Question

Consider a firm that makes bags of Jelly Belly jellybeans. For each bag, the upper spec limit is 365 jellybeans, the lower spec limit is 333 jellybeans, and the standard deviation of the process is 4 jelly beans. a) If the mean (target) of the process is 350 jellybeans, is the process capable?

Answer 1

The process of making bags of Jelly Belly jellybeans is capable, with a process capability index (Cp) of 1.33, which is greater than the threshold of 1.0.

Step-by-step explanation:

Process Capability

To determine if the process of making bags of Jelly Belly jellybeans is capable, we calculate the process capability indices. The process capability index (Cp) compares the width of the process spread (six times the standard deviation) to the width of the specification limits (USL-LSL). The formula for Cp is:

Cp = (USL - LSL) / (6σ)

Given: USL = 365, LSL = 333, and standard deviation (σ) = 4. The mean (target) is 350 jellybeans.

Cp = (365 - 333) / (6*4) = 32 / 24 = 1.33

A process is generally considered capable if Cp > 1.0. Since 1.33 > 1.0, the process of making jellybean bags is capable.