Final answer:
The comparison between Cp and Cpk shows that Cp does not account for the process centering, and the denominator is indeed twice that for Cpk. Thus, the correct answer is 'II and III only' as Cpk takes into account the process mean and Cp measures process variability without the mean.
Step-by-step explanation:
A comparison between Cp and Cpk for a process would find the following to be true:
- The Cp value measures the process capability, which is the inherent variability of the process output relative to the allowable tolerance range, without considering the process mean.
- Cpk value takes into account both the process variability and the process mean location relative to the tolerance limits, which represents the capability to produce output within spec limits taking into account the mean. It is not necessarily larger than Cp; it could be the same or smaller, especially if the process is off-center.
- The denominator of the Cp calculation is the total tolerance range (upper spec limit - lower spec limit), whereas the denominator for the Cpk calculation considers the distance from the process mean to the nearest spec limit.
- The Cp value does not account for centering, while the Cpk does, which can affect the capability index, especially if the process mean is off-center.
- Neither calculation requires a stable process. Process stability is an entirely different aspect of process control. However, it is important to note that interpreting Cp and Cpk values without considering the stability of the process can be misleading.
Based on these points, the correct answer to the question would be option b. II and III only, as the denominator for Cp is indeed twice that of Cpk, and the Cp value does not account for centering of the process.