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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?

Respuesta :

Answer:

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

                  Canine Gourmet Super Breath dog treats

  • Is the packaging process​ capable :

Cp= tolerance range

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

Cp= 354-334/6*1.02

Cp= 3.27

Cp>1.33

Thus, the process is capable.

  • Is an adjustment​ needed:

Given information:

  • 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]

  • Cpk= min.[354-336/3*1.02,336-334/3*1.02]
  • Cpk= min.[5.88,0.65]
  • Cpk=0.65

Process variability is too large therefore adjustment is required.

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