The Goodman Tire and Rubber Company periodically tests its tires for tread wear

Question

The Goodman Tire and Rubber Company periodically tests its tires for tread wear under simulated road conditions. To study and control the manufacturing process, 20 samples, each containing three radial tires, were chosen from different shifts over several days of operation, the data collected are shown below. Assuming that these data were collected when the manufacturing process was believed to be operating in control, develop the R and charts. Click on the datafile logo to reference the data. Use Table 19.3 DATA file Sample Tread Wear 18 35 35 30 40 17 17 32 17 35 18 30 32 18 Hundredths of an inch R Chart: (to 2 decimals). If your answer is zero enter "O UCL LCL = Chart: (to 1 decimal) UCL - LCL =

Explanation / Answer

FROM above:

R chart : for n=3 sample size constnat D3 =0 ; D4=2.575

hence UCL =D4*Ravg =2.575*11.4 = 29.36

LCL =D3*Ravg =0*11.4 =0

X chart : for n=3 ; constant A2 =1.023

hence UCL =xbar +A2*Ravg =40.8

LCL =xbar -A2*Ravg =17.5

sample no Range 1 31 42 28 14 2 26 18 35 17 3 25 30 34 9 4 17 25 21 8 5 38 29 35 9 6 41 42 36 6 7 21 17 29 12 8 32 26 28 6 9 41 34 33 8 10 29 17 30 13 11 26 31 40 14 12 23 19 25 6 13 17 24 32 15 14 43 35 17 26 15 18 25 29 11 16 30 42 31 12 17 28 36 32 8 18 40 29 31 11 19 18 29 28 11 20 22 34 26 12 total 566 584 600 228 average 11.4

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