Question

"The Crunchy Potato Chip Company packages potato chips in a process designed for 10.0 ounces of chips with an upper specification limit of 10.5 ounces and a lower specification limit of 9.5 ounces. The packaging process results in bags with an average net weight of 9.8 ounces and a standard deviation of 0.12 ounces. The company wants to determine if the process is capable of meeting design specifications."

Answer 1

The process does not meets the specifications.

Explanation:

It is provided that the Crunchy Potato Chip Company packages potato chips in a process designed for 10.0 ounces of chips.

The value of upper specification limit is, USL = 10.5 ounces.

The value of lower specification limit is, LSL = 9.5 ounces.

The mean weight of the chips bags is,
`\bar X=9.8\ ounces`.

And the standard deviation weight of the chips bags is,
`\sigma=0.12\ ounces`.

Compute the value of process capability as follows:

`C_{p_(k)}=min \{C_{p_(L)},\ C_{p_(U)}\}`

Compute the value of
`C_{p_(L)}` as follows:

`C_{p_(L)}=(\bar X-LSL)/(3 \sigma)=(9.8-9.5)/(3* 0.12)=0.833`

Compute the value of
`C_{p_(K)}` as follows:

`C_{p_(K)}=(USL-\bar X)/(3 \sigma)=(10.5-9.8)/(3* 0.12)=1.944`

The value of process capability is:

`C_{p_(k)}=min \{C_{p_(L)},\ C_{p_(U)}\}`

`=min\{0.833,\ 1.944\}\\=0.833`

The value of process capability lies in the interval 0 to 1. So the process is not capable of meeting design specifications.

Thus, the process does not meets the specifications.