Q 243. The process capability assessment is sometimes associated with subgrouping of data. This has led to the concepts of Zwithin being compared to Zoverall. While assessing process capability, when is it that subgrouping makes sense? When will you decide to not use subgrouping? Explain with examples. 

 

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Subgrouping in Process Capbility determination:

-As process capability varies inversely to standard deviation, so to enhance process capability (Cp,CpK), there should be decreased variation  within subgroups  and for enhancing  process performance ( Pp,Ppk), there has to be reduced  overall variation( sum of within subgroup and in between subgroup variations).Target should be elimination of between subgroup variation and marked reduction  of within subgroup variation.

- Data should be collected in rational/logical  subgroups, which are made of similar item-usually in 3 to 5, produced during a short span of time. Subgroups have to be representative of output and the items included in subgroups have to be collected in same conditions and inputs- suppliers, equipments,  personnel, place  etc.  The data needs to be of long duration to account for process variation. 

-So the variation obtained  with in  these small subgroups, can be termed as natural variation.  The variation obtained between subgroups is due to some special cause variation, which needs to be identified and eliminated to improve process performance.  For example, a heavy industrial  machine produces 500  metallic parts per hour. Five random samples are collected every hour and constitute a subgroup.

The total variation  = Variation within groups of 5 +Variation between different subgroups.

 Subgrouping not done in process capability calculation:

-It may not be feasible to collect rational subgroup data in all the situations, example- In Manufacturing, If there  has to be change of batch or raw material, the number of defects and defectives, with each  batch may be significantly different. Logical subgrouping  may not be possible , as the conditions are different in each batch of products. 

Process Capability Assessment is the main step in Measure phase where the Baseline Metric is calculated. Following are the metrics that can be used for assessment

1. Sigma Level Long Term (Zlt or Zoverall) and Sigma Level Short Term (Zst or Zwithin)

2. Pp, Ppk (using overall standard devaition) and Cp,Cpk (using within standard deviation)

3. DPMO, DPU and Defective %

 

Zwithin uses the within standard deviation for calculation while Zoverall uses overall standard deviation for calculation. The difference between within and overall standard deviation is how you perceive the collected data. If the entire data set is (or the population data) is used, it results in Overall Standard Deviation. While if we divide the entire data into rational subgroups then we get Within Standard Deviation (which is also known as Pooled standard deviation)

 

Another common method to understand the difference

within overall standard deviation is when only common cause variation is considered

overall standard deviation is when both common cause and special cause variation is considered

 

Sub-grouping or Rational subgroups is the collection of data under similar process conditions thereby resulting in lesser variation leading to the following concept

within standard deviation < overall standard deviation

 

Following are few scenarios where sub-grouping is NOT preferred

1. Rational sub-groups do not make sense while working with discrete data. For e.g. if we do weekly sub-groups and are collecting data on defects. For a particular week, if there are no defects (though unlikely but still), then within standard deviation will be 0. Hence does not make much sense to use sub-grouping when dealing with discrete data. On the contrary, one should check for possibility of sub-grouping in case of continuous data

 

2. Consistent and standardized process that does not change very often. E.g. Temperature control for stem cells. Assuming that it is maintained at -4 Celsius, it is unlikely that it will show a lot of common cause variation. In such cases, even if we do sub-grouping, the variation within and overall will be more or less same (unless there was a presence of a special cause)

 

3. Project scope deals with a specific product or service being delivered to a specific client. E.g. delivery time of same kind of pizza by only one pizza outlet and to a specific corporate customer (assuming this corporate customer orders almost on a daily basis and orders the same pizza everytime from the same outlet)

 

4. All process inputs are well controlled. If all the process inputs are all well controlled, then there are less chances of variation in the process. In such a scenario, one could avoid doing rational sub-grouping. Closest example I can think of is the process of making a burger at McDonald's. All the process inputs are well controlled and hence we get the same taste of the burger. One could argue that it is not a perfect example. And I tend to agree because it is very difficult to find a process where all inputs could be controlled. There will always be fatigue, wear and tear etc. Like they say, there is no "perfect process"

 

Important thing to note here is that irrespective of whether you do sub-grouping or not, one should be consistent with the approach for doing a pre vs post project comparison. If baselined with Zwithin, then compare the improvement with Zwithin only.

 

P.S. - If all of this is too tedious, one could simply use the empirical formula Zwithin = Zoverall + 1.5 (however, one should remember that if the data is continuous, both these can be determined independently as well)

While Shashikant Adlakha and Natwarlal have both given correct answers, Natwarlal has provided very good examples for when to NOT use subgrouping. 
 

Natwarlal’s response is the winner for this question.