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Rational Subgrouping

Vishwadeep Khatri


Rational Subgrouping


Rational Subgrouping - is the process of organizing data into groups of items that were produced under similar conditions in order to measure the variation between the subgroups instead of between individual data points. Since the items in a subgroup are relatively homogenous, dividing the data set into rational subgroups helps in analysing the difference between subgroups and the underlying assignable reasons (special causes) using control charts.



An application oriented question on the topic along with responses can be seen below. The best answer was provided by Venugopal R on 27th October 2017. 




What would an excellence practitioner lose if he does not utilise the concept of rational subgrouping in the pursuit of process improvement? 


Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday.


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What would an excellence practitioner lose if he does not utilize the concept of rational subgrouping in the pursuit of process improvement?


The principle underlying the concept of Rational Sub-grouping

As per the Central Limit Theorem, the distribution of sample averages taken from a population will be normal distribution. The sample mean value of the sample averages will equal to the population average and the standard deviation of the sample averages will be σ / √n, where σ is the population standard deviation and n is the sample size.

This principle is used for deriving the control limits for a control plan.


By Rational sub-grouping, we mean samples taken in succession during a particular time. Usually the number of samples in a rational sub-group (i.e. the sample size) will be very small, say, 4 or 5. The next such sample has to be taken after a time interval. The reason for taking the samples in succession is to ensure that they will (predominantly) have only variations due to chance causes, since they are produced under very similar conditions. The reason to keep the sample size small is to minimize any assignable variations that could creep in due to too much time gap between samples.


The below table gives a representation of how data may be organized in sub-groups.



What if an excellence practitioner does not utilize the concept of rational subgrouping?

Let’s consider the following possibilities, instead of picking up the rationalized sub-group as explained above.


1.     If he picks ups one large set of samples with no sub-groups:

Using such a sample, he will be able to prepare a frequency diagram with class intervals and study the characteristics such as mean and overall variance. The two types of variation, i.e. due to chance causes and assignable causes will be combined and he would not be able to distinguish them separately. He will not be able to construct a control chart to assess the different types of variabilities.

2.     If he picks up sub-groups with large no. of samples in each sub-group:

Each sub-group is likely to exhibit variations other than chance causes. This can magnify the range and widen the control limits, if a control chart is constructed using this data. This will reduce the sensitivity of the control chart to detect instabilities.

3.     If he picks up the samples for the sub-group with larger time interval:

Any variability due to special causes that could have happened between the intervals could be missed out. The causes that lead to any drift of mean value or expansion of variation (range) could get unnoticed. This could impact the correctness of the control limits derived.

4.     If he does not give sufficient intervals between picking up each sub-group:

The conditions of samples in one subgroup are likely to overlap with that of adjacent sub-group, depriving the practitioner from obtaining a realistic ‘between’ subgroup variation. This could result in reduced R values and lead to narrower control limits.

5.     If he picks up just one (or two) sample each time:

In the case of picking just one sample, the range will not get estimated and there will be no possibility of working out the control limits. In the case of picking just 2 samples, he is at risk of narrowing the range and hence the control limits.


Thus, by not using the concept of rational sub-grouping, practitioner will fail to come up with the best assessment of the 3 types of variabilities viz Instability, Off-target, and Variation the existing process

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Concept of rational subgrouping plays a very important role in pursuit of process improvement. Excellence practitioner will loose some important aspects if he ignore this concept.  The method used to select samples for a control chart must be logical or rational.  In the case of x bar and r chart,  it is desirable that x bar chart detects a process shift,  while the r chart should capture only common cause variation. That means there should be a high probability of variation between successive samples while the variation within the sample is kept low. 


There will be no exact idea of central tendency and dispersion of process over time.  It means excellence practitioner will not be able first d out the answer of follow questions:

1. Has a special cause of variation caused the central tendency of this process to change over the time period observed or not? 

2. Has a special cause of variation caused the process distribution to become more or less consistent? 


Rational subgrouping is the base of control charts.  Rational subgroups are composed of items which were produced under essentially the same conditions. The subgroup provides a snapshot of the process at that moment in time. 

A fundamental aspect of the subgroup is thus to estimate the common cause variation within the process,  since the within subgroup variation is used to define the width of the control limits.  Therefore it is critical that the causes of within subgroup variation be representative of the causes of variation between subgroup. 

