Bias and Variance for Benchmarking Outcomes in Force Measurement

The successful design of any force measurement system, from factory automation to structural monitoring, relies on a critical understanding of the two fundamental error types: bias and variance.

Bias is considered a systematic error that occurs when a predicted value differs from an actual value. Variance is viewed as a random error representing the average distance between data points and the mean.

Understanding these two different types of errors is crucial because, when engineers design systems or products, they often encounter outcomes that various stakeholders prioritize. By finding consensus and using benchmarks for testing, measurable improvements are achieved through accurate measurements before and after benchmarking, which is a key part of the iterative design process for determining the final design.

In the world of load cells, these engineering concepts translate directly into quantifiable specifications that dictate the reliability and precision of the final sensor design. Reminder, check out our Load Cell Performance Starts by Design Webinar Recap for an engineering perspective.

Defining the Errors in Force Measurement

In engineering metrology, the concepts of bias and variance are defined by their relationship to a target true force. 

• Bias is the difference between the average of many measurements and the actual applied force. It indicates a consistent, predictable offset. For example, if a load cell consistently reads 480 pounds of force (lbf) when 500 lbf is actually applied, it has a negative 20 lbf bias. This kind of error is systematic because it shifts the average reading away from the true value.
• Variance is the spread or dispersion of individual measurements around their mean value. It indicates unpredictable fluctuations. If readings for the 500 lbf range are between 495 and 505 lbf, the system shows high variance, reflecting random results and a lack of precision.

Immediate Performance in End-Effector Precision

In immediate operational applications, such as a high-speed assembly line or a robotic end-effector, bias and variance translate directly into critical performance specifications.

Consider a robotic press that must apply a force using a load cell. If the mechanical setup is subtly misaligned and not perfectly perpendicular to the load cell’s axis, a systematic bias is introduced. This force, intended for pure compression, is now slightly applied as a side (shear) load. The resulting readings are tightly clustered, indicating low variance, but consistently below the true applied force. Review Mechanical Installation Load Cell Troubleshooting 101.

This issue is reflected in load cell specifications such as nonlinearity and hysteresis. Non-linearity describes how the bias changes across the operating range, while hysteresis shows a bias that depends on the loading direction, increasing or decreasing load. The engineering solution here is structural. Correcting the mechanical interface to eliminate the parasitic load, thereby shifting the systematic bias back to zero. Review our article, Why Is Load Cell Zero Balance Important to Accuracy?.

The Problem of Variance from Environmental Noise

Now consider a high-speed checkweigher. This system must filter out random noise from motor vibrations, electrical spikes, and package impacts. These environmental factors introduce rapid, unpredictable fluctuations in the load cell’s output, resulting in high variance. While the average weight might be correct, a low bias in individual readings makes them unreliable, leading to improper rejection rates.

The key load cell specification for random error is non-repeatability. A sensor with poor repeatability will exhibit wide scatter in output values under identical loading conditions. The engineering solution involves mitigating random factors: increasing mechanical damping, implementing higher-quality electrical shielding, and using digital signal processing (filtering) to reduce noise, thereby tightening the data distribution and improving precision.

Long-Term Stability in Structural Health Monitoring

The distinction between bias and variance is even more crucial in applications requiring long-term stability, such as structural health monitoring (SHM) of bridges, dams, or large industrial structures. Here, the errors manifest over time as creep and zero drift.

When a load cell is subjected to a constant static force over an extended period, the sensing element’s material slowly deforms. This phenomenon, known as creep, causes the load cell’s output signal to gradually change over time, even though the actual physical load remains constant.

Creep is a time-dependent bias. It systematically shifts the reading away from the initial actual value. The relevant specification, creep, measures the sensor’s material quality and stability. Engineers designing for SHM must specify load cells with minimal creep to ensure the measured data remains systematically accurate for years, often complementing the material choice with algorithms that compensate for the load cell’s predicted rheological behavior.

Zero drift is the fluctuation in the sensor’s output over time when no load (or only the tare load) is present. In permanent installations, zero drift is often driven by environmental variations, primarily temperature. Temperature changes can cause the load cell’s strain gages and surrounding compensating circuitry to shift their electrical resistance.

While part of this can be a systematic temperature effect on zero (a form of bias), rapid, random temperature swings and moisture changes introduce variance into the baseline reading. Fighting zero drift requires rigorous environmental hardening (high IP ratings for moisture) and meticulous thermal compensation built into the load cell’s design, ensuring that the sensor’s baseline remains stable against unpredictable environmental variables.

Diagnostic Framework to Bias and Variance

The most valuable contribution of analyzing bias and variance is the diagnostic framework it provides for design improvement.

• If the system is inaccurate but precise (low variance, high bias), the solution is systemic and correctable. It is time to fix the mechanical alignment, adjust the scaling factor, or apply a formal calibration map.
• If the system is accurate but imprecise (low bias, high variance), the solution is structural and noise-related: introduce damping, improve shielding, or choose a load cell with a superior non-repeatability specification.

By clearly separating systematic errors from random errors, engineers can select appropriate load cell specifications and allocate resources, ensuring measurable and successful improvements in the reliability and fidelity of products and systems. Learn more about these vital specifications in our recorded Demystifying Specifications Webinar excerpt below.