Standard deviation reproducibility

At 30% conversion a replicate analysis showed that composition could be determined with 1.4% reproducibility (standard deviation as a % of mean) and conversion with -h 2.1%. A duplicate at 52% conversion showed a relative error ( fference/mean) of 1.7% and 2.7% respectively. Between 30 and 80% conversion, although no gel effe t is evident in the data the polymer/monomer mkture becomes sticky and difficult to handle. Somewhat beyond 80% conversion the n-butyl meth rylate content for these compositions becomes too small to be detected with the procedure developed. Additional optimization of concentration injected and det tor utilized is required for very high conversions. 

The closeness of agreement between independent results obtained with the same method on identical test material but under different conditions (different operators, different apparatus, different laboratories, and/or after different intervals of time). The measure of reproducibility is the standard deviation qualified with the term reproducibility as reproducibility standard deviation. In some contexts reproducibility may be defined as the value below which the absolute difference between two single test results on identical material obtained under the above conditions may be expected to lie with a specified probability. Note that a complete statement of reproducibility requires specification of the experimental conditions which differ. 

It is a well-known fact that the precision in trace analysis decreases with diminishing concentration in a similar way as it does with decreasing sample weight (Sect. 2.1). The dependency of the repeatability and reproducibility standard deviation on the concentration of analytes has been investigated systematically at first by Horwitz et al. [1980] on the basis of thousands of pieces of interlaboratory data (mostly from food analysis). The result of the study has been represented in form of the well-known Horwitz trumpet which is represented in Fig. 7.3. 

The precision limits r and R are given by equations (4.3a) and (4.3b), respectively, where tv>a is the Student /-value for v degrees of freedom and a corresponds to the stated probability, sr is the repeatability standard deviation and Sr is the reproducibility standard deviation calculated from (v + 1) results ... 

If the analytical method used by participants in the proficiency testing round has been validated by means of a formal collaborative trial, then the repeatability and reproducibility data from the trial can be used. The repeatability standard deviation gives an estimate of the expected variation in replicate results obtained in a single laboratory over a short period of time (with each result produced by the same analyst). The reproducibility standard deviation gives an estimate of the expected variation in replicate results obtained in different laboratories (see Chapter 4, Section 4.3.3 for further explanation of these terms). 

If or represents the reproducibility standard deviation and ar represents the repeatability standard deviation, the between-laboratory standard deviation, CTl, is calculated from the following ... 

Reproducibility Standard Deviation Reproducibility Limit R Ruggedness Test Selectivity... 

If we take the reproducibility standard deviation from a standard we have to prove that we are able to perform in accordance with the standard, i.e. that we have no reasonable bias and the repeatability of our measurement is close to that described in the standard. If this is the case, our expanded uncertainty U is twice the reproducibility standard deviation. 

Reproducibility standard deviation from a standard Example - Mercury according to EN 1483... 

Reproducibility Standard Deviation from a PT Example - Mercury in a Univ. Stuttgart PT... 

We have seen two different approaches to estimate the measurement uncertainty. One was using data from control charts, CRM analysis, PT results and/or recoveiy tests and sometimes maybe also experience of the analyst, the other was just using the reproducibility standard deviations from interlaboratory tests. In most cases the second method delivers higher estimates. 

The top-down approach is often used when there are method validation data from properly conducted interlaboratory studies, and when the laboratory using reproducibility as the measurement uncertainty can demonstrate that such data are applicable to its operations. Chapter 5 describes these types of studies in greater detail. In assigning the reproducibility standard deviation, sR, to the measurement uncertainty from method validation of a standard method, it is assumed that usual laboratory variables (mass, volume, temperature, times, pH) are within normal limits (e.g., 2°C for temperature, 5% for timing of steps, 0.05 for pH). Clause 5.4.6.2 in ISO/ 17025 (ISO/IEC 2005) reads, In those cases where a well-recognized test method specifies limits to the values of the major sources of uncertainty of measurement and specifies the form of presentation of the calculated results, the laboratory is considered to have satisfied this clause by following the test method and reporting instructions. ... 

