# Lower Limit Factor: Improve Calibration Accuracy for Load Cells and Other Force Measurement Equipment

## Lower Limit Factor: Improve Calibration Accuracy for Load Cells and Other Force Measurement Equipment

LLF, or Lower Limit Factor, is a statistical estimate of the error in forces computed from the calibration equation of a force-measuring instrument when the instrument is calibrated following ASTM E74 standard practice for calibration and verification for force-measuring instruments.

The LLF is important because it provides a measure of the error in forces computed from the calibration equation of a force-measuring instrument. The LLF is to set and maintain test accuracy ratios where the first point in the Class A verified range of forces shall not exceed 0.25 %, and the first point in the Class AA verified range of forces shall not exceed 0.05 %.

LLF is calculated as 2.4 times the standard deviation. If the calculated LLF is less than the instrument resolution, the LLF is then defined as that value equal to the resolution (Section 8.5 of the ASTM E74-18 Standard). It is expressed in force units, using the average ratio of force to deflection from the calibration data.

This limit of 2.4 standard deviations was determined empirically from an analysis of a large number of force-measuring instrument calibrations. Per section 7.1.2 of the ASTM E74-18A standard, “A statistical estimate, called the lower limit factor, LLF, is derived from the calculated standard deviation and represents the width of the band of these deviations about the basic curve with a probability of approximately 99 %.”

In the context of load cell calibration, the Lower Limit Factor often represents a large component of measurement uncertainty known as the reproducibility condition of the measurement. Though it also includes the deviation from the interpolation equation, the LLF could be said to represent the “expected performance” of the force-measuring instrument when used under the same conditions at which it was calibrated.

The contributions due to other uncertainty components must be included in an uncertainty budget. Meaning using the device under different conditions such as equipment that may not be as plumb, level, square or rigid than what was used for calibration, may impact the results. Using the force-measuring device under different environmental conditions, will impact the measurement uncertainty. Stability from one calibration to the next, the uncertainty of the standard used to calibrate the force-measuring device, and so on will impact the measurement uncertainty.

It is important to note the LLF is only one source of measurement uncertainty. For more information on calculating measurement uncertainty, we recommend using our Excel Spreadsheet and following the A2LA guidance document G126.

If the ASTM E74 standard is followed, the calculated LLF is used with the proper multiplier and conditions being met to determine the usable range, maintaining the ratios required by the standard, as shown below.

The first tier is that of using deadweight primary standards. These standards must have a measurement uncertainty of better than 0.005 % to calibrate a force-measuring instrument to use as a Secondary Standard. Morehouse uses deadweight primary standards up to 120,000 lbf known to be within better than 0.0025 % of applied force; thus, we can assign a Class AA verified range of forces for any force-measuring instrument we calibrate up to 120,000 lbf.

The second tier is that of using Secondary Standards that were calibrated by primary standards.

The lowest point in the Class AA verified range of forces is calculated by multiplying 2000 times the LLF. If the LLF is 1 lbf, the first point in the verified range of forces will be 1 x 2000 or 2000 if we divide 1/2000, 0.0005, converted to a percentage of 0.05 %.

Note: Other ASTM Standards such as ASTM E10 & E18 reference the ASTM E74 standard and require the force-measuring device to be calibrated using deadweight primary standards to establish a Class AA verified range of forces.

Morehouse uses custom load cells standards up to 2,250,000 lbf known to be within better than 0.05 % of applied force; thus, we can assign a Class A verified range of forces for any force-measuring instrument we calibrate up to 2,225,000 lbf.

The lowest point in the Class A verified range of forces is calculated by multiplying 400 times the LLF. If the LLF is 1 lbf, the first point in the verified range of forces will be 1 x 400 or 400 if we divide 1/400, 0.0025, converted to a percentage of 0.25 %.

The last tier is the testing machine that is typically calibrated using ASTM E4 and requires a force-measuring device to have a Class A verified range of forces. The concept is quite simple in how the LLF is used to set the appropriate accuracy ratios contained in the ASTM E74 standard to control risk.

If you are interested in how the LLF is calculated, we tackled how to calculate calibration and measurement capability using the ASTM Lower Limit Factor (LLF) in a blog earlier this year. Read it here:  https://mhforce.com/astm-lower-limit-factor-llf/.

Morehouse Instrument Company can give guidance on calculating your CMC per point.   A professional consultant should be contacted if you need assistance figuring out CMC or what to report.   We offer training focusing on measurement uncertainty and an independent consultant twice or thrice yearly.

For more insights into force and torque calibration, metrology, and load cell reliability, explore our comprehensive blog at https://mhforce.com/blog/.

We believe in changing how people think about force and torque calibration in everything we do. This includes setting expectations on load cell reliability and challenging the "just calibrate it" mentality by educating our customers on what matters and what causes significant errors.

We focus on reducing these errors and making our products simple and user-friendly. This means your instruments will pass calibration more often and produce more precise measurements, giving you the confidence to focus on your business.

Companies around the globe rely on Morehouse for accuracy and speed. Our measurement uncertainties are 10-50 times lower than the competition. We turn around your equipment in 7-10 business days so you can return to work quickly, saving you money.

When you choose Morehouse, you're not just paying for a calibration service or a load cell. You're investing in peace of mind, knowing your equipment is calibrated accurately and on time.

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