Correctly understanding the concepts of repeatability and reproducibility

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Repeatability and reproducibility are both used to evaluate the precision of analytical results. Most people do not make a strict distinction, and some literature often uses them interchangeably. However, their practical meanings are different. The concepts of repeatability and reproducibility are broad in scope and have a wide range of applications. Reproducibility has a limited meaning and is generally used for “phenomena”. I. Repeatability (r) Qualitative definition: The degree of consistency among a series of results obtained using the same method, with the same test material, under identical conditions. The same conditions refer to the same operator, the same equipment, the same laboratory, and a short time interval. 　　Quantitative definition: A value such that, under the aforementioned conditions, the absolute difference between the results of two experiments is below this value with a certain specified probability. Unless otherwise specified, the generally assigned probability is 0.95. 　　(Repeatability is the maximum difference between the results of two separate tests on the same sample, conducted under normal and proper operating conditions by the same operator in the same laboratory using the same instrument over a short period of time, at a 95% probability level.) ) II. Reproducibility (R) Qualitative definition: The degree of consistency among individual results obtained under different conditions, using the same method and with the same test material. Different conditions refer to different operators, different laboratories, and different or the same times. 　　Quantitative definition: A value such that, for the same test material and using the same method, under the aforementioned different conditions, the absolute difference between two test results has a probability of being lower than this value. Unless otherwise specified, the generally assigned probability is 0.95. 　　(Reproducibility is the maximum difference between the results of two independent tests conducted on the same sample by two different operators in different laboratories, under normal and proper operating conditions, with a 95% probability level.) Three concepts related to precision are commonly found in foreign literature: 1. Replicability: the relative standard deviation among multiple parallel tests performed on the same sample in the same laboratory, using the same analyst and analysis method; 2. Repeatability: the relative standard deviation among repeated measurements of the same sample taken by the same analyst in the same laboratory over a short period of time, using the same analysis method; 3. Reproducibility: the relative standard deviation among measurements of the same sample taken by different analysts in different laboratories, using the same analysis method. 　　In my opinion, in our country it is common to confuse parallelism with repeatability. As for the difference between these three concepts, parallelism refers to the coefficient of variation among parallel samples created by adding samples; repeatability is the coefficient of variation among repeated measurements taken of the same sample at different times; reproducibility, on the other hand, is quite straightforward – it refers to the coefficient of variation among results obtained from different laboratories. 　　Operator 1: 29.5; 28.0; 28.3; 29.3; 28.8; 29.6; 28.8; 28.6; 27.9; 28.0 Operator 2: 28.6; 28.1; 29.7; 27.4; 27.5; 28.4; 27.0; 28.4; 28.2; 27.7 Operator 3: 26.9; 28.1; 28.1; 28.2; 29.4; 29.2; 27.0; 26.0; 26.5; 27.9 For the data above, if Operators 1, 2, and 3 are from different laboratories, the average of the 10 measurement values for each operator is calculated, and then the relative standard deviation is determined for each average; this represents “reproducibility”. If they are all from the same laboratory, I believe that the relative standard deviation among these three operators indicates the precision within that laboratory, while the relative standard deviation of the 10 data values for each individual represents “parallelism” or “repeatability”.