Accuracy of glass test results

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How accurate are glass optical & thermal test results?

All customers are concerned of the measurement accuracy in glass optical & thermal property testing. We are also working hard to improve our measurement accuracy consistently. This article aims to explain the following in glass optical & thermal property testing:

  1. Typical intra-lab and inter-lab accuracies
  2. Factors influencing measurement accuracy
  3. Estimated measurement uncertainties

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Typical intra-lab and inter-lab accuracies

In the context of this article:

  • Intra-lab accuracy means the result variation when the same sample is repeatedly measured by the same lab. It indicates the result repeatability in a lab
  • Inter-lab accuracy means the result variation when samples of the same product are measured by different labs. It indicates the overall result accuracy of a lab, when its results are compared with one or a group of competent labs.

Both intra-lab accuracy and inter-lab accuracy are not rigorous metrological terms, but they are useful in measurement result assessment:

  • When a group of samples are measured by the same lab, the intra-lab accuracy should be considered in assessing the results;
  • When comparing results measured by different labs, the inter-lab accuracy should be considered in assessing the results.

Measurement uncertainty is a rigorous metrological term. Refer to the estimated uncertainties section for details.

Typical intra-lab accuracy: an example

A retained sample (a laminated glass without coating) was repeatedly measured 50 times between 12/2015 and 07/2020 in our lab. Shown below are the result variations of two results, i.e. visible light transmittance and solar energy transmittance.

Intra-lab accuracy of visible light transmittance results
Intra-lab accuracy of solar energy transmittance results

It is clear that, when the same sample was repeatedly measured in our lab over a few years, the result variation is very small. In the two examples presented above, the variation of the visible light transmittance is within ±0.002 (±0.2%) from the average; the variation of the solar energy transmittance is within ±0.001 (±0.1%) from the average.

We also conduct our quality assurance tests every quarter and the reports are published in our quarterly newsletters (link). It is also clear that the typical result variation is ±0.002 (±0.2%) for all optical results.

Typical inter-lab accuracy: two examples

For inter-lab comparisons, it is often not possible for different labs to test the same sample. Sample-to-sample variation becomes an influential factor in inter-lab comparisons. Two examples are presented here:

  • Example 1: inter-lab accuracy on samples with small sample-to-sample variation
  • Example 2: inter-lab accuracy on samples with moderate sample-to-sample variation

Both examples are from the inter-lab comparison organized by LBNL in 2015. 36 labs participated in this comparison.

In example 1, the sample is a clear glass without coating, with small sample-to-sample variation (less than ±0.005 or ±0.5%). Shown below are the result comparisons in terms of the visible light transmittance and solar energy transmittance results.

Inter-lab accuracy on samples with small sample-to-sample variation

In example 2, the sample is a laminated glass without coating, with moderate sample-to-sample variation (less than ±0.010 or ±1.0%).  Shown below are the result comparisons.

Inter-lab accuracy on samples with small sample-to-sample variation

It is evident that the inter-lab accuracy is strongly dependent on the sample-to-sample variation. In example 1, the inter-lab accuracy is better than ±0.005 (±0.5%), whereas it increases to better than ±0.010 (±1.0%). This increase is coincident with the sample-to-sample variation increase.

It is also obvious that the inter-lab accuracy is worse than the intra-lab accuracy, due to the additional errors introduced by different instruments, operators, procedures, etc.

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Factors influencing measurement accuracy

The measurement accuracy is dependent on not only technical factors (e.g. instruments), but also management factors (e.g. lab practices).

Listed below are the 3 key technical factors influencing the measurement accuracy:

  1. Instrument random variation: instrument readings fluctuate in certain range inherently.
  2. Instrument drift: instrument performance drifts slowly and the drifts cause small changes to instrument readings. Instrument drift can be compensated by regular instrument calibration.
  3. Instrument calibration error: calibration can compensate errors caused by instrument drift, but calibration itself is not perfect and is with certain inherent errors.

The errors caused by the technical factors can be effectively minimized with a robust lab quality system.

The measurement accuracy is also influenced by test samples:

  1. Sample non-uniformity: for non-uniform samples, the results are dependent on the area sampled in each measurement
  2. Sample-to-sample variation: as explained earlier, the inter-lab accuracy is highly dependent on the sample-to-sample variation.

Most test samples are with good uniformity, but it is not easy to control sample-to-sample variation. When assessing lab test results, the errors caused by sample-to-sample variation need to be always considered.

