Question: Problem 1 The table below shows the actual temperature (in degrees Fahrenheit) of 6 cups of coffee bought from a gourmet coffee shop on 10

Problem 1 The table below shows the actual

Problem 1 The table below shows the actual temperature (in degrees Fahrenheit) of 6 cups of coffee bought from a gourmet coffee shop on 10 consecutive days. Federal health regulations require that coffee temperatures be between certain limits. Assuming the standard deviation for the temperature population is 9, use statistical process control (SPC) method to find the control limits for the average temperature of each sample and verify if the process is under control. Day 1 160 Day 2 165 Day 3 169 Day 4 155 Day 5 159 Day 6 163 166 Day 7 155 Day 10 171 Day 8 172 163 166 173 162 164 165 167 162 156 167 Day 9 174 165 169 167 180 171 168 168 169 167 162 Cup 1 Cup 2 Cup 3 Cup 4 Cup 5 Cup 6 169 159 155 165 164 165 159 157 173 162 169 163 166 168 172 164 159 164 179 171 168 173 159 174 173 169 168 172 172 Recently the following data were collected: Day 11 158 Day 12 160 Day 13 145 Day 14 155 150 170 153 150 157 168 154 Cup 1 Cup 2 Cup 3 Cup 4 Cup 5 Cup 6 157 159 163 152 164 172 170 160 150 150 165 155 155 Using SPC method, find out whether the process is still under control. Problem 2 Solve the previous problem assuming that we do not know the standard deviation of the temperature population. A1 fx A F G H 1 J L M 1 1 2 Day 5 Day 10 171 3 159 4 165 162 B D E Measure of Performance: Average temperature Day 1 Day 2 Day 3 Cup 1 160 165 169 Cup 2 173 156 162 Cup 3 171 167 168 Cup 4 159 165 157 Cup 5 164 159 173 Cup 6 171 168 173 X_bar Day 4 155 164 168 155 159 159 5 Day 6 163 166 167 165 164 173 Day 8 172 163 166 168 172 Day 7 155 167 162 163 166 169 Day 9 174 165 169 167 180 169 162 169 174 6 169 164 179 7 8 8 168 172 172 9 10 11 Sigmar 9 12 Sample Size (n) = Number of Samples (m) = 13 14 15 16 X_bar_bar = UCL =X_bar_bar+3(sigma/sqrt(n))= LCL =X_bar_bar-3(sigma/sqrt(n))= 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Is the process under control? What are recommended actions? 36 37 38 39 Day 13 145 40 Day 12 160 170 157 41 Future samples: Day 11 Cup 1 158 Cup 2 150 Cup 3 157 Cup 4 159 Cup 5 164 Cup 6 155 153 42 168 Day 14 155 150 154 152 150 165 43 163 170 44 172 160 150 45 155 Is the process under control? What are recommended actions? Day 12 160 Day 13 145 Day 14 155 150 170 153 Future samples: Day 11 Cup 1 158 Cup 2 150 Cup 3 157 Cup 4 Cup 5 164 Cup 6 155 X bar 157 168 154 159 163 170 152 172 160 150 165 155 150 Is the process still under control? What are recommended actions

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