Question

Canine Gourmet Super Breath dog treats are sold in boxes labeled with a net weight of 9 ounces ​( 255 ​grams) per box. Each box contains 6 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 44.0 grams so that the average net weight per box of 6 packets will be 264 grams. Tolerances are set for the box to weigh 264 plus or minus ± 15 15 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 43.0 grams.

Is the packaging process​ capable? Is an adjustment​ needed? Since the process capability​ index, Cpk​, is ​, the process...is not capable is capable

Answer 1

USL = 264 + 15 = 279 gm
LSL = 264 - 15 = 249 gm

Process mean = 43.0*6 = 258 gm

Note that the std. dev. of 1.02 grams is for the packet filling process.

For the entire box of 6 samples, it will be 1.02 * SQRT(6) = 2.4985

C_pl = (Mean - LSL) / 3.Sigma = (258 - 249) / (3*2.4985) = 1.20
C_pu = (USL - Mean) / 3.Sigma = (279 - 258) / (3*2.4985) = 2.81

C_pk = min(C_pl, C_pu) = 1.20 which is less than 1.33 and the process ia not capable.