U∑ ⬚( ()) =
"$% [" −\& −1
This serves as a measure of spread across multiple labs using the average values as a
baseline, and we can use it to further extrapolate precision results across labs. With ) calculated, we then determine the Reproducibility Standard Deviation (SR) using the following formula:
(*) = O())& +[(')& ∗ ` −1 a]
Just like Repeatability Standard Definition, this is the standard deviation of the test results obtained under reproducibility conditions. It also does not account for 95% confidence. Therefore, we multiply SR by 2.8 to calculate reproducibility accounting for 95% confidence.
() = * ∗ 2.8
Like with repeatability, you can repeat this sequence to calculate the reproducibility value of other samples in the set.
Example Calculations Example Calculations
To demonstrate these calculations, we generated a series of random numbers. In these sample calculations, we generated 10 different samples, labelled A through J, and 5 different labs, with 6 trials per lab. The test data for the fi rst sample is shown below, with the calculated average and standard deviation per lab set. Lab # Lab 1
To demonstrate these calculations, we generated a series of random numbers. In these sample calculations, we generated 10 different samples, labelled A through J, and 5 different labs, with 6 trials per lab. The test data for the first sample is shown below, with the calculated average and standard deviation per lab set.
Lab 2 Lab 3 Lab 4
Trial # Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Trial 1 Trial 2
Sample A Lab Average Lab Standard Deviation 87.41667
89.1 87.9 86.6 84.6 88.1 88.2 87.3 85.3 84.3 88.6 85.7 88.1 85.2 83.1 85.2 86.8 88.7 84.8 89.3 89.5
1.596768 References
1. ASTM International. “Standard Practice for Determination of Precision and Bias Data for Use in Test Methods for Petroleum Products, Liquid Fuels, and Lubricants.” ASTM International. 2021. [Online]. Available:
https://www.astm.org/d6300-21.html
2. Lau, Alex. “What Are Repeatability and Reproducibility? Part 1: A D02 Viewpoint for Laboratories.” ASTM Standardization News.
astm.org. March/April 2009.
3. ASTM International. “Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method.” ASTM International. 2022.
86.55 1.703819
The authors sincerely thank Dr. Fred Passman ( an excellent mentor and brilliant scientist) for his suggestions and edits and criticisms provided. He is the president of Biodeterioration Control Associates, Inc. and a very active astm member.
Both Dr.’s Shah and Dr. Passman are also advisors to the student astm club at State Univeristy of New York, Stony brook.
85.63333 1.910672 The authors especially wish to thank 85.15 3.46742
Dr. Alex Lau (guru of astm statistics) for perusing the article and for his invaluable comments. Attending his astm statistics course offered several times a year in various location worlwide is one of the best way to get profi cient in understanding the statistics used and implemented in various
ASTM.METHODS. Alex.
L.is an inspiration in this fi eld ad the authors thank him for his invaluable suggestions
Like with repeatability, you can repeat this sequence to calculate the reproducibility value of other samples in the set.
Again, this value is multiplied by 2.8 to account for normal expectation cutoffs, leaving us with this formula for reproducibility.
Conclusion
ASTM D6300 offers an accurate method to determine both repeatability and reproducibility, which are both invaluable to the reliability and production effi ciency of many procedures and production lines. With the formula outlined in this report, the repeatability and replicability values can be calculated by hand, saving valuable time and money from manufacturing errors and benefi tting the fi eld of petroleum and lubricant testing.
Analytical Instrumentation 11
About the Authors
Dr. Raj Shah is a Director at Koehler Instrument Company in New York, where he has worked for the last 25 plus years. He is an elected Fellow by his peers at IChemE, AOCS, CMI, STLE, AIC, NLGI, INSTMC, Institute of Physics, The Energy Institute and The Royal Society of Chemistry. An ASTM Eagle award recipient, Dr. Shah recently coedited the bestseller, “Fuels and Lubricants handbook”, details of which are available at ASTM’s LongAwaited Fuels and Lubricants Handbook 2nd Edition Now Available
https://bit.ly/3u2e6GY.
The repeatability (r) of Sample A is calculated below:
He earned his doctorate in Chemical Engineering from The Pennsylvania State University and is a Fellow from The Chartered Management Institute, London. Dr. Shah is also a Chartered Scientist with the Science Council, a Chartered Petroleum Engineer with the Energy Institute and a Chartered Engineer with the Engineering council, UK. Dr. Shah was recently granted the honourifi c of “Eminent engineer” with Tau beta Pi, the largest engineering society in the USA. He is on the Advisory board of directors at Farmingdale university (Mechanical Technology), Auburn Univ (Tribology), SUNY, Farmingdale, (Engineering Management) and State university of NY, Stony Brook ( Chemical engineering/ Material Science and engineering). An Adjunct
Professor at the State University of New York, Stony Brook, in the Department of Material Science and Chemical engineering, Raj also has over 680 publications and has been active in the energy industry for over 3 decades. More information on Raj can be found at
https://bit.ly/3QvfaLX
Contact:
rshah@koehlerinstrument.com
The Repeatability of Sample A is roughly equal to 7.101. For repeatability, a lower value is preferred, as numerical measures of variability act as inverse measures of precision. High precision would indicate that repeatability is very low.
The reproducibility (R) of Sample A is calculated below:
Mr. Beau Eng is part of a thriving internship program at Koehler Instrument company in Holtsville and is a student of Chemical and Molecular Engineering at Stony Brook University, Stony Brook, New York where Dr. Shah is on the external advisory board of directors.
Beau Eng
Author Contact Details Dr. Raj Shah, Koehler Instrument Company • Holtsvile, NY11742 USA • Email:
rshah@koehlerinstrument.com • Web:
www.koehlerinstrument.com
READ, SHARE or COMMENTon this article at:
PETRO-ONLINE.COM
The Reproducibility of Sample A is roughly equal to 7.134. Again, reproducibility is a measure of variability, with lower values indicating higher precision.
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