Question

The specification for the weight of a box of cereal is 18.9 oz ± .2 oz. The actual mean and standard deviation from a sample of 200 boxes is 18.70 oz and 0.10 oz, respectively. What are the Cp and Cpk?

Answer 1

Cp = 0.667, Cpk = 0

Step-by-step explanation:

Given the following :

Specification = 18.9 oz ± .2 oz

Actual mean (m) = 18.70 oz

Standard deviation (sd) = 0.10 oz

Upper specification limit (USL) = (18.9 + 0.2) = 19.1 oz

Lower specification limit (LSL) = (18.9 - 0.2) = 18.7 oz

Cp formula :

(USL - LSL) / 6(sd)

(19.1 - 18.7) / 6(0.1)

Cp = 0.4 / 0.6 = 0.667

Cpk = min(CpU, CpL)

CpU = (USL - m) / 3(sd)

CpU = (19.1 - 18.7) / 3(0.1)

CpU = 0.4 / 0.3 = 1.333

CpL = (m - LSL) / 3(sd)

CpL = (18.7 - 18.7) / 3(0.1)

CpL = 0 / 0.3 = 0

Cpk = min(1.333, 0)

Minimum value is 0, hence Cpk = 0