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Estimated measurement uncertainties

As a general guideline, the following estimated measurement uncertainties are applicable for glass optical & thermal property testing in our lab:

  • ±0.010 for all optical & thermal properties, except U-value
  • ±0.10 W/(m2K) for U-value

The actual estimated uncertainties are dependent on the glass type and they are stated in the test reports accordingly. Shown below is an example:

Statement of the estimated uncertainties in a test report

Measurement uncertainty is a rigorous metrological terms, replacing other terms such as “accuracy” or “error”. A good explanation about measurement uncertainty is available here. The measurement uncertainties are estimated based on well-defined guidelines (e.g. SAC Technical Guide 1 or GUM).

When the shading coefficient (SC) of a glass is reported as 0.300, with an estimated uncertainty of ±0.015, it means for the SC of the glass sample:

  • The best estimate by our lab is 0.300.
  • We do not know the true value, but there is 95% probability that the true value of SC lies between 0.285 and 0.315 (0.300 ± 0.015).

The estimated measurement uncertainties are larger than the typical intra-lab and inter-lab accuracies, because the measurement uncertainties are estimated in a conservative manner with the worst case scenarios assumed. Typically, we do not encounter such worst cases and the actual measurement uncertainties are smaller.

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How often are the instruments in OTM calibrated?

There are two purposes for instrument calibration:

  • Performance verification: to give confidence that the instrument is fit for use
  • Performance adjustment: to compensate changes due to instrument drift

With the two purposes in mind, instrument calibration is more than a formality (e.g. a calibration certificate), but a necessity for high measurement accuracy.

Our instruments used in glass optical & thermal property testing are calibrated regularly, with the calibration frequencies justified according to the risks and magnitudes of possible performance drifts. The relevant guidelines in the instrument manual and test standards are observed too.

In practice, some instruments are calibrated at high frequency, such as re-calibration after every 5 consecutive operations, whereas some instruments are only calibrated every 2 years.

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Can the measurement accuracy be improved by re-testing a sample multiple times?

As most glass samples are with good uniformity, re-testing a sample multiple times only results in a marginal variation of the optical results, e.g. ±0.001 (±0.1%). This variation is negligible for most applications and, therefore, re-testing a sample multiple times does not improve the measurement accuracy noticeably.

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What are the typical glass sample-to-sample variations?

Glass production variation is inevitable, particularly when the glasses are manufactured in different lots or even different plants.

Glass color difference is a typical result of glass production variation. Sometimes, the glass color differences are significant enough to be distinguished by human eyes.

Many glass manufacturers declare a production variation of ±0.03 for optical & thermal performance data (excluding U-value) in their product data sheet.

Based on our experiences, the typical glass sample-to-sample variations are between ±0.01 and ±0.02 (for all optical & thermal properties, except U-value):

  • Glasses with hard low-e coating or window films are with the largest sample-to-sample variations
  • Glasses with soft low-e coating are with moderate sample-to-sample variations, and result variations in the visible light spectrum (380 nm -780 nm) are very common
  • Laminated glasses are with moderate sample-to-sample variations, caused by interlayer thickness variation (e.g. the interlayer is thinner at one corner or one side).
  • Uncoated glasses are with small sample-to-sample variations

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What is the allowed tolerance in glass test result assessment?

It is common and inevitable that the glass test results are slightly off from the manufacturer’s specifications due to measurement uncertainties and sample-to-sample variation.

We often encounter the scenario that the requirement is SC (shading coefficient) < 0.3, but the number reported by our lab is slightly higher, e.g. SC = 0.302.

If the 0.002 difference is considered small, how about SC = 0.308, SC = 0.314 or SC = 0.325? Are they considered small too? Is there an allowed tolerance for test results slightly higher to pass?

Below are our comments on this (critical) issue:

  • There is no allowed tolerance specified in government regulations or international standards at this moment. Private negotiations between the relevant parties are required.
  • We recommend an allowed tolerance of ±0.02 for shading coefficient (SC), as ±0.02 is sufficiently stringent and still practical based on our experiences.
    • This ±0.02 tolerance of SC is our recommendation only and it is up to the relevant parties to decide if it is acceptable
  • If no tolerance is allowed, some tolerance needs to be budgeted in glass selection
    • Example: if the requirement is SC < 0.3, one may select glasses with slightly smaller SC (e.g. SC = 0.29 or SC =0.28) to meet this SC < 0.3 requirement.

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Why are the lab test results different from the manufacturer’s specifications?

When our lab test results are compared with manufacturer’s specifications, it is a type of inter-lab comparison and some differences are inevitable. There are 3 reasons for the result differences:

  • The measurement accuracy by our lab
  • The specification accuracy by the manufacturer
  • The sample-to-sample variation between the lab test and the specification test

We will have a separate article on this topic in the future. We will also propose a few practical advices in that article.

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