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?

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

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