A Bulk Sampling Question

Question from a Lean Six Sigma Black Belt Student

The calculator sheet is very useful. But for my situation here in my plant, we produce bulk product (1200 MT of Refined Canola Oil). Suppose we need to test for “linoleic value” at the finished product, which is fluctuating between 1.75 and 2.39 values (margin of 0.64), sigma estimate is 0.26 and average of 2.06. So if we put this data in the sample size calculator we’d get a sample size of 1 (N unknown) or 0 (N known) at 0.05 Alpha risk. What is 1? 1 Metric Ton or 1 sample? And if it is one sample as I think it is, how large should be the sample? 4 Oz container or 1 Liter? Also if it is 1 MT that’s huge and expensive sample. Also I am confused about the zero number I got for the know N. How come that I do not need sampling at all?

For your info, this is one of the main reasons I decided to pursue six sigma is to be able to identify sample size when I needed to. That has been a question in my mind since long time specially about bulk product and I feel good now that I am in touch with you so you can help me out on this.

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Answer

Jack,

The sample size tools presented in the training are for what is known as “discrete sampling.” That is, for sampling discrete units such as people, automobiles, or other such distinct “widgets” that are separate entities. They can’t be used to calculate sample sizes for processes such as yours, which are referred to as bulk processes. That’s why your results make no sense.

Bulk process sampling is a unique application of statistical sampling. There are two primary bulk sampling questions: the science of testing and homogeneity. The science question asks what sample size is needed to obtain scientifically valid results. This is not a question of statistics per se, but one of science. It needs to be answered by subject matter experts. The question of homogeneity is also scientific, but it has statistical implications and statistics can help answer it. If the solution is perfectly homogeneous with respect to the property being measured, then all samples will produce the same result (except for measurement error, which is discussed at a later point in the training). However, if the material is heterogeneous then you must construct a representative sample to properly characterize the lot of material. In this case the proper sample size will be whatever sample size is needed to characterize the lot. You may also find this article to be useful.

Another important topic is the sampling interval (as distinct from the size of a single sample). If your canola oil is produced continuously rather than in discrete batches, you will want to look into this. However, from your description it sounds as if the canola oil is produced in discrete batches and I assume you’ll want to sample each batch using the procedure described above.

You mention that one of the main reasons you are pursuing a Lean Six Sigma Black Belt is to be able to identify sample size for bulk processes. I should point out that this is a specialized application of quality engineering rather than Six Sigma. While the Black Belt learns many of the tools of quality engineering, it doesn’t cover all of the QE body of knowledge. (The Black Belt also learns a number of soft skills that the QE doesn’t learn.) In fact, even traditional quality engineering training doesn’t cover the specialized topic of bulk process sampling, although it does go deeper into sampling than Black Belt training. What I’m saying is the you may want to supplement your Black Belt training with additional studies specific to your industry.