Final answer:
The Canine Gourmet super breath dog treats packaging process has a high capability ratio despite the average weight drifting down to 42 grams per packet. The process is capable in terms of variability, but an adjustment is needed to meet the average net weight per box requirement.
Step-by-step explanation:
To ascertain whether the packaging process for Canine Gourmet super breath dog treats is capable, we have to consider the process capability ratio (Cp) and the mean weight drift in the packet-filling process. A target Cp of 1.33 indicates a good process ability to meet the requirements within given tolerances. The packet-filling process has a specification limit of 344+/- 10 grams (tolerances), set on the basis of 8 packets per box, leading to a target weight of 355 grams.
The process capacity can be calculated using the formula:
Cp = (USL – LSL) / (6 * standard deviation)
Where USL and LSL are the upper and lower specification limits, respectively.
Given the drift to an average of 42 grams per packet, the box's average weight decreases:
Average weight per box = 42 grams per packet * 8 packets = 336 grams
This average is below the target of 355 grams, and also below the lower specification limit after considering the tolerance. The stated standard deviation of the packet-filling process is 1.02 grams. Substituting in the Cp formula, we get:
Cp = (354 - 334) / (6 * 1.02) = 20 / 6.12 = 3.27, which is much higher than the target Cp of 1.33.
Therefore, although the capability ratio is adequate, the process mean is off target (the average weight has drifted down), so an adjustment is necessary to bring the mean weight back up to the specified 43 grams per packet to ensure that the average net weight per box meets the 355-gram target.
By considering the actual drift in process and the calculation for process capability with respect to the standard deviation, we can conclude that the packaging process is capable in terms of variability, but it is not correctly centered, necessitating an adjustment.