(Statistical Process Control) A wood shop produces processed wood chips with high precision. The shop wants to know whether the process is still controlled using statistical process control methods. The shop owner measured the length with 5 samples every day for 10 consecutive days according to the results in the table below. Day Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 1 174 147 145 141 144 2 139 134 135 135 174 3 135 150 130 174 143 4 142 136 145 141 133 5 142 132 146 134 149 6 143 143 141 145 144 7 134 174 144 141 144 8 133 139 146 140 145 9 140 135 135 133 174 10 136 132 130 174 145   From the data above, the shop owner asks you as a quality expert to determine whether the production process is still under control with regard to quality. Calculate LCL-X and UCL-X from these measurements and make a sketch of the X-Chart Calculate the LCL-R and UCL-R from these measurements and make a sketch of the R-Chart Analyze whether the process is still controlled or not. Explain your reasons.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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(Statistical Process Control)

A wood shop produces processed wood chips with high precision. The shop wants to know whether the process is still controlled using statistical process control methods. The shop owner measured the length with 5 samples every day for 10 consecutive days according to the results in the table below.

Day

Sample 1

Sample 2

Sample 3

Sample 4

Sample 5

1

174

147

145

141

144

2

139

134

135

135

174

3

135

150

130

174

143

4

142

136

145

141

133

5

142

132

146

134

149

6

143

143

141

145

144

7

134

174

144

141

144

8

133

139

146

140

145

9

140

135

135

133

174

10

136

132

130

174

145

 

From the data above, the shop owner asks you as a quality expert to determine whether the production process is still under control with regard to quality.

  1. Calculate LCL-X and UCL-X from these measurements and make a sketch of the X-Chart
  2. Calculate the LCL-R and UCL-R from these measurements and make a sketch of the R-Chart
  3. Analyze whether the process is still controlled or not. Explain your reasons.
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