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September 2020 / 19 in the final data's accuracy. In some cases, we may want more than 20 samples. With more samples, there's less sampling variation in the final data. The correct sample size for the acetaminophen tablet is the amount of powder needed to make one tablet, which is about 0.5 grams. Grabbing an individual sample that small is difficult, so a larger sample can be taken, say 5 grams, and a 0.5-gram sample can be withdrawn from the larger sample using a sam- ple splitting method. Sample timing should be ran- dom. If the mixer takes 2 minutes to discharge and we want 20 sam- ples, then we would expect to take a sample every 6 seconds. Yet we don't want to grab the samples in such an ordered way. If segregation is going to occur during discharge, it will happen at the beginning and end of the discharge period. So, it would be better to take 5 samples in the first 10 seconds of discharge and 5 samples very near the end of the discharge sequence. The remaining 10 samples can be taken some- what more evenly throughout the remaining 100 seconds of discharge. Even with those middle sam- ples, some randomness is preferred. They shouldn't be taken exactly every 10 seconds. Mixers can some- times cause a slight segregation periodicity (slightly segregating at regular intervals) during discharge. If the tested mixer has a 10-second segregation interval and samples are taken every 10 seconds, the samples would mask the period- icity of the mixer. So, over the 100 seconds, one sample might be taken 4-6 seconds after the previous sam- ple, the following sample might be taken 14 seconds later, and so on. The randomness will help uncover any segregation intervals that might exist. Now that we've got the sam- ples for one blend time, we have over running just one batch and taking samples from that batch at various times using a sample thief. A note about sample thieves. A sample thief is essentially a hol- low tube within a hollow tube; it's lowered into a material bed, then twisted to expose an opening in the tubes. Material enters the hole, the tubes are twisted to close the open- ing, and the thief is removed from the material bed. Figure 2 shows how a sample thief can provide false data. In Figure 2a, sugar crystals are layered (segregated) in three colors, and in Figure 2b, a pencil repre- senting a sample thief penetrates the sugar, dragging down the top layers. If the pencil were an actual sample thief, the resulting sample would misrepresent the material as being mixed when in reality there was no mixing at all. This is why sampling multiple batches after the blending has taken place is the preferred sampling method when evaluating a mixer. When, where, and how to sample Now that we know we're going to take multiple samples, the next questions are when, where, how much, and how often to sample. The ideal method of sampling pow- ders is to sample from a flowing stream. With a mixer, the flowing stream occurs during the unit's dis- charge. This takes a lot of upfront planning. We'll need to have sample cups prepared and staged before the mixing test is even started so that we can take samples quickly. Each sample cup will be used to dip into the flowing stream and grab a portion of it. Having the cups ready beforehand allows us to quickly take samples when mixer discharge starts. From a statistical perspective, we'll need to take 20 samples or more from each mixed batch to have a 95 percent confidence level randomized variance, the mixing index reaches 1. Figure 1 illustrates two examples. The top curve shows that a good random mix has been achieved with a combination of the correct mixer and the appropriate mixing time. The bottom curve shows that a truly random state wasn't achieved at any blending time. This shows that the mixer was a poor choice for this product. The recommended method for doing this testing is to mix a batch for a set time period — for example, 5 minutes — and then take samples while the material discharges from the mixer. Then prepare a second batch and mix it for another time period — for example, 10 minutes. A third and fourth mixing time should proba- bly also be chosen, and appropriate samples should be taken from all of the batches. This method of eval- uating mixing times is preferred FIGURE 2 Effect of using a sample thief with sugar crystals a. Layered sugar crystals b. Top layers dragged into bottom layer