Comprehending the relationship between Cp, Cpk, Pp and Ppk
As technical support role, I have come across many scenarios where the manufacturer’s process is not acting well. NC products occurs, but no direction for improvement. To evaluate the manufacturer’s process capability , we need to understand what reveals their process capability and performance, meaning exact index to indicate qualified products be delivered not only in the past but also in the future.
There are four indices of capabilities or performance indices most commonly used, which are Cp, Cpk, Pp, Ppk.
The Cp capability index uses the difference between the upper and lower limits to define the available range and compares it with the common range required for processes running with minimum variance. The required common range is six times the standard deviation within the group, i.e. 6 sigma (σ).
Cp is how many times the specification range of data compared to the fluctuation range. The higher the value, the smaller the fluctuation range of data and stronger process capability. However, Cp does not consider the center position of data, and it is possible that the fluctuation range of data is very small, but it is outside the specs range.
Whereas, Cpk considers the center position of data fluctuation on the basis of Cp, so it can be used to measure the central capability of the process.
The following figure shows the difference between Cp and Cpk. The fluctuation amplitude of the data is consistent. When the data center shifts, Cp remains unchanged, but Cpk becomes smaller.
The Pp performance index uses the difference between the upper and lower specifications as the available range, and compares it with the standard deviation of the actual performance of the past process. In the calculation of capability index, we use sigma (σ) as the intra group standard deviation, while in the calculation of performance index, we use S as the sample standard deviation.
Therefore, the performance index Pp can be used to evaluate the past process performance. However, it does not consider the center position of the past process performance. And the center performance index Ppk takes the center position into account by defining the effective available range of the process.
The relationship between the four indexes is shown in the figure below. Cp and Cpk in the upper part of the graph describe the potential capability of the process, while Pp and Ppk in the lower part describe the performance of the process in the past. As the progressing of a process gets closer and closer to its full potential, Pp and Ppk will move up, close to the upper Cp and Cpk.
The two indices on the left assume that the process center overlaps the specification center, while the right takes the degree of deviation between the two into consideration. When the process center is close to the center of the specification, the value on the right is close to the value on the left.
When a process runs stably, the index of the top and bottom level will have similar values, but there will be some differences between the values on the left and right sides, which is the impact of the process center offset.
When a process is running stably and without offset, the four indexes will be four estimates of the same object and the four values will be very close to each other.
Cp is the potential process capability value under the best condition, and the performance index Ppk describes the process performance in the past. The gap between the two is our opportunities for process improvement.