As laboratories scale their operations to include multiple instruments, statistical process control strategies must evolve. The combined Z-chart offers a highly flexible solution.

By John Carson and Polona Carson

May 01, 2026

Introduction to Statistical Process Control 

Laboratories must ensure their testing processes consistently produce reliable and accurate results. To help achieve this, laboratories use control charts to monitor testing process targets and variation. The committee on quality and statistics (E11) provides guidance on establishing these programs in the standard practice for use of control charts in statistical process control (E2587) and the standard practice for quality control of routine testing in a laboratory (E3500).

Every laboratory testing process experiences natural, expected error variation. This is known as common cause or inherent variability. When a process operates solely under the influence of inherent variation, it is considered to be in a predictable state of statistical control. However, when unexpected events or failures occur, they introduce “special cause” or “assignable cause” variations. These special causes manifest as unexpected spikes, sudden shifts, or trends in the analytical testing output. The primary purpose of implementing a control chart is to signal the presence of these special causes so laboratory personnel can detect, investigate, identify, and eliminate them.

Table 1

The Challenge of Multiple Instruments 

As laboratory testing volumes increase, facilities frequently expand their overall capacity by adding multiple instruments to support their most popular analytical methods. This expansion introduces a complex quality control challenge. Operators must manage statistical process control across multiple instruments via testing a single control material using a common method. In addition, many analytical methods, especially environmental and clinical methods, are multianalyte – that is, testing simultaneously for multiple measurands in each
test sample.

Managing statistical process control for these scenarios requires charting strategies that go beyond basic, traditional methods. Hotelling’s control charts offer a solution for monitoring a method using a multianalyte control material on a single instrument. Each analyte is a dimension, and all measurements are essentially made simultaneously. However, this approach cannot work for multiple instruments, even measuring the same control material, because the measurements cannot be made simultaneously, and instruments can be added or removed from testing at any time for a variety of reasons. In addition, such control charts are more demanding for analysts to interpret.

Standardizing Data with Combined Z-Charts 

To overcome these limitations, laboratories can use Z-charts. The fundamental principle behind a Z-chart is statistical standardization. To create this chart, the specific mean and standard deviation derived from individual instrument/analyte charts of control materials are used to convert laboratory measurement results into standardized Z-scores, which have a mean of approximately zero and a standard deviation of one. Thus, Z-scores derived from completely different sources can be plotted together on the same control chart. This combined plotting can be executed whenever there is a useful, underlying logic that justifies grouping these specific sources together, such as monitoring a group of instruments testing the same analyte under the same analytical method.

The Westgard Quality Control framework, used in clinical laboratories, also uses Z-charts to combine information from multiple individual control charts. It is discussed further in the following.

Investigating Signals and Understanding Blind Spots 

When a combined Z-chart generates a signal —indicating an out-of-control condition — laboratory personnel must investigate the root cause in a very specific manner, as often specified in a laboratory’s “Out-of-Control Action Plan.” Technicians and engineers must clearly understand the specific types of nonconformances that a combined Z-chart is sensitive to, as well as the types of problems it is likely to miss.

A signal on a combined Z-chart typically points to a systemic or broad-based issue that affects the grouped sources simultaneously. For example, if a shared control material degrades, all instruments utilizing that material will show a shifted Z-score. Similarly, the chart is highly sensitive to issues related to the training or supervision of analysts, systemic problems with routine laboratory maintenance, and contaminated or expired shared reagents. Broader issues with the laboratory environment, such as substantial fluctuations in ambient temperature, may also trigger a combined Z-chart alarm. While the combined Z-chart is excellent for detecting these widespread systemic issues, it can also detect a large failure occurring within a single instrument.

Despite its high utility for monitoring systemic laboratory health, the combined Z-chart is not a perfect diagnostic tool. A combined Z-chart is inherently blind to small changes in the response of an individual instrument. A minor drift in just one instrument will likely be masked by the stable data generated by the rest of the grouped instruments. Therefore, laboratories must continue to use control charts for individual instruments alongside combined charts to catch subtle, instrument-specific deviations.

Supplemental Rules 

Standard control charts use Shewhart Limits, placing the upper and lower control limits at three standard deviations away from the center line. A single point falling outside these limits is an immediate signal of a process upset. To detect smaller, subtle process shifts before they breach these absolute three-sigma limits, laboratories sometimes apply supplemental pattern rules (multi-rules) involving two or more successive chart values. The Western Electric rules and derivatives, like the Westgard Rules, can increase sensitivity to small changes but at the cost of higher false signal rates. E2587 warns that when multiple pattern rules are applied together, they significantly inflate the risk of a false positive signal, indicating a lack of statistical control when only inherent variation is present in the process.

Westgard acknowledges this and proposes that “a practical design objective … would be only a 5% or less chance or false rejection.”¹ While this false signal error rate is apparently acceptable in clinical chemistry, it is not likely to be acceptable in manufacturing, industry, or analytical chemistry, especially not in environmental or petroleum laboratories, where throughput and cost control of analytical work is important. Interestingly, Westgard himself points out that combined Shewhart-CUSUM charts outperform multi-rule approaches.^2,3 Lucas shows the same, and Lucas and Saccucci demonstrate that Shewhart-EWMA combination charts also outperform multi-rule charts. ^4,5

Conclusion

As laboratories scale their operations to include multiple instruments and multiple control materials, statistical process control strategies must evolve. The combined Z-chart offers a highly flexible solution, especially when used in a Shewhart-CUSUM or Shewhart-EWMA configuration. ●

References

1.Westgard training web site. https://westgard.com/lessons/basic-qc-practices/lesson15full.html.

2.Westgard, J. O., Groth, T., Aronsson, T., & de Verdier, C. H. (1977a). Combined Shewhart-CUSUM control chart for improved quality control in clinical chemistry. Clinical Chemistry, 23(10), 1881–1887. 

3.Westgard J.O., Groth T, Aronsson T, Falk H, deVerdier C-H. (1977b) Performance characteristics of rules for internal quality control: Probabilities for false rejection and error detection. Clinical Chemistry, 23,1857-67.

4.Lucas, J. M. (1982). Combined Shewhart-CUSUM quality control schemes. Journal of Quality Technology, 14(2), 51–59. https://doi.org/10.1080/00224065.1982.11978791.

5.Lucas, J. M., & Saccucci, M. S. (1990). Exponentially weighted moving average control schemes: Properties and enhancements. Technometrics, 32(1), 1–12. https://doi.org/10.1080/00401706.1990.10484583.

Recommended Articles

Preservation of the Military Standards for Acceptance Sampling

Determining Useful Models

A History of the Subcommittee on Statistical Quality Control