Question

A barbecue sauce producer sells their product in a​ 20-ounce bottle. Their historical process mean has been 20 ounces with a standard deviation of 0.25 ounces. If their tolerance limits are set at 20 ounces plus or minus 1​ ounce, what is the process capability ratio of the bottle filling​ process?

Answer 1

The process capability ratio for the BBQ sauce bottle filling process, with a specification range of ±1 ounce and a standard deviation of 0.25 ounces, is approximately 1.33, indicating a capable process.

Step-by-step explanation:

The process capability ratio (Cp) is a measure of how well a process can meet its specification limits. It is defined as the ratio of the specification range to the process variation, where the specification range is the difference between the upper and lower specification limits, and the process variation is generally 6 times the standard deviation (σ) assuming a normal distribution.

In this case, the upper tolerance limit is 21 ounces (20 + 1), and the lower tolerance limit is 19 ounces (20 - 1), which means the total tolerance range is 2 ounces (21 - 19). With a standard deviation of 0.25 ounces, the process variation is 6×0.25 = 1.5 ounces. Hence, the process capability ratio (Cp) is calculated as the tolerance range divided by the process variation: Cp = 2 / 1.5 ≈ 1.33.

Therefore, the process capability ratio for the barbecue sauce bottle filling process is approximately 1.33, indicating that the process is capable of producing within the specification limits provided.

Answer 2

1.33

Step-by-step explanation:

Data provided in the question:

Mean = 20

Tolerance limit = 20 ± 1

Standard deviation, s = 0.25 ounces

Now,

Upper specification limit, USL = 20 + 1 = 21

Lower specification limit, LSL = 20 - 1 = 19

also,

capability ratio =
`(USL-LSL)/(6s)`

Thus,

Capability ratio =
`(21-19)/(6*0.25)`

or

Capability ratio =
`(2)/(1.5)`

or

Capability ratio = 1.33