The data below represent the proportion of rejected castings for various defects

ID: 3205795 • Letter: T

Question

The data below represent the proportion of rejected castings for various defects on a particular production line. Make a P-chart using the data on the daily proportion of defects. Draw any useful information that can be gleaned from these data based on the P-chart.

5/1 5/2 5/3 5/6 5/7 5/8 5/9 5/10 5/13 5/28 5/29 5/30 5/ 31 6/3 6/12 Date No. made 115 192 146 350 284 236 353 193 212 174 329 289 238 157 162 No. Inspected 26 3177 128 150 230 236 204 143 171 1136 276 156 234 108 85 1 54 43 63 67 73 69 49 42 44 100 47 98 43 36 No. defected 6/13 6/14 6/15 6/17 6/18 6/19 6/20 6/21 6/24 6/25 6/ 26 6/27 6/28 7/1 72 Date No. made 151 158 180 135 305 191 169 170 309 104 190 162 313 138 295 No. Inspected 55 158 150 88 305 147 167 159 266 93 190 128 259 127 158 69 61 73 101 126 46 94 85 135 43 51 No. defected 290 104 112 137 7/3 7/5 7/8 7/9 7/10 7/11 7/29 7/30 7 31 8/1 8/2 8/5 8/6 8/7 8/8 Date No. made 164 174 188 149 164 134 319 135 184 180 141 152 142 182 159 164 170 140 94 151 83 240 124 173 166 141 103 128 161 140 nspected No, No. defected 70 74 80 51 84 43 144 57 63 78 69 38 44 42 39 8/9 8/12 8/13 8/14 8/15 8/16 8/28 8/29 8/30 8/ 31 9/3 9/4 9/5 9/6 9/7 Date No. made 266 225 346 355 308 173 101 352 165 333 322 188 179 125 335 No. Inspected 142 3192 302 329 273 147 23 255 165 296 236 172 144 80 270 No. defected 51 68 128 161 125 66 7 49 35 79 77 36 28 25 65 9/9 9/10 9/12 9/13 9/24 9/25 9/26 9/27 Date No. made 170 157 239 85 130 188 188 150 142 212 76 99 129 14 No. Inspected 147 35 60 21 26 62 2 4 No. defected

Explanation / Answer

Date

No. made

No. defected

Proportion

01-May

115

0.008695652

02-May

192

0.28125

03-May

146

0.294520548

06-May

350

0.18

07-May

284

0.235915493

08-May

236

0.309322034

09-May

353

0.195467422

10-May

193

0.25388601

13-May

212

0.198113208

28-May

174

0.252873563

29-May

329

100

0.303951368

30-May

289

0.162629758

31-May

238

0.411764706

03-Jun

157

0.27388535

12-Jun

162

0.222222222

13-Jun

151

0.19205298

14-Jun

158

104

0.658227848

15-Jun

180

112

0.622222222

17-Jun

135

0.511111111

18-Jun

305

137

0.449180328

19-Jun

191

0.319371728

20-Jun

169

0.431952663

21-Jun

170

101

0.594117647

24-Jun

309

126

0.40776699

25-Jun

104

0.442307692

26-Jun

190

0.494736842

27-Jun

162

0.524691358

28-Jun

313

135

0.431309904

01-Jul

138

0.311594203

02-Jul

295

0.172881356

03-Jul

164

0.426829268

05-Jul

174

0.425287356

08-Jul

188

0.425531915

09-Jul

149

0.342281879

10-Jul

164

0.512195122

11-Jul

134

0.320895522

29-Jul

319

144

0.451410658

30-Jul

135

0.422222222

31-Jul

184

0.342391304

01-Aug

180

0.433333333

02-Aug

141

0.489361702

05-Aug

152

0.25

06-Aug

142

0.309859155

07-Aug

182

0.230769231

08-Aug

159

0.245283019

09-Aug

266

0.191729323

12-Aug

225

0.302222222

13-Aug

346

128

0.369942197

14-Aug

355

161

0.453521127

15-Aug

308

125

0.405844156

16-Aug

173

0.38150289

28-Aug

101

0.069306931

29-Aug

352

0.139204545

30-Aug

165

0.212121212

31-Aug

333

0.237237237

03-Sep

322

0.239130435

04-Sep

188

0.191489362

05-Sep

179

0.156424581

06-Sep

125

0.2

07-Sep

335

0.194029851

09-Sep

170

0.205882353

10-Sep

157

0.229299363

12-Sep

239

0.251046025

13-Sep

0.247058824

24-Sep

130

0.2

25-Sep

188

0.329787234

26-Sep

188

0.010638298

27-Sep

150

0.026666667

14047 4317

n-bar=En/k

=14047/68

=206.5735

p-bar=4317/14047

=0.3073

=0.31 approx

p-bar+-3*sqrt(p-bar(1-p-bar)/n-bar)

0.31+-3*sqrt(0.31(0.69)/206.5735)

0.31+-0.0965

LCL=0.31-0.0965=0.2135

UCL=0.31+0.0965=0.4065

Conclusion: The proportion of defects is too high.