Question

53.6 521 16. The full size for a small bag of peanuts distributed by popular airline is 50 grams. The producer wishes to set up a set of control charts for this process and collects the data shown in the table. Sample Item 31 Item #2 Item 3 7 54.5 54.3 54.1 53.3 216.2 50.6 535 53.7 211.4 54.3 50.4 207.9 527 52.1 51.3 52.3 208.4 52.2 51.2 54.2 54.1 211.7 51.6 51.5 54.7 52.4 210.2 52.8 53.8 53.6 214.2 50.4 53.4 52.8 209.8 50.2 50.7 52.2 205.0 From these data, determine: (a) what are the upper and lower control limits of their X-bar chart? (b) what are the upper and lower control limits of their R-chart? UCL Page 5 of 7

Answer 1

H I A 1 Sample B C D E F G Item #1 Item #2 Item #3 Item #4 Average Range 54.5 54.3 54.1 53.3 54.05 1.2 50.6 53.5 53.7 53.6 52.85 3.1 51.1 54.3 50.4 52.1 51.975 52.7 52.1 51.3 52. 3 52.1 52.2 51.2 54.2 54.1 52.925 51.6 51.5 54.7 52.4 52.55 54 52.8 53.8 53.6 53.55 53.2 50.4 53.4 52.8 52.45 51.9 50.2 52.2 51.25 2 9 50.7 52.63333 2.444444 12 Average 13 14 15

Formula

1 Sample 2 1 32 4 3 5 4 Item #1 54.5 50.6 51.1 52.7 52.2 51.6 54 53.2 51.9 Item #2 54.3 53.5 54.3 52.1 51.2 51.5 52.8 50.4 50.2 Item #3 54.1 53.7 50.4 51.3 54.2 54.7 53.8 53.4 50.7 Item #4 53.3 53.6 52.1 52.3 54.1 52.4 Average Range =AVERAGE(B2:E2) =MAX(B2:E2)-MIN(B2:E2) SAVERAGE(B3:E3) =MAX(B3:E3)-MIN(B3:E3) AVERAGE(B4:54) =MAX(B4:54)-MIN(B4:54) FAVERAGE(B5:E5) =MAX(B5:E5)-MIN(B5:E5) =AVERAGE(B6:E6) =MAX(B6:16)-MIN(B6:16) FAVERAGE(B7:E7) =MAX(B7:E7)-MIN(B7:E7) FAVERAGE(B8:E8) =MAX(B8:58)-MIN(B8:E8) SAVERAGE(B9:E9) =MAX(B9:E9)-MIN(B9:19) =AVERAGE(B10:E10) =MAX(B10:E10)-MIN(B10:E10) 53.6 52.8 76 87 98 10 9 11 12 Average 13 52.2 =AVERAGE(F2:F10) =AVERAGE(G2:G10)

a)
UCL = x-bar-bar + A2*R-bar [for sample size 4 , A2 = 0.729]

= 52.63333333+ 0.729*2.444444444 = 54.41533333

LCL = x-bar-bar - A2*R-bar [for sample size 4 , A2 = 0.729]

= 52.63333333- 0.729*2.444444444 = 50.85133333

b)

R-chart

UCL = D4*R-bar [for sample size 4 , D4 = 2.282] = 2.282*2.444444444 = 5.578222221
LCL = D3*R-bar [for sample size 4 , D3 = 0] = 0