The quality controller of a large pastry production wants to monitor the usage-r

Question

The quality controller of a large pastry production wants to monitor the usage-rate consistency of chocolate chips by one of her operators who uses a scoop to sprinkle chocolate chips on cookies. To that end, she asked the operator to take eight samples of five scoops each over a four hour period. The following table presents her findings 3 Measurement Time 8:30 a.m 9:00 a.m 9:30 a.m 10:00 a.m 10:30 a.m 11:00 a.m. 11:30 a.m. 12:00 noon Sample ms of chocolate chips in the scoo 195 210 170 + n 69 +n 168 + n 172 +n 175 + n 165 + n 178 + n 171 +n 210 160 220 205 180 200 220 174 215 185 235 160 210 235 180 200 205 190 195 3 205 214 190 205 170 Example: Measurement for the first scoop of Sample # 1-170 + n 170 + 45-215 grams Measurement for the first scope of Sample # 2-169 + n-169 + 45-214 grams Measurement for the first scope of Sample # 3-168 + n-168 + 45-213 grams Measurement for the first scope of Sample # 4-172 + n-172 + 45-217 grams Measurement for the first scope of Sample # 5-175 + n-175 + 45-220 grams Measurement for the first scope of Sample # 6-165 + n-165 + 45-210 grams Measurement for the first scope of Sample # 7 = 178 + n = 178 + 45 = 223 grams Measurement for the first scope of Sample # 8 = 171 + n = 171 + 45 = 216 grams

Explanation / Answer

A.

B.

C.

D.

E.

If X bar bar = 200

R bar = 68

Avg of X 1 to X5 Range of R1 to R5 Sample X1 X2 X3 X4 X5 X bar R UCLx LCLx UCLr LCLr n= 5 1 218 195 190 210 210 204.6 28 229.513 178.737 93.016 0 UCL (R) = R-bar x D4 93.016 2 217 210 215 160 210 202.4 57 229.513 178.737 93.016 0 LCL(R) = R-bar x D3 0 3 216 215 185 220 235 214.2 50 229.513 178.737 93.016 0 UCL (X-bar) = X-bar-bar + (A2 x R-bar) 229.513 4 220 205 235 205 180 209 55 229.513 178.737 93.016 0 LCL(X-bar) = X-bar-bar - (A2 x R-bar) 178.737 5 223 215 160 180 200 195.6 63 229.513 178.737 93.016 0 For N=5 6 213 214 205 200 205 207.4 14 229.513 178.737 93.016 0 D4 2.114 7 226 190 210 220 190 207.2 36 229.513 178.737 93.016 0 D3 0 8 219 205 170 174 195 192.6 49 229.513 178.737 93.016 0 A2 0.577 204.125 44.0000 X bar bar R bar

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