejection rule.
Core Statistical Measures
Fundamental Statistical Formulas
- Mean ($\bar{x}$): Measure of central tendency (accuracy): $\bar{x} = \frac{\sum x_i}{n}$
- Standard Deviation ($s$ or $\text{SD}$): Measure of dispersion (precision/reproducibility): $s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}$
- Coefficient of Variation ($\text{% CV}$): Relative standard deviation independent of concentration unit: $\text{% CV} = \left( \frac{s}{\bar{x}} \right) \times 100$
Levey-Jennings Charts & Westgard Multirule Algorithm
Quality control data are plotted sequentially on Levey-Jennings control charts against established mean and standard deviation limits ($\pm 1s, \pm 2s, \pm 3s$):
- $1_{2s}$ (Warning Rule): One control value exceeds $\pm 2s$. This is a screening warning; patient testing may continue while other rules are evaluated.
- $1_{3s}$ (Rejection Rule): One control value exceeds $\pm 3s$. Rejects the run for Random Error (or severe systematic shift).
- $2_{2s}$ (Rejection Rule): Two consecutive control observations exceed the same $+2s$ or $-2s$ limit. Rejects the run for Systematic Error.
- $R_{4s}$ (Rejection Rule): One control exceeds $+2s$ and another exceeds $-2s$ in the same analytical run (a span of $\ge 4s$). Rejects the run for Random Error.
- $4_{1s}$ (Rejection Rule): Four consecutive control values exceed $+1s$ or $-1s$ on the same side of the mean. Rejects the run for Systematic Error.
- $10_{\bar{x}}$ (Rejection Rule): Ten consecutive control values fall on one side of the mean. Rejects the run for Systematic Error.
Shifts versus Trends
- Shift: An abrupt, permanent step-change in the control mean. Caused by: introduction of a new uncalibrated reagent lot, incorrect calibrator assignment, sudden optical alignment change, or major temperature fluctuation.
- Trend: A gradual, progressive drift of control values in one direction over days/weeks. Caused by: reagent expiration/deterioration, light source aging (photometer bulb decay), gradual protein accumulation in flow cell/aperture, or aging electrode membranes.
Delta Checks & Critical Value Protocols
- Delta Checks: Automated laboratory information system (LIS) algorithms comparing a patient's current test result with their previous recent result. Flags severe, physiologically improbable discrepancies to detect specimen misidentification, IV fluid contamination, or acute occult hemorrhage.
- Critical Value Reporting: Critical test values (e.g., $\text{Platelets} < 20 \times 10^9/\text{L}$, $\text{WBC} > 50.0 \times 10^9/\text{L}$, $\text{Hb} < 6.0\text{ g/dL}$, or intracellular microorganisms in sterile body fluids) mandate immediate direct verbal notification to the licensed caregiver, mandatory read-back of patient identifiers and results, and full LIS documentation (date, exact time, staff name, recipient name).
Random versus Systematic Error
| Feature | Random Error | Systematic Error |
|---|---|---|
| Appearance on the chart | Scattered, unpredictable outliers | A shift (abrupt step) or a trend (gradual drift) |
| Rules that detect it | $1_{3s}$, $R_{4s}$ | $2_{2s}$, $4_{1s}$, $10_{\bar{x}}$ |
| Statistic affected | Standard deviation and CV rise | Mean moves |
| Typical causes | Bubbles, clots, short sampling, unstable power, imprecise pipetting | New reagent lot, miscalibration, deteriorating reagent, aging lamp, drifting temperature |
Quality Control Practice in Hematology
- Frequency. CLIA requires at least two levels of control every 24 hours for most nonwaived tests; most hematology laboratories run three levels (low, normal, high) each shift, plus after maintenance, after a reagent lot change, and after any repair.
- Corrective action. When a run is rejected the results are not reported. The technologist identifies the cause, corrects it, repeats the controls, and repeats patient testing; every step is documented. Repeating the control until it passes without identifying a cause is a documented CLIA deficiency.
- Moving average (Bull's algorithm, XB). Hematology has a patient-based control unique to the discipline: the red cell indices MCV, MCH, and MCHC are stable in a population, so a smoothed moving average of batches of 20 patient samples detects analytical drift even between control runs. It monitors calibration stability, not individual patient accuracy.
- Delta checks and specimen-level checks supplement, but never replace, statistical quality control.
- Calibration verification confirms that the reportable range remains valid and is performed at least every six months, after major maintenance, and when controls show unexplained drift.
During morning quality control on an automated hematology analyzer, the Level 2 normal control for hemoglobin yields a value that is +2.2 standard deviations above the established mean for the second consecutive daily run. All other CBC parameters and control levels are within ±1 SD. According to the Westgard multirule algorithm, which rule is violated, what type of analytical error does it indicate, and what is the required laboratory action?
Two hematology analyzers measure the same control. Analyzer A reports a mean hemoglobin of 12.0 g/dL with a standard deviation of 0.24 g/dL. Analyzer B reports a mean platelet count of 250 x 10^9/L with a standard deviation of 12.5 x 10^9/L. Which analyzer is more precise for its analyte, and what statistic proves it?
Over eight consecutive days, the normal-level hemoglobin control drifts steadily upward from the mean to +1.8 standard deviations, without any single value exceeding 2s. Which error type is present and which cause fits best?
Which statement about the moving average (Bull's algorithm, XB) in hematology is correct?