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1. For constructing a X-bar chart, subgroup sample average (x bar) and range(r) are computed for each of 24 preliminary sampl


24 1 1. For constructing a X-bar chart, subgroup sample average (x bar) and range (r) are computed for each of 24 preliminary
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Answer #1

(a) x̅bar = 816/24 = 34

UCL = x̅bar + A2Rbar = 34 + 0.577*4.7083 = 36.7167

LCL = x̅bar - A2Rbar = 34 - 0.577*4.7083 = 31.2833

(b) Rbar = 113/24 = 4.7083

UCL = D4*Rbar = 2.114*4.7083 = 9.9533

LCL = D3*Rbar = 0.0000

(c) P (z = (36 - 34)/ 0.9056) - P (z = (32 - 34)/ 0.9056) = P (z = 2.21) - P (z = -2.21) = 0.9864 - 0.0136 = 0.9728

The fraction of defectives = 1 - 0.9728 = 0.0272 = 2.72%

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