The specifications for a product are 6 mm ± 0.1 mm. The process is known to operate at a mean of 6.05 with a standard deviation of 0.01 mm. What is the Cpk for this process?
A) 3.33
B) 1.67
C) 5.00
D) 2.50
E) 1.33

Question

Quizplus · Accepted Answer

The first step in calculating Cpk is to determine the process capability index (Cp) using the formula:

Cp = (Upper specification limit - Lower specification limit) / (6 * standard deviation)

Cp = (6.1 - 5.9) / (6 * 0.01) = 1.67

Since Cp only considers the distance between the specification limits and the process mean, it doesn't take into account any potential shift or drift in the mean. To account for this, we use Cpk, which considers both the distance and the variability of the process from the target.

Cpk can be calculated as:

Cpk = min [(Upper specification limit - mean) / (3 * standard deviation), (mean - Lower specification limit) / (3 * standard deviation)]

Cpk = min [(6.1 - 6.05) / (3 * 0.01), (6.05 - 5.9) / (3 * 0.01)] = min [1.67, 5.00] = 1.67

Therefore, the correct answer is B) 1.67.

The Specifications for a Product Are 6 Mm ± 0