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# Process Performance or Process Capability Analysis?

### Answer

This is a common question asked to which different scholars have different opinions. Two of these are examined now.

One school of thought suggests that Process Performance should only be performed during Phase I of SPC applications and Process Capability during phase II. The reasoning follows Dr. Walter Shewhart’s assertion that an out-of-control process cannot be used to predict Process Capability. During Phase I the process is out-of-control and hence Process Performance analysis is more appropriate. During Phase II the process has been bought under control, and thus behaves predictably making Process Capability analysis more appropriate.

It is unlikely that Dr. Shewhart intended for his comments to be used literally, for he has shown to be a very pragmatic and practical statistician, who believed that just because criteria have a history of high-brow statistics, does not justify their use.

A more practical school of thought asserts that during Phase I performing an exploratory Capability Analysis enables management to estimate the worth of bringing the process in control. Although the process may be out-of-control, this does not always make a Process Capability analysis unreliable. The reason is that a Process Capability analysis is based on within sub-group variation, whereas a Process Performance analysis is based on total variation.

Within sub-group variation tends to be robust to the overall stability of the process, as shown in the image below. Here the distribution curves are based on within sub-group variation and remains constant even though the process is clearly out-of-control.

It is thus not unreasonable to perform a Process Capability on an unstable process, if it can be proven that within sub-group variation is stable during Phase I SPC. This can be done with machine powered dynamic capability charts, such as shown above and below, or classical statistical tests such as Bartlett’s or Levene’s test.

It is of course possible that the variation within subgroups is also unstable, such as shown in the image below.

In this instance a Process Capability analysis appears futile and it would make sense to at least try and stabilize the within sub-group variation and then perform a Process Capability the conventional way using within subgroup variation.

One option is to take many samples during a period when the within subgroup variation is near its lowest, or at a level believed to be achievable consistently and perform a Process Capability analysis on this snapshot of data. This would estimate Process Capability on the premise that within subgroup variation can be maintained near the chosen level of within subgroup variability.

It thus makes sense to conclude that there is no reason why a Process Capability analysis cannot be performed during Phase I as well and why a Process Performance Analysis cannot be applied during Phase II as well. The latter because it is prudent to always see how the process is performing. If a process capability is performed during Phase I then this fact must be clearly documented and the reasons and limitations explained.

As a customer it can be argued that it makes more sense to know what the process performance is as opposed to what the process is capable off, i.e. a Process Performance Analysis should also be performed during Stage II. Although a process may be perfectly capable of producing non-conforming product then surely if the process does not produce non-conforming product then this is more important information than the theoretical possibility. This brings us to the point where we need to understand the terms process capability and performance to further answer the question, process performance or process capability?

Capability generally is defined as the ability of something performing a required task. For quality assurance purposes the task is producing near zero non-conformance. In this instance whether the process can perform this task is measured by the range of inherent variations. Historically inherent variation is measured from within subgroup variation. This demonstrates an incorrect assumption that only within subgroup variation is inherent. Between process variation can also be inherent, such as processes dependent on mother nature, which does not practice SPC. A classical process capability may thus be far too optimistic making a process performance analysis a better choice.

If the only inherent variation is within subgroup variation then this begs the question, what is better during Phase II. A process Capability or Performance Analysis. The former assumes a perfectly stable process. But no process is always perfectly stable. So, it seems more pragmatic to perform both analyses to see if the process is deteriorating relative to what it is capable of.

Another consideration affecting the answer is the actual method used to calculate process capability statistics. Historically the Cp and Cpk index is obtained by pooling the within subgroup standard deviations or averaging the subgroup ranges or standard deviation and then applying these to a formula which assumes a Normal Distribution. What happens when the data is non-normal? It is no longer possible to relate the within subgroup standard deviations directly to the capability indexes. In this instance a process performance analysis can be the only option where a non-normal distribution is fitted to all the data. But, this only works if the process mean is stable which can be established with a change analysis. If the mean is not stable, then the current mean must be mathematically stabilized prior to performing the performance analysis using machine powered algorithms provided by the BISNet Capability App.

The overall conclusion is that there should not be a hard-line drawn, for when a Process Capability or performance analysis is applied, no matter whether recommended by high-brow statistical theory. Practical considerations dictate that both provide important information at all stages. What is important is documenting the state of the process at the time of the analysis and the phase of operation, listing the limitations and caveats of the analysis.

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