CUSUM Charts: Detecting Subtle Shifts Invisible on Levey-Jennings Plots

Category: Advanced Quality Instruments | Estimated reading time: 9 minutes

When Levey-Jennings is Not Sensitive Enough

Levey-Jennings charts are excellent at detecting large deviations — one point out by ±3SD, or two consecutive points out by ±2SD in the same direction. But there is one type of problem that often slips past the LJ radar: small shifts that occur consistently, day after day, but are never large enough in a single point to violate any Westgard rules.

This is where the CUSUM (Cumulative Sum) Chart comes in — a statistical control chart that monitors the cumulative sum of small deviations between measurement results and the target value (mean). CUSUM is specifically designed to detect small but consistent changes in a process — which are often early signs of system instability, long before any single point looks suspicious on an LJ chart.

A Brief History

This method was first introduced by E. S. Page in 1954, in his classic paper "Continuous Inspection Schemes" published in the journal Biometrika — it was originally developed for the manufacturing industry as a way to detect shifts in process parameters faster than conventional control chart methods (such as Shewhart).

The adaptation of CUSUM to medical laboratories came several decades later. Westgard, Groth, Aronsson, and de Verdier (1977) published the "combined Shewhart-CUSUM" method in the journal Clinical Chemistry — a simplified version of CUSUM using a decision limit (with parameters k and h) instead of the older and more visually complex V-mask method. It is this decision-limit version that remains the standard for CUSUM implementation in clinical laboratories today, as it can be calculated directly numerically without needing to draw a mask over a chart.

Reasons for Use

• Identifying small trends or gradual shifts in analytical systems that might not be apparent on a Levey-Jennings chart.
• As an early warning system for non-conformities in instruments or reagents.
• Part of Quality Improvement and long-term drift detection.

Advantages

• More sensitive than Levey-Jennings charts to small, consistent changes.
• Can monitor long-term stability more effectively.
• Suitable for highly stable processes, where even small changes are clinically significant.
• Sharper trend visualization — easy to recognize when the accumulation of values begins to move significantly in one direction.

A study by Rowlands, Wilson, Nix, Kemp, and Griffiths (1980) on the advantages of the CUSUM technique in clinical chemistry confirmed that CUSUM is consistently superior to Shewhart-type control charts in detecting small shifts, despite a common misconception that CUSUM is weak at detecting large variations or outliers — an assumption that the study proved incorrect when the control scheme design is appropriate.

Disadvantages

• More complex in calculation and interpretation compared to Levey-Jennings.
• Does not directly show the type of error (random vs. systematic) — requires additional interpretation.
• Requires setting initial parameters such as target value, allowable deviation (k), and decision threshold (h).
• Not commonly used in all laboratories — requires additional training and statistical understanding for medical laboratory technologists (ATLM).

Required Data

• Daily internal quality control (IQC) results.
• Target value (mean) of the control material — obtained from preliminary testing.
• Standard deviation (SD) from historical data — also from preliminary testing.
• Tolerance threshold for deviation (k) and decision interval (h), used to determine when an alarm should be triggered.

How to Use

a. Determine base values:

• Mean/Target Value (TV)
• SD
• k = minimum deviation considered significant (usually 0.5 SD)
• h = decision interval, threshold for an alarm (usually 4 or 5)

b. Calculate daily deviation (Z-score):

For every test result i:

Zᵢ = (xᵢ − Target) / SD

c. Calculate positive and negative CUSUM:

Cᵢ⁺ = max(0, Cᵢ₋₁⁺ + Zᵢ − k)
Cᵢ⁻ = max(0, Cᵢ₋₁⁻ − Zᵢ − k)

C⁺ detects shifts upward (positive bias), C⁻ detects shifts downward (negative bias). Both start from 0, and are reset to 0 whenever the result is negative — this is what makes CUSUM only "remember" consistent deviations in one direction, rather than random noise that cancels itself out.

d. Plot results cumulatively and compare with h:

• C⁺ or C⁻ exceeds h → out-of-control (OOC) signal: there is a consistent systematic shift.
• C⁺ chart rises continuously → increasing trend (positive bias).
• C⁻ chart rises continuously → decreasing trend (negative bias).

Case Study: Drift Invisible in Levey-Jennings

Imagine a Creatinine parameter with Target = 100 and SD = 2. For 15 consecutive days, QC results moved slowly upward — from 100.5 on the first day to 103.6 on the 15th day. Every individual point is still well within ±2SD (range 96–104), so not a single Westgard violation is triggered. Visually on an LJ chart, this looks like normal variation that is slightly skewed upward — it might not get special attention from an ATLM glancing at it.

But when calculated with CUSUM (k = 0.5, h = 5): because the Z-value is positive and consistently increasing every day, C⁺ continues to accumulate without ever resetting to 0. Around days 13–14, C⁺ has exceeded the threshold h = 5 — triggering an out-of-control signal days before this drift is large enough to be noticeable on an LJ chart, and long before violating any formal Westgard rules.

This is the primary value of CUSUM: it captures the accumulation of evidence, not just individual points — allowing it to provide an early warning for calibration drift or slowly degrading reagents, long before the issue grows into a clear rejection.

Best Used When

• The testing process is highly precise, and small changes are clinically significant (e.g., hormone testing, toxicology, or instruments with very low CV).
• You want to monitor long-term stability with high sensitivity.
• As a complementary tool to Levey-Jennings for detecting slow shifts — not a replacement, but an additional layer.
• When drift or changes in instruments/reagents occur that do not immediately cause outliers, but start to lead toward non-conformity.

Try the CUSUM Calculator

Conclusion

The CUSUM chart is a highly useful statistical control tool for detecting small but consistent changes in laboratory test results. Compared to the Levey-Jennings chart, CUSUM has higher sensitivity to gradual shifts from the target value — enabling early detection of potential problems in the analytical system before test results exceed visually apparent control limits.

Although its use requires deeper statistical understanding and more complex calculations, CUSUM is highly effective for long-term monitoring, especially in high-precision testing. By integrating CUSUM into the laboratory's quality control system — as a supplement, not a replacement for Levey-Jennings and Westgard rules — laboratories can increase their vigilance toward trends pointing toward instability and take corrective actions more quickly and accurately.