anine Gour zi Supo B est dog tra s are sold in ba s labs d wth ret weght o 9 oun

Question

anine Gour zi Supo B est dog tra s are sold in ba s labs d wth ret weght o 9 ounces 255 gra ms per bo E ch bc o n ns 6 ncivídua 1 5-ounce pad 3. redus re chances o sho ang thc cus mer, product design spo ations cal cr 1n packet-filing p cce s "verage o be at at 43.5 gro sa that the average net weight per bo cre packets wil be 261 grams. To ances are set or the Dax bo wegh 261 1 1 1 grams. Tho st ??? devation for the pec er fil? process s 1.01 grams. The target process capabity to s 1 33. ne day, the p a et Ring proces8 average weght drifts down to 42.5 grams. Is the packsging procasa capable? la an adjustment neaced? r the peckesfling Snce the process capability index, Cktherocess snct capable nteryourresponse ounded to three decime'ciaces.) is not capabie capable

Explanation / Answer

Std deviation of Filling process for 1 packet = 1.01 grams

Variance of Filling process for 1 packet = 1.01^2 = 1.0201

Variance of Filling process for 6 packets = 1.01^2 + 1.01^2 + 1.01^2 + 1.01^2 + 1.01^2 + 1.01^2 = 6.1206

Std of Filling Process for 6 packet = Std Deviation for 1 box = sqrt(6.1206) = 2.474

From the problem statement we can see-

USL = 261+11 = 272

LSL = 261-11 = 250

Average = 261

We have calculated Std Dev = 2.474

CpU = (USL-Average)/(3*Std Dev) = (272-261)/(3*2.474) = 1.482

CpL =  (Average-LSL)/(3*Std Dev) = (261-250)/(3*2.474) = 1.482

Cpk = Min(CpU,CpL) = 1.482

Since the Process Capability index Cpk is 1.482, the process is capable and hence no adjustment is required.

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