As reproducibility standard deviation from interlaboratory method validation studies has been suggested as a basis for the estimation of measurement uncertainty if it is known sR can be compared with a GUM estimate. It may be that with good bias correction, the estimate may be less than the reproducibility, which tends to average out all systematic effects including ones not relevant to the present measurement. Another touchstone is the Horwitz relation discussed in section 6.5.4. A rule of thumb is that the reproducibility of a method (and therefore the estimated measurement uncertainty) should fall well within a factor of two of the Horwitz value. 

Typical moisture content results for soybean samples are shown in Table Al.3.1. Three samples were prepared and each was measured three times in the same minispec analyzer. The NMR percentage moisture was found to be very reproducible (standard deviation for three measurements was typically better than 0.03) and agreement of NMR with the reference method was typically 0.15% moisture or better. 

The reproducibility standard deviation is typically two to three times as large as that for repeatability. Precision decreases with a decrease in concentration. This dependence has been expressed as RSD = 2° 0 5 exp 108 C), where RSD is expressed as a percentage and C is the concentration of the analyte [38]. For the concentration ranges typically found in pharmaceutical dosage forms (1—10 3), the RSD under conditions of repeatability should be less than 1.0%, and less than 2.0% under conditions of reproducibility [21]. These are similiar to the 1.5% recommendation made for RSD of system repeatability after analyzing a standard solution six times [35]. For method repeatability, which includes sample pretreatment, six replicate assays are made with a representative sample. A RSD no greater than 2% should be obtained. 

The factor 2I/Z is based on the fact that r and R are related to the difference between two measurement results. For distributions which are approximately normal and in the case of not too small a number of measurements, the factor f does not vary much from 2 and one can use the approximate value of 2.8 for f-2I/2. Because in practice the true repeatability and reproducibility standard deviations are not known, they are replaced with estimated values sr and sR from the inter-laboratory study and one obtains then ... 

By preference, an RM is analyzed under reproducibility conditions. Since the reproducibility standard deviation is not known in a single laboratory validation... 

According to ISO 5725 [7] the total mean X, the repeat standard deviation Sr, the between laboratory standard deviation 5 and the reproduce standard deviation Sr were determined. The relation is given by... 

The repeat standard deviation describes the scattering of the measuring results under repeat conditions (same laboratory, same equipment, same staff). Whereas, the between laboratory standard deviation expresses the differences between the laboratories. The reproduce standard deviation contains the two above mentioned scatter components. It is the deviation under reproduce conditions (different laboratories, different equipment, different staff). To get a unique repeat standard deviation it must be assumed that it does not vary (significantly) with the laboratory. For this reason the standard recommends a statistical outlier test (Cochran test) for the individual standard deviations of the laboratories. Furthermore, the individual laboratory means are a subject to an outlier test (Grubbs test). 

The mercury intrusion measurements were performed with a good precision within each individual laboratory (repeat standard deviation) as well as in different laboratories (reproduce standard deviation) for all mortar samples Bl, Gl, B2, G2, B3, G3. The reproduce standard deviations are 1.5 to 2 times higher than the repeat standard deviations. In particular cases,... 

The repeat and the reproduce standard deviations of the total pore volume and the median pore radius are only slightly affected by different moisture contents of the samples (Tab-... 

The results of B3 and G3 dried by the laboratories by a method of their own choice happen to fall in between that of the other two samples. They were averaged from samples, which were dried by 13 different procedures. As expected, the reproduce standard deviations are relatively high. But it is remarkable that they lie below the value of the wet sample B2. Every laboratory treated B3 and G3 by their own method very well so that proper dried samples with low moisture contents were produced. Thus measuring samples of almost similar state could be measured relatively precisely. 

---