Six Sigma Black Belt Certified Practice Exam

In a normally distributed process, if the nominal is set at the center and specification limits are ±3σ, what is the Cpk?

1. -0.25

2. 1.00

3. 1.33

4. 1.67

The correct answer is: 1.00

When dealing with a normally distributed process, the process capability index (Cpk) is an essential measure to understand how well a process can produce output within specified limits. The Cpk is calculated by taking the minimum of two values: the capability relative to the upper specification limit and the capability relative to the lower specification limit. In the scenario described, where the nominal is at the center of the distribution and the specification limits are set at ±3σ (three standard deviations) above and below the mean, the standard deviations from the mean encompass a significant portion of the data in a normal distribution. For a process to have a Cpk of 1.00, it indicates that the process is producing output at the edge of the specification limits without exceeding them. Since the specification limits are set at ±3σ, the highest point of the process capability approaches the limits precisely at 1.00, as the mean aligns perfectly with the center. This implies that one-third of the output generated by the process will fall within the specification limits with some safety margin, reflecting that the process is operating at a capable level but not optimal. Thus, when the nominal value is exactly centered and the specification limits are ±3σ, the theoretical Cpk value is