# Step 2: Select the Correct Sampling Plan

Once the metrics have been chosen, one needs to establish the correct sampling plan. In large organization, there are likely to be thousands and even millions of instances of each variable over a given period of time, hence one cannot map all of them to establish control. Rather a representative sample is chosen and then the analysis takes place on that given sample.

We have already studied the various ways in which a sample can be drawn in the Measure module. However when it comes to establishing a control plan, there are certain additional conditions that must be taken into account before a control plan is established. The most important concept here is that of rational subgrouping.

### Concept of Rational Subgrouping

To understand the concept of rational subgrouping, we must understand that there are variations within the given sample subgroup as well as between the sample subgroups. In our Six Sigma endeavour, we are looking to spot the differences between the sample subgroups. Therefore the variations within the same sample subgroup must be minimized. This may sound too complicated given all the jargon involved. However an example will help simplify it.

Example:

Let’s take the case of a car manufacturing corporation. Let’s say that they want to check their automobile production for defects in the brakes. Would it make sense to collect all the samples at 2:00 pm in the afternoon from all the different factories every day? Obviously it wouldn’t, it would be more advisable to collect samples at different times of the day to understand the influence of other factors. Hence, the need of a sub-group is evident.

Now, would it make sense to collect 10 observations every two hours, when 4 out of the 10 observations come from one factory, 3 from another and 3 from yet another! Even if you found out the variation, it would be a task to identify which factory is the cause of the problem.

Rational subgrouping simply means making all the elements of any given sample subgroup as homogenous as possible. It is then that they will stand in stark contrast with another subgroup and lead you to the cause. In this case, samples at one factory may contrast with that from another and lead the management to the faulty practises at that particular factory.

### How to Create a Rational Subgroup

Like all things in Six Sigma, rational subgrouping is also all too obvious and deceptively simple. Yet projects after projects have issues implementing it. Here are some tips to ensure that your sample subgroups are homogenous within themselves:

Size: The size of the sample subgroup must be small enough to facilitate easy collection and quick analysis, yet large enough to be representative of the population. There is a statistical method to find out the sample size which can be implemented.

Frequency: The measurements of all the elements of a given rational subgroup must be recorded at the same frequency of time. This helps negate the influence of external factors and makes all measurements homogenous.

Composition: As proved by the above example, different subgroups must not be mixed together. The subgroup must be as homogenous as possible.

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