The Background of the Question and a Suggested Approach

Consider that, e.g., a tensile strength test has been performed with, say, three replicate specimens per specimen type on an inhomogeneous or anisotropic material like wood. Why do the strength property determinations typically not consider the number of collected data points? As a simplification, imagine, e.g., that replicate specimen 1 fails at 1.0 % strain with 500 collected data points, replicate 2 at 1.5 % strain with 750 data points and replicate 3 at 2.0 % strain with 1 000 data points. For the sake of argument, let us assume that the replicates with a lower strain are not defective specimens, i.e., they are accounted for in natural variation(s). Would it not make sense to use the ratio of the collected data points per replicate specimen (i.e., the number of data points a given replicate specimen has divided by the total number of data points for all replicates of a given specimen type combined) as a weighing factor to potentially calculate more realistic results? Does this make sense if one were to, e.g., plot an averaged stress-strain curve that considers all replicates by combining them into one plot for a given specimen type?

Questioning of the Weighing

Does this weighing approach introduce bias and a significant error(s) in the results by emphasising the measurements with a higher number of data points? For example, suppose the idea is to average all repeat specimens to describe the mechanical properties of a given specimen type. In that case, the issue is that the number of collected data points can vary significantly. Therefore, the repeat specimen with a higher number of data points is emphasised in the weighted averaged results. Then again, if no weighing is executed, then, e.g., there are 500 more data points between replicates 1 and 3 in the above hypothetical situation, i.e., the averaging is still biased since there is a 500 data point difference in the strain and other load data and, e.g., replicate 3 has some data points that neither of the preceding replicates has. Is the “answer” such that we assume a similar type of behaviour even when the recorded data vary, i.e., the trends of the stress-strain curves should be the same even if the specimens fail at different loads, strains, and times?

Further Questions and Suggestions

If this data point based weighing of the average mechanical properties is by its very nature an incorrect approach, should at least the number of collected data points or time taken in the test per replicate be reported to give a more realistic understanding of the research results? Furthermore, when averaging the results from repeat specimens, the assumption is that the elapsed times in the recorded data match the applied load(s). However, this is never the case with repeat specimens; matching the data meticulously as an exact function of time is tedious and time-consuming. So, instead of just weighing the data, should the data be somehow normalised concerning the elapsed time of the test in question? Consider that the overall strength of a given material might, e.g., have contributions from only one repeat specimen that simply took much longer to fail, as is the case in the above hypothetical example.