Interleaved Sampling Protocol
Hello Will,
When I introduced in 1984 the concept of "interleaving" samples in "Sampling and Weighing of Bulk Solids, I expected it to become popular because it gives so much information at affordable cost. I didn't realize that it would be reborn as "interleaving" samples before it turned into "interleaved" samples earlier this year. I don't mind as long as it is based on partitioning the set of primary increments into a pair of interleaved primary samples such that one consists of all odd-numbered increments and the other of all even-numbered increments (A- and B-primary samples, test samples and test portions in ISO parlance).
Precision always comes at a price! You are aware that a pair of A- and B-samples gives a single degree of freedom, and that 10-20 pairs give an acceptable degree of precision and reasonably low t-values. If your operator switches buckets diligently, the statistics will be reliable. Human nature being what it is, the statistics are not likely to pass your litmus test. Heath & Sherwood manufactures a mechanical module that routinely collects interleaved samples from a slurry flow.
The first variance term of temporally ordered online data for a single shift gives a degree of precision for the central value that cannot possibly be matched by a pair of interleaved samples. So the central value for online data should fall between the lower and upper limit of the symmetric 95% confidence range for the central value of all A- and B-samples, and not the other way around! This comparison verifies the online analyzer's state of calibration.
A paper titled "Borehole Simulation with Spreadsheet Software" may be of interest to you. I have an Adobe copy of the text but the numerical examples are in Lotus templates. In fact, I did bet on Betamax and Lotus. Nowadays, I have Appendices A and B in Excel format, and I'll email the works if you wish.
Kind regards,
Jan W Merks ■
Interleaving Samples for Float Plant
Hi there sampling and statistics experts, I've got a very basic question for you, and I hope you can help me.
In a research project I'm currently undertaking, part of my task is to attempt to quantify the variance for various measurements and sampling points in a mining/processing operation. Knowledge of the specific elements of variance (i.e. differents stages of sampling, analysis, etc) isn't as important as knowledge of the overall variance for my particular task (which is to use these variances in an overall mass balance for improved metallurgical accounting).
To my question: Is it appropriate to use an "interleaving samples" experiment to determine the variances associated with various float plant streams (feed, intermediate streams, con, tails) that are currently sampled using an on-stream analyzer. Composite samples are collected for each stream every 24 hours partly as a check to the online analysis. I would like to determine the varaince of both the online analyzer readings as well as the composite analysis (which goes to the lab for assay). If interleaving samples is appropriate (and I assume it is), do you have any suggestions as to an appropriate methodology?
If I understand the concept correctly, I simply collect two samples at each point where one is normally collected. So in the case of the composite sample, which is made up of many cuts of slurry throughout the 24 hour period, would it be appropriate to collect every second cut in a separate bucket, so that there are two buckets of sample for each 24 hour period instead of just one? This would only give one degree of freedom for hte calculation, so does this mean that I would have to repeat this for 10-20 days (or more) to get meaningful data? I would think so, but the fact is that doing something like this would mean tending the composite samples all day for many days (switching buckets between cuts, etc.)
Well, that's my question... I would appreciate some feedback. The only info I've read on interleaving samples is from Merks' "Sampling in Mineral Processing" (and I couldn't find Appendices A and B to which the text refers the reader for more information on this topic) and from the ISO 12745-1996 standard (AS 4595-1999). Does anybody have any more useful information/examples?
Thank you very much for your attention,
Will ■