Problem: The data shown in the table below are concentration readings from a chemical process, made every 30 minutes (read down; then across from left to right e.g. 204, 202, 201, etc.)
Chemical Process Concentration Readings
204 202 201 202 197 201 198 188 195 189 195 192 196 194 196 199 197 197 192 195
190 196 199 203 199 207 204 207 209 205 202 200 208 214 205 211 212 214 210 208
208 209 209 206 200 203 202 195 196 203 196 197 197 203 205 194 199 201 198 202
207 204 201 197 189 189 196 193 193 198 194 198 199 204 200 203 200 197 196 202
200 202 202 207 206 211 205 210 210 198 189 194 194 198 196 200
(a) Calculate the sample autocorrelation function and provide an interpretation.
(b) Construct an individuals control chart with the standard deviation estimated using the moving range method. Provide an interpretation of this control chart.
(c) Given the first-order autoregressive model xt = 50.77 + 0.746xt-1 + €t, apply this model to the data. Set up an individuals control chart on the residuals from this model. Interpret this chart.
(d) Explain your observations in parts (b) and (c).