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 43.5 grams so that the average net weight per box of 8 packets will be 348 grams. Tolerances are set for the box to weigh 348plus or minus13 grams. The standard deviation for the​ packet-filling process is 1.03 grams. The target process capability ratio is 1.67. One​ day, the ​packet-filling process average weight drifts down to 42.5 grams. Is the packaging process​ capable? Is an adjustment​ needed?

Answer 1

The packaging process is capable, but an adjustment is needed due to the deviation in average weight. Calculating the process capability index will provide more insight.

Step-by-step explanation:

The packaging process in question is capable, as the process capability ratio is 1.67 which exceeds the target of 1.0. However, an adjustment is needed as the average weight per packet has drifted down to 42.5 grams, which is below the design specification of 43.5 grams.

To determine if the adjustment is required, we can calculate the process capability index (Cpk) which takes into account the deviation from the target mean as well as the variability of the process. Cpk can be calculated using the formula:

Cpk = min((USL - μ) / (3σ), (μ - LSL) / (3σ))

where USL is the upper specification limit, LSL is the lower specification limit, μ is the mean, and σ is the standard deviation. Comparing the calculated Cpk value with the target process capability ratio will help determine if the adjustment is needed.

Answer 2

Cp= tolerance range/process range

=( upper specification limit – lower specification limit)/6*sigma

= 354-334/6*1.02

= 3.27

Cp>1.33, the process is capable

upper specification limit(usl) =354gms

lower specification limit(lsl) = 334gms

Target Process capability is 1.33

Packet filling process average weight = 42 gms.

Average weight of box = 8*42 = 336gms

Cpk=min. [usl-mu/3*sigma,mu-lsl/3*sigms]

= min.[354-336/3*1.02,336-334/3*1.02]

= min.[5.88,0.65]

=0.65

Process variability is too large therefore adjustment is required