Is absence of rational subgrouping practices will not able to find out short term within subgroup variation which leads to non prediction of longer term between subgroup variation,  causing g the statistically uncontrolled.  When the longer term variations is not predicted by shorter term within subgroup variation,  then a special cause has been identified but in this case of absence of rational subgrouping central tendency is not defined exactly so special cause will not be the correct to resolve the problem. 

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Rational  Subgrouping


It is the rational or logical way in which data are organised into subgroups to be used in process charts. Subgroups can be used to classify two types of variation in a process –within subgroup and the between the subgroup.


1. Within Subgroup  - variation seen within a subgroup ;  This is also called common cause

2. Between Subgroup – variation observed between subgroups due to one-off factors/conditions

    or special factors/conditions ;   otherwise known as special cause variation


Upper and Lower control limits in a control chart are calculated using the ‘within subgroup’ variation and hence it becomes imperative to choose a subgroup so that the process has a common cause variation. So here, the key objective in choosing a rational subgroup is to have minimal variation within subgroup. This is where an excellence practitioner would miss out, if he/she does not make use of the rational subgrouping method properly.


Let us see with an example.

In a banking IT support project, the support for the project is provided in 3 shifts.  The team is a mixture of freshers and experienced professionals.  Now there were so many defects that cropped out. The team did not have a clue as how to address these defects.  Two rational subgrouping could be done – one on shift and the other with experience level. We need to find which one has minimal variation in ‘within subgroup’. Apart from that, we also need to eliminate ‘between the subgroups’ variations.


Let us see with ‘Shift’ as a rational subgroup.   There are 3 shifts.


Shift1 is having an average 10 defects /day, Shift 2 has 10-12 defects/day and Shift 3 has on rare occasions, 20 defects/day and on other occasions 9-10 defects.  Defects include cosmetic, high, severity 2 and severity 1 defects.  While the shifts, Shift 1 and Shift2 do not have much difference, Shift 3 has a considerable variation at times.  This is due to the fact that on rare occasions SME availability is not available for a key application.  


Now with the ‘Shift’ as a rational subgroup, shift 1 and shift 2 has minimal variation.  To eliminate the special cause reason for SME unavailability, remove the dependency on the SME, by ensuring more SMEs are available in that shift.  Spread out the SMEs across shifts.   

Let us see with ‘Experience Level’ as a rational subgroup. 3 categories.  1-2 years ; 2-5 years; 6-10 years.


Team members with experience level – 1-2 years produced 14 defects on an average/day sometimes and 20 defects/day on an average on some other days, team members with experience level – 2-5 years produced 6 defects/day on an average sometimes and 15 defects/day on some other days, and team members with experience level 6-10 years produced 2-3 defects on an average and occasionally produced 5 defects .


 As we see the variation within subgroup is high and also variation between the subgroups – 1-2 years and 2-5 years is large.  Eliminating the variation between the subgroups is not straight-forward.  


So the best subgroup in this case is ‘Shift’ which will have minimal ‘within the subgroup’ variation



Thus an excellence practitioner has to choose the right subgroup to ensure minimal within subgroup variation.








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Rational Subgrouping helps in clearing the haze from over the data; which limits analysis otherwise, when the data is seen as one. When not done or not done right, the Observer :

1) Fails to identify/ capture the sub group properties & behavior

2) Might arrive at incorrect Statistical findings

3) Wrong Inferences will follow

4) Efforts to Improve/ influence the future of the process might fail


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Rational subgrouping identifies and separates special cause variation and through rational subgrouping variation between subgroups due to specific identifiable causes is minimised. Rational subgrouping is one of the most important thing for the successful implementation of control charts.

If the concept of rational subgrouping is not implemented properly, an excellence practitioner will not be able to make meaningful inferences from his statistical analysis and the purpose of analysis will be defeated.


