# Process Capability Calculations - Six Sigma

Having achieved stability (or statistical control) in a process we can move on to the improvement phase of Juran’s Trilogy. The start point to this phase is to compare the pattern of variation in a process to the acceptable limits (often tolerance or specification limits). This way we can understand if the equilibrium position we have reached by bringing the process into control meets the minimum company requirements.

Process Capability Calculations

Process capability in general terms can be seen graphically in section. If we wish to be more scientific about it we can actually calculate to what extent the voice of the process (as defined by the control charts) aligns with the voice of the customer (as defined by the specification limits). The first calculation we need to make is the process potential. This is denoted Cp. This essentially compares the process spread to the width of the tolerances. If the tolerances are wider than the process spread then, potentially at least, the process can achieve what is being asked of it.

It is clear that this measure however is not the whole of the picture. This measure would not, for example distinguish between processes B and C in the example as they have the same spread and Cp takes no account of setting. A better measure is one which takes account of setting and establishes the likelihood of producing non - conforming product for the process. This measure is shown above as Cpk. The two measures individually compare the distance from the process centre to either tolerance against the distance from the process centre to the top or bottom of the process (half the process spread in either case).

Each of these tests basically ensure that the process will not overlap either limit. Clearly you could maximise one whilst minimizing the other so we take the worst case in order to establish the overall Cpk.

Whichever is Lower

Things to note about Cpk, include the fact that it’s best achievable value is to equal Cp. This will occur when the centre of the process is equidistant from the two limits (i.e. the process is exactly on target). It is not possible for Cpk to exceed Cp. It is perfectly possible for Cpk to take a negative value if the centre of the process is outside one of the tolerances. This would represent over 50% non - conforming product but is not unknown.

Interpreting Process Capability Indices

Firstly it is necessary to state that the aim should always be for Cp = Cpk. This is analogous to saying that the process should always be set on target. This conforms to Taguchi’s definition of ‘Quality’ as ‘on target, minimum variation’. The aim for the values for Cp and Cpk is always the bigger the better. A value of 1 indicates that the process is operating at a minimum level of capability (i.e. at least one end of the process is bang up against a tolerance). Less than 1 means an incapable process. By using the properties of the normal distribution it is possible to predict percentages out of tolerance for any given capability value provided that the process is:

• Stable
• Normally distributed (approximately)
• Properly centred (Cp = Cpk)

The approach to improving process capability is essentially about reducing common cause variation. This will mean action on the process which is fundamental and probably management responsibility relating to things such as operator training, machine maintenance, extruding etc.The effect of such actions can be seen below:

Improving process capability

It can sometimes be confusing trying to explain the meaning of capability indices. This might be best avoided and discussions centred on actual or expected levels of defective product for accessibility. Similarly, for improvement purposes Cp plus a statement of process offset from the target might be more helpful for process improvement than a Cpk figure. This is because the actions which affect spread and those that affect centering are usually very different and this notation separates the two. Cpk is a figure which may be used for high - level tracking of overall process goodness’ but, due to its composite nature it is less helpful in showing what has to change.

Finally it is possible to calculate the percentage of tolerance consumed by inverting the Cp figure and multiplying by 100%. thus a Cp of 1.33 takes up 75% of tolerance and a Cp of 2.0 takes up only 50% of tolerance.

Establishing Process Capability Values

There are several ways of gaining the data for such calculations. The most robust is to estimate the process variability from an established control chart. This mechanism ensures that we have checked for stability in the data before establishing capability.

TableConstants of proportionality (process capability from a control chart)

There are other ways of establishing standard deviations from the sample, but this is the most effective.

The calculations for process capability arose from a need to understand whether process output was likely to meet design intent. This can only be calculated with confidence for a stable process. There are various indices which give numerical interpretations of diagrammatic information. For conceptual understanding the diagrams are more useful than these summary statistics. Always try to communicate process capability information in the most accessible and useful way for the target audience.

Process fallout tables assume normality. Other calculations start from an assumption of normality but are robust enough to work without it based on the pragmatic rules discussed in the introductory sessions.