SAMPLING CONSIDERATIONS


Suppose we are making simple pens. We make about 10,000 per hour . In these pens, we are also responsible for many dimensions and most ” if not all ”must be controlled. Examples of our controlling characteristics are as follows : length of the pen, length of the cap, diameters of the hole, tapering, no fill, thickness , and many more.

The point here is that no one will be able to check every characteristic of all 10,000 pens per hour. We would try to measure just the important ones, but even then, if we decide that the diameter of the hole is very important, we would still have to contend with 10,000 measurements. If we assume that each diameter of the hole takes 10 seconds to measure and record, we will need more than 27.5 {[(10 seconds — 10,000)]/3,600} hours to check every pen produced. Of course, this is for only one characteristic and for only one hour's production.

Obviously, something is not right. How can we possibly tell whether our pens are good or bad without looking at all of them? How can we tell whether other characteristics are changing without seeing and/or measuring all of them?

We can use a sampling plan. In a sampling plan, a selection of a few parts out of the operation are checked, and then the results are projected onto the entire population. It is not necessary to look at every pen to see what is happening to the whole process. We can use a sampling plan. For an excellent discussion on sampling plans, see Deming (1966), Juran et al. (1976), Grant and Leavenworth (1980), and Duncan (1986).

There are several types of sampling plans. It is very important for the analyst to select the type that will result with the most and best information of our needs. For example, in manufacturing, more often than not, we chose the consecutive sampling plan.

What is a consecutive plan? It is a plan that takes a few parts in the order in which they are made so that we can determine how things should be done. Why would we choose such a plan? Because using a consecutive sampling plan will allow us to discover exactly when something starts to change. We can then pinpoint the reason for any change. This is very important information, because even if we find that nothing has changed ” which is good ” we must find out what has kept the process the same. Either way, this information can be very helpful for our understanding in the improvement of our process.

Additional considerations for sampling are rational samples and rational sub-samples.

Rational samples: What are they?

  • Groups of measurements subject only to common-cause variation

  • Collections of individual measurements, the variation among which is attributable only to a constant system of chance causes

How should they be chosen ?

  • Strive to choose samples to minimize the occurrence of special causes within the sample.

  • Strive to maximize the opportunity to detect special causes when they occur between samples.

Rational subsamples: The small number of observations taken periodically should be rational subsamples. This means that they should be taken in such a way that only common-cause variability can be attributed to the points in a particular sub-sample. There should not be any assignable causes of variability that affect some of the points in the subsample and not others. Typically, rational subsamples are obtained by taking observations nearby in time. For example, every half hour you might examine five consecutive soda cans coming off the production line. However, if you are not careful, even with a rational subsample, you may end up in trouble. Make sure that you review your sampling plan with a statistician or with a quality professional before you start taking samples.

Rational sampling pitfalls: To be sure, rational sampling is a very important concept and is used very frequently in practice. However, there are some cautions . The three major ones are:

  1. With several machines making the same product, the product should be combined and a single control chart maintained .

  2. With stratification, each machine should contribute equally to the sample composition.

  3. With mixing, output of several machines should be combined into a single stream and then sampled.




Six Sigma and Beyond. Statistical Process Control (Vol. 4)
Six Sigma and Beyond: Statistical Process Control, Volume IV
ISBN: 1574443135
EAN: 2147483647
Year: 2003
Pages: 181
Authors: D.H. Stamatis

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