How to calculate Cp and Cpk (Capability indexes)?
The Cp index is a fundamental measure of process capability. It compares customer requirements – the Voice of the Customer (VoC) to the variation of the process being analyzed – the Voice of the Process (VoP). The Voice of the Customer is typically expressed by the Specification Limits, while the Voice of the Process is expressed by 6 standard deviations.
Voice of the Customer and Voice of the Process can be expressed in engineering units, as shown in the figure below. The higher the Cp level, the more capable the process is of meeting customer requirements.
Cp = 1
Cp = 1
Cp = 1
Cp only compares the specification width and the process width – it doesn’t indicate whether these specifications will be met. The figure above shows various scenarios for Cp = 1.
Cp only reflects variation, which is why the Cpk indicator appears, which also considers the process’s position relative to the requirements using the so-called Distance to the Nearest Specification (DNS) (figure below). The idea behind the calculations is the same – we compare the Voice of the Customer to the Voice of the Process, this time answering not only the question of whether we can meet them, but also whether we are meeting them.
Cpk will always be less than or at most equal to Cp when the process is perfectly centered: Cpk ≤ Cp
In many processes, we don’t have both upper and lower specifications, but only one-sided specifications. This makes it impossible to calculate the Cp value.
When the specification is one-sided, we only calculate Cpk.
Cp=1 Cpk=1
a barely capable and centered process
Cp=Cpk is a centered process
Cp=2 Cpk=2
process capable and centered
Cpk ≥1 process within specifications
Cp=3 Cpk=1
a very capable and shifted process,
completely within specifications
Cp=3 Cpk=1
a very capable and shifted process,
completely within specifications
Cp=0,67 Cpk=0,11
process incapable and shifted
Cpk <1, part of the process outside of specifications
Cp=3 Cpk= – 1
very capable process, but completely outside of specifications
Cpk <0, most of the process outside of specifications.
We calculate the Pp and Ppk (Performance indexes) in the same way, using the same formulas shown above. What’s the difference? We calculate σ differently.
Cp i Cpk:
variation within a subgroup
n – subgroup size
d2 – constant for range based std dev
Pp i Ppk:
total variation (ignore subgroups)
k – numer of subgroups
Cp Cpk
Pp Ppk
- Has the measurement system that provided the data used in the calculations been validated and is sufficiently precise? Has an MSA been conducted and was it done correctly?
- How was the data collected? Does it come from a rational sampling plan that reflects the sources of variation present in the process on a daily basis?
- Is the process stable? Or is there only natural variation? Remember! Stability comes first, then capability.
- Are the specifications reliably defined?
- Are the data normally distributed?
- How much data was used to calculate the capability indexes?
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