Question

Canine Gourmet super breath dog treats are sold in boxes labeled with a net weight of 12 ounces (340 grams) per box. Each box contains 8 individual 1.5-ounce packets. To reduce the chances of shorting the customer, product design specifications call for the packet-filling process average to be set at 43 grams so that the average net weight per box of 8 packets will be 355 grams. Tolerances are set for the box to weigh

344+/- 10 grams. The standard deviation for the packet-filling process is 1.02 grams. The target process capability ratio is 1.33 . One day, the packet-filling process average weight drifts down to 42 grams. Is the packaging process capable? Is an adjustment needed?

Answer 1

The packaging process for the dog treats initially had a capability ratio well above the target, indicating it was capable. However, after drifting to a lower average fill weight, while still being capable, the process average is too close to the lower specification limit. An adjustment is recommended to ensure continued compliance with weight specifications.

Step-by-step explanation:

To determine if the packaging process for Canine Gourmet super breath dog treats is capable and whether an adjustment is needed, we consider the given process capability ratio, tolerances, and the standard deviation of the packet-filling process. The process capability ratio (Cp) is calculated using the formula Cp = (USL - LSL) / (6 * σ), where USL is the upper specification limit, LSL is the lower specification limit, and σ is the standard deviation. The tolerances provided for the box are 344 ± 10 grams, meaning USL = 354 grams and LSL = 334 grams. Given the standard deviation of 1.02 grams, we first calculate the original capability ratio using 43 grams as the process average before the drift.

Original Cp = (354 - 334) / (6 * 1.02) = 20 / 6.12 = 3.27, which is higher than the target capability ratio of 1.33, indicating the process was initially capable.

However, with the process average drifting down to 42 grams, the new average weight per box is 8 * 42 = 336 grams, which is just within the lower specification limit. We now need to determine if the process is still capable with the new average. Assuming this new process average and maintaining the same standard deviation and tolerances, the new capability ratio needs to be recalculated.

New Cp = (354 - 336) / (6 * 1.02) = 18 / 6.12 = 2.94, still higher than the target of 1.33.

Although the new Cp exceeds the target, the average has drifted too close to the lower specification limit. Even with a capable process, there's an increased risk of producing boxes that are underweight. Therefore, an adjustment to the filling process is recommended to maintain a safety margin within the specification limits and reduce the risk of customer dissatisfaction.

Answer 2

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.