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Rational subgrouping first of all helps Excellence Practitioner to make analysis a cost efficient one, unlike targeting big set of data for analysis, this help to gather reasonable amount of data that represent a population. In case if rational subgrouping is not considered then in pursuit of process improvement, we will not be able to distinguish between what is the key influencing factor for the behavior of the process samples. Ideally it’s expected that the sub grouped sample have a consistent behavior and are produced under similar condition. This helps to make meaning out of the behavior of the group, else it will be difficult to attribute the behavior to a specific cause. Understanding variations in the process is an important aspect of process improvement, so if the subgroup is not consistent with its behavior then studying variations will become complex due to varied behavior of different data set in the sampled group. At a basic level, if rational subgrouping is not considered then it may increase the need of increasing the sample size that adds on to the cost.

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In case the excellence operator doesn't utilize the concept of rational sub grouping than It would incorporate the variations from the different streams.

Identification of corrective actions once an out of control condition cannot be done.

their would be inconsistency of data from processes.



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A person who needed to complete a long journey within a short time was in such a hurry that he could not spare the time to fill his car with fuel, with the result that the journey could not be completed at all as his car ran out of fuel, leaving him stranded midway. Similar is the fate of the Business Excellence professional who ignores rational sub-grouping in problem solving.


The need or the opportunity to use rational sub-grouping occurs almost in all problem solving attempts. In a typical such case, the variation in a performance parameter will need to be identified, then root-cause analysed and corrective actions need to be implemented.


The real, disruptive variations are caused mainly by special causes. These special causes normally do not carry a label and put their hands up to be identified. They have to be identified by meticulous study of the process data. For the special causes to be easily identifiable from the data, factors that can distract or obscure the special causes need to be got out of the way. One of the most frequent such factors that can obscure special causes are their own “cousins”, i.e. chance causes.


Therefore, even before looking for special causes, the problem-solver needs to take steps to ensure that special causes are not masked by chance causes. This is most effectively done by being aware of, taking cognisance of, applying and using, “Rational Sub-grouping”. Rational Sub-grouping, by definition and practice, does an effective job of preventing the obscuring of special causes by chance causes. This it does by clustering together or grouping together, those data points, each of which could represent a product or transaction produced under same or similar conditions. By this clustering, the variation between “homogeneously” produced products, mostly due to chance causes are also clustered, thereby allowing the observer to look for special causes that cause variations between sub-groups. As the chance cause variations are wrapped up in their sub-groups, they do not get in the way of the observer’s line of vision when looking for special causes. Rational subgrouping thus, organizes data into groups that were produced under similar conditions in order to measure the variation between the groups rather than between individual data points.


If when creating control charts to investigate a process or a problem, an excellence practitioner ignores or does not use a rational sub-grouping strategy, these control charts may not provide the correct answers required to identify the source of variation of a process. The practitioner may not be able to, atleast immediately zero down on the special causes, which were the primary targets of his investigation. The practitioner may end up searching for among the chance causes, the proverbial needle called special causes in the haystack. There may be a high probability of going on the wrong track and investing time, energy and money in irrelevant actions and solutions to try to eliminate what really are just chance causes, which may not be effective to really solve the problem. The special causes would not even have been identified, let alone be eliminated.


In conclusion, without the fuel of “Rational Sub-grouping”, the practitioner would get stranded in the “Problem Solving” journey and not reach the targeted destination of implementing an effective solution to solve the problem under focus.

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Rational Subgrouping is the process to organise data into groups of items that were produced under similar Conditions in order to measure variation between the subgroups instead of between individual data Points.

It is used in Process sampling situations where real time data is collected during live operations. The conditions are kept constant (Controlled).

The idea is to create sets of observation in a moderately stable process with controlled variations. These sets of observation are considered as sub groups and then plotted as a single point on a control chart.

For Example ,At a The service counter in a QSR, we might choose to group the service time readings taken at different day parts in to subgroups , where  operational conditions/ factors are  kept as close to similar as can be, with the LSL and USL for Service time defined. The said subgroups are then plotted as a single point on the control chart.

The Control charts help the excellence practitioner to monitor the stability of the process and helps to turn this data into a picture that indicates when there are points out of control or if there is an abnormal shift in the process. Thus the non random sources of variation can be detected. Simplistically , it means that it helps to separate  or distinguish between variation caused due to common causes or special causes.

Where, Common Cause Variation is naturally inherent in the process and always present – Like in the above example – A Trainee on one of the service Counter Tills.

