Final answer:
The correct answer is b. I, II, and III because Cpk calculations assume that the process output is normally distributed, centred, and stable over time, and can be misleading if any of these conditions are not met.
Step-by-step explanation:
The use of the process capability index (Cpk) may be misleading if the process output is not normally distributed, the process is not centered, or the process is not stable. Therefore, the correct answer is b. I, II, and III.
Cpk is a statistical tool used to measure how well a process can produce output within specified limits. The assumptions behind Cpk calculations generally include that the process output is normally distributed, the process is centered between the specification limits, and that it is in statistical control, i.e., stable over time.
- When the process output is not normally distributed, Cpk may not accurately represent the ability of the process to produce within specifications.
- If the process is not centred, even if it is capable, the Cpk value can be misleading because it will not reflect the uneven distribution of data within the specification limits.
- A process that is not stable (where the process variability is unpredictable over time) will not yield a reliable Cpk value because the index assumes a stable process.