Coffee Drinks, Inc. bottles a specific type of coffee. Each bottle should have a

Question

Coffee Drinks, Inc. bottles a specific type of coffee. Each bottle should have a net weight of 4 ounces. The machine that fills the bottles with coffee is new, and the operations manager wants to make sure that it is properly adjusted. The operations manager takes a sample of 8 bottles and records the average range in ounces for each sample. The data are given below. Also, note that every sample size for each sample is 10 bottles. (12 Points) Sample Mean 4 4.06 3.99 4 4.11 3.93 3.98 4.01 Range 41 .55 .48 .56 62 54 Identify the upper and lower control limits for the mean and range at a sigma of 3 a. b. Is the machine properly adjusted and in control? Explain your answers.

Explanation / Answer

a) here for mean : at sample size n=8 ; constnat A2 = 0.373

for LCL =Xbar -A2*Rbar = 4.01-0.373*0.505=3.822

UCL =Xbar +A2*Rbar = 4.01+0.373*0.505=4.198

for range at sample size n=8 ; constant D3 =0.136 ; D4 =1.864

hence LCL =D3*Rbar =0.136*0.505=0.069

and UCL =D4*Rbar =1.864*0.505 =0.941

b) as all values are within control limits therefore machine is properly adjusted

sample mean Range A 4 0.41 B 4.06 0.55 C 3.99 0.44 D 4 0.48 E 4.11 0.56 F 3.93 0.62 G 3.98 0.54 H 4.01 0.44 average 4.01 0.505

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