And, Special Cause Variation are the ones which are not a regular part of the process- Like in the above example- repeated Bulk Orders(High number of orders)- Or Orders with Promotional Offer, Less number of customer due to traffic outside the restaurant etc. It is noteworthy that special causes can be either unfavourable or favourable to the process flow.

The Control limits on the control chart are calculated using the variability “within” the subgroups. Hence, it is imminent that the subgroup is selected so that only common cause variation in the process is represented. In the example mentioned above, The objective is to improve the service time at the counter, by eliminating between various subgroup variation and reducing within each subgroup variation.

Thus, the base for creation of control charts is to have the right subgroups of the available data. A Practitioner who does not use the concept of sub grouping will not be able to create worthwhile control charts and thus will not be able to measure the impact of actions taken to improve process- It is noteworthy that even control charts created on Minitab are useless if right subgroups are not used from the available data.



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A group of units produced under the same set of conditions is call as rational subgrouping. It is used to represent the process with same conditions. The selection of rational subgroups should be consistent with the structure of the data from the process.


What would an excellence practitioner lose if he does not utilise the concept of rational subgrouping in the pursuit of process improvement? 


1.    Variation in same groups cannot be identified.

2.    If variation is not identified then minimizing the variation is difficult.

3.    Stability of the process is questionable.

4.    Successful control charts cannot be plotted

5.    Differentiation of common causes and special causes are difficult

6.    Process changes or process behavior cannot be studied over time

7.    Monitoring of the process improvement and its efforts are not possible.

8.    Cannot predict unexpected changes in a process

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Question: What would an excellence practitioner lose if he does not utilise the concept of rational subgrouping in the pursuit of process improvement? 


Rational subgrouping is set of observations made under the similar set of production environment.  Sample or subgroup is in a way same only.  Sample is subgroup of the population. But the only difference is when different samples are picked from the same population.


Rational subgrouping reflects the process that you are working. Also, It usually represents the in-built variation of the process, which is called as common cause variation or within subgroup variation. It will tell you how the data been collected. The individual data points collected is usually independent of each other though it is all sub grouped.

For Eg. If the coder produces 20 charts per hour and 50% of the chart to be audited. Hence the Auditor picks systematically every even numbered charts for auditing throughout the day or at even regular intervals. Sample of 10 per hour represents a subgrouping. Sample usually denotes a individual sample of the group. Sub group would always represent homogenous condition’s data points.


Two types of variation:

Within subgroup Variation: variation within the group / process sampled. Also called as common cause variation.

Between subgroup variation: variation between the measurements of the sub groups. Also called as special cause variation, which has to eliminated for any quality improvement project.


Control limits & Variations:

Control limits are calculated using common cause variation. Sub group averages and variances are calculated from the homogenous set of data points. Subgroup is represented as individual point on the control chart with control limits inhibiting common cause variation.

The goal of the project is eliminating the special cause variation and reducing the common cause variation.


Usability: Sub grouping is done to help in decision making using the sample for the population.

·      Helps to reduce the common cause variation and eliminate the special cause / assignable cause variation.

·      Sub grouping along with control charts will create the base of decision making.

·      Helps us to find out how much of variation exists within subgroup.

·      Helps us to visible the process.


When Rational subgrouping is not possible?

When each and every items are checked or 100% audited, the rational subgrouping is of no use. For Eg. In case of automated inspection method / technology built audit method followed while processing and submitting a chart, rational subgrouping is of no use. Since all the charts are getting inspected.

When medication effect is analyzed in preparation of medicine in pharmaceutical company or hospital, repeated analysis is done. Hence rational subgrouping is no use.


In conclusion, in any business excellence project, if rational subgrouping is not done, common cause will be identified and reduced. This subgrouping will help identify the types of variation and the context of data like how they are collected, how time ordered the data is and highlights the variations and helps eliminating the special causes.




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Rational Subgrouping is a process of grouping items that were produced under the same set of conditions to measure the variation between the subgroups and within Subgroups. It is a “snapshot” of the process over a very small-time window i.e. samples taken in a time-ordered sequence.

  • The variation measured within a Subgroup is Common Cause variation.
  • The variation measured between Subgroups is Special cause variation.


A Rational Subgroup helps an excellence practitioner to differentiate between common cause and special cause variations in a control chart and make corrective decisions when the charts are plotted using a sample of the data from the process.


