At regular intervals during the last three work shifts, technicians at the Willard Bolt Company have taken a total of 40 samples, each with n = 5 bolts. The measurement taken is the bolt diameter, in inches, and the data are listed below.

1. Using only the first 20 samples, construct 3-sigma control charts for the mean and range. For each chart, plot all 20 sample means or ranges. Using the mean and range charts together, does the process appear to have been in control when each of these samples was taken?
2. If the process was in control for samples 120, use the upper and lower control limits from these samples in a second set of control charts that includes all 40 samples. On this basis, was the process in control during the collection of samples 2140? Use the mean chart and the range chart together in evaluating process control.
3. If the process was not in control for each of samples 120, assume that an assignable cause has been identified for those that were outside the limits. Use the remaining samples as the basis for UCL and LCL values with which to evaluate samples 2140. Note: The preceding possibilities would be likely to occur in practice, since data that have already been gathered through sample 20 might be employed in monitoring the process through samples 2140. In part 2, all of the samples will be considered at once.

Diameter

1.355

1.301

1.277

1.263

1.329

1.335

1.330

1.244

1.300

1.253

1.389

1.235

1.342

1.397

1.243

1.287

1.319

1.231

1.276

1.260

1.249

1.297

1.342

1.313

1.300

1.348

1.280

1.322

1.359

1.310

1.305

1.327

1.293

1.369

1.358

1.340

1.257

1.339

1.351

1.335

1.347

1.327

1.314

1.292

1.314

1.206

1.400

1.300

1.325

1.214

1.281

1.289

1.321

1.308

1.210

1.319

1.287

1.327

1.336

1.297

1.204

1.267

1.236

1.356

1.306

1.317

1.325

1.259

1.335

1.307

1.280

1.300

1.317

1.351

1.348

1.316

1.335

1.282

1.232

1.287

1.199

1.367

1.256

1.395

1.175

1.230

1.372

1.410

1.345

1.340

1.281

1.271

1.332

1.387

1.321

1.375

1.197

1.337

1.368

1.294

1.300

1.276

1.258

1.232

1.267

1.343

1.244

1.328

1.331

1.198

1.267

1.290

1.299

1.279

1.311

1.258

1.321

1.248

1.313

1.308

1.323

1.137

1.207

1.263

1.231

1.281

1.412

1.208

1.316

1.247

1.342

1.235

1.311

1.323

1.193

1.274

1.266

1.293

1.282

1.434

1.322

1.309

1.366

1.271

1.352

1.242

1.283

1.316

1.251

1.256

1.376

1.258

1.253

1.307

1.348

1.404

1.350

1.305

1.424

1.630

1.308

1.319

1.290

1.294

1.319

1.313

1.220

1.423

1.330

1.227

1.168

1.360

1.368

1.236

1.342

1.235

1.337

1.233

1.343

1.230

1.259

1.278

1.225

1.231

1.392

1.346

1.314

1.322

1.269

1.268

1.311

1.343

1.258

1.326

1.240

1.319

1.282

1.298

1.207

1.362