Six Sigma Green Belt Certification Practice Exam

What is the Cpk for a process with specification limits of 48 and 30, a process mean of 29, and sigma of 4?

1. 1.58

2. 0.08

3. -0.08

4. -1.58

The correct answer is: -0.08

To determine the process capability index (Cpk), you need to assess how well a process can meet its specification limits in relation to its mean and standard deviation (sigma). The formula for Cpk is: Cpk = min[(USL - mean) / (3 * sigma), (mean - LSL) / (3 * sigma)], where USL is the upper specification limit and LSL is the lower specification limit. Given the specific limits are 48 (USL) and 30 (LSL), the mean is 29, and the sigma is 4: 1. Calculate the first part: (USL - mean) / (3 * sigma) - (48 - 29) / (3 * 4) = 19 / 12 = 1.58 2. Calculate the second part: (mean - LSL) / (3 * sigma) - (29 - 30) / (3 * 4) = -1 / 12 = -0.0833 (approximately -0.08) Now, find the minimum of these two calculations: Cpk = min(1.58, -0.08) The minimum value between the two results is -