Without utilising the concept of Rational Subgroup, I feel a excellence practitioner would not be able to:

  1. Make correct decisions using control charts plotted with a sample of the process data.
  2. Correctly distinguish between common cause and special cause variations

Example of Ration subgroup creation


(1): Consider two Machines – X and Y with Operators 1 and 2 respectively producing a product say, metal disks.


Rational Subgroup 1 will be, say, 10 random disks picked from Machine-X Operator 1 in the 1st of production.

Rational Subgroup 2 will be, say, 10 random disks picked from Machine-Y Operator 2 in the 1st of production.


 (2): Consider two Machines – X and Y and Shifts A and B and the following production schedule:

Machine X -> Shift A -> Operator 1

Machine X -> Shift B -> Operator 2

Machine Y -> Shift A -> Operator 3

Machine Y -> Shift B ->  Operator 4


Rational Subgroup 1 will be, say, 10 random disks picked from Machine-X Shift A Operator 1 in the 1st of production.

Rational Subgroup 2 will be, say, 10 random disks picked from Machine-X Shift B Operator 2 in the 1st of production.

Rational Subgroup 3 will be, say, 10 random disks picked from Machine-Y Shift A Operator 3 in the 1st of production.

Rational Subgroup 4 will be, say, 10 random disks picked from Machine-Y Shift B Operator 4 in the 1st of production.

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Rational subgrouping is a process of organizing data in different groups, which were produced under similar conditions. With this we can measure the variation between the subgroups instead of individual points.

If we dot use rational subgrouping properly, and use only individual data points, we will miss the drift in the variability of the process that happens over a period of time.

  With help of rational subgrouping we will be able to know whether the control limits are too tight or too wide

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Rational subgrouping is the process of organizing data into groups of items that were produced under similar conditions in order to measure the variation between the subgroups instead of between individual data points. The organization of subgroups is generally established to sample a subset of the population within relatively homogeneous conditions -- a short duration of time (shift), or a small region of space (machine) or a designated amount of output (batch).

The subgrouping strategy directly determines the sensitivity, and therefore the usefulness, of the control chart by bearing on the sampling plan for the charts. Without a rational subgrouping strategy, the control charts will not answer the right questions related to identifying the source of variability of a process.

When is it used?

•Employed when sample data from a process is used to make decisions, but especially when using control charts to develop the data serving as the foundation for those decisions.

• Used to answer the following questions generally during the Measure phase of a DMAIC project:

§  Can the variation in this process be captured between subgroups?

§  How should we draw the subgroup samples?

§  Is there too much variation within subgroups (are control limits artificially wide)?


Rational subgrouping is a very important concept in Statistical Process Control (SPC), but it is often forgotten.  Far too often, we do not give enough (or any) thought about how to subgroup their data when constructing an  X-R control chart or any other control chart that involves putting the data into subgroups

We need to remember that control charts are really a study of the variation in our process.  And the variation displayed on the control chart depends on how we subgroup your data – which may or may not be the variation you would like to study. 


Rational subgrouping starts with how we sample and measure your process.  For any process, we need to decide the following four items:

  1. What will be measured
  2. How it will be measured
  3. Where it will be measured
  4. How often it will be measured

Of course, we need to be concerned with how accurate and precision your measurement process is, but, for this example, we will assume that we have a great measurement system.  We can measure our quality characteristic X without any problems.

Remember that one purpose of control charts is to monitor a process for out of control points.  When a process goes out of control, a special cause of variation is present and you will need to search for what caused this out of control situation.  Thus, it is important that you know when and where the sample was produced.  Without that information, it is impossible to go back and see what happened.   


1.       Variation in the Process can’t be easily identified

2.       Maximization of the Variation occurs within the Subgroup

3.       It increases the Variation between One Sub group to the Other Sub group

4.       Variation in the Product cannot be effectively identified

5.       Datas of the Same Batch cannot be collected


So in order to prevent the All above mentioned Losses, Rational Sub Grouping must be effectively used to improve the Process.



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It was nice to see that most people understood the importance of rational subgroups and are actively using it in their projects. R Rajesh gave a very good example to identify the right subgroup but the best answer goes to Venugopal for providing detailed definition and scenarios thus winning my vote !

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