Pulley Engineering manufactures needle bearings for use in high-tech machinery. The target diameter for one particular bearing is 0.125 inches. The quality control staff has taken 15 samples of five observations each when the manufacturing processes were under control and has measured the diameter. The results are as follows:

Use these data to develop control limits for the X and R charts. In addition, suppose engineering has established upper and lower tolerance limits of 0.129 inches and 0.121 inches, respectively.
Calculate the process capability ratio and interpret the results.

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Observation SAMPLE 1 2 3 4 5 1234567 1 0.1253 0.1262 0.1254 0.1240 0.1230 2 0.1242 0.1247 0.1251 0.1238 0.1241 0.1225 0.1258 0.1229 0.1242 0.1255 0.1249 0.1259 0.1249 0.1240 0.1257 0.1245 0.1252 0.1261 0.1238 0.1225 6 0.1273 0.1234 0.1248 0.1241 0.1260 0.1226 0.1239 0.1227 0.1252 0.1259 8 0.1244 0.1238 0.1254 0.1261 0.1260 9 0.1236 0.1262 0.1250 0.1247 0.1250 10 0.1251 0.1264 0.1233 0.1233 0.1246 11 0.1253 0.1248 0.1237 0.1252 0.1226 12 0.1232 0.1251 0.1259 0.1263 0.1257 13 0.1231 0.1242 0.1256 0.1252 0.1257 14 0.1256 0.1240 0.1246 0.1250 0.1252 15 0.1243 0.1240 0.1239 0.1262 0.1246