Question

What is the process capability index (Cpk) for the given situation where the product's target specification is 24 ounces with a tolerance of +/- 1.0 ounce, the observed mean of the current process is 24.2 ounces, and the standard deviation is 0.5 ounces?

A. 0.2
B. 0.4
C. 0.6
D. 1.2

Answer 1

The process capability index (Cpk) for the given situation is approximately -0.133.

Step-by-step explanation:

The process capability index (Cpk) measures how well a process is performing within specification limits. It is calculated by taking the minimum of two values: (1) the difference between the target specification and the observed mean divided by three times the standard deviation, and (2) the difference between the observed mean and the target specification divided by three times the standard deviation. In this case, the target specification is 24 ounces with a tolerance of +/- 1.0 ounce, the observed mean is 24.2 ounces, and the standard deviation is 0.5 ounces.

1. Calculate Cpk using the first formula: (Target Specification - Observed Mean) / (3 * Standard Deviation) = (24 - 24.2) / (3 * 0.5) = -0.2 / 1.5 = -0.133
2. Calculate Cpk using the second formula: (Observed Mean - Target Specification) / (3 * Standard Deviation) = (24.2 - 24) / (3 * 0.5) = 0.2 / 1.5 = 0.133
3. Take the minimum of the two calculated values: Cpk = min(-0.133, 0.133) = -0.133

The process capability index (Cpk) for the given situation is approximately -0.133.