TEMA 2 S se analizeze n repartiiile normal i lognormal rezistenele de curgere

ale unui oel dac rezultatele ncercrilor la compresiune pe 250 de epruvete sunt cele din tabel.

Datele de intrare vor fi grupate pe intervale de mrimea 2

5,2mm

N .

Se vor calcula: - valoarea central a intervalului; - frecvenele absolute; - frecvenele relative;

ale datelor din fiecare interval. Apoi ve vor calcula media, abaterea i coeficientul de variaie ale

rezistenelor cu formulele:

171

171

1

j

j

X

x

m - media

171

171

1

2

j

Xj

X

mx

X

XX

mV

Pentru repartiia lognormal se vor calcula:

2ln 1ln

x

xx

V

mm

,

2ln 1ln xx V

xx km

p exlnln

%

Se vor calcula fractilii pentru:

5,01,005,001,000135,0001,0 ,,,,, xxxxxx

Nr crt Nr lucru Val de lucru

Nr lucru final

Val de lucru finale

1 2.360127 552.360127 3.202249869 554.1786964

2 4.259484 554.259484 3.646652651 550.6514102

3 3.559688 553.559688 3.273114937 550.3705346

4 3.079683 553.079683 3.647905812 554.591913

5 1.958407 551.958407 1.585418 552.5156845

6 1.642161 551.642161 2.300784767 551.6059122

7 1.261712 551.261712 0.955099089 553.798182

8 4.368803 554.368803 2.390335957 553.9920714

9 0.133517 550.133517 4.067485637 550.1044707

10 1.350693 551.350693 3.308129922 552.7150154

11 2.68882 552.68882 1.038080158 554.8004504

12 0.241163 550.241163 2.939439723 552.3549724

13 0.983956 550.983956 0.473459674 551.9794194

14 3.845681 553.845681 4.506172285 554.3253409

15 3.946805 553.946805 3.694217368 550.7732779

16 3.405743 553.405743 2.527458682 550.8572293

17 2.786688 552.786688 4.148491734 554.8631478

18 3.114445 553.114445 4.557055898 552.6771661

19 0.553993 550.553993 3.081885939 551.1930263

20 2.315032 552.315032 4.184878207 550.1647073

21 0.800522 550.800522 4.203592345 550.7838905

22 4.132741 554.132741 3.982780461 553.6111559

23 2.882999 552.882999 0.978420348 552.692744

24 2.243402 552.243402 3.54653856 552.9976242

25 4.328409 554.328409 1.723448324 550.678582

26 4.975709 554.975709 0.230785884 554.6558799

27 0.889332 550.889332 0.692402685 553.4290211

28 2.317022 552.317022 4.694762303 554.8765869

29 4.700773 554.700773 1.055412248 552.3545018

30 3.827134 553.827134 0.502600814 551.9039532

31 1.145292 551.145292 0.193710132 554.2893078

32 3.640622 553.640622 3.97514762 550.0265199

33 4.540477 554.540477 1.171278407 554.9758308

34 3.478613 553.478613 4.126511302 551.8365585

35 4.52744 554.52744 3.251715835 551.566956

36 0.798856 550.798856 1.878578351 554.6688215

37 0.711435 550.711435 2.670288471 553.9756627

38 4.54624 554.54624 4.789094311 552.8878666

39 0.907668 550.907668 2.154058058 553.4708308

40 4.641366 554.641366 1.822934881 551.8497822

41 4.267662 554.267662 0.584768675 550.4981158

42 2.817173 552.817173 3.305181235 550.6488391

43 1.199318 551.199318 4.382824505 550.1177652

44 4.304469 554.304469 4.286666214 552.0542352

45 1.708095 551.708095 2.888114467 553.7352251

46 4.593036 554.593036 1.451257115 550.428303

47 3.291374 553.291374 1.923550066 554.5599993

48 1.497111 551.497111 2.683791957 552.3730128

49 1.906334 551.906334 2.808851965 552.2115072

50 0.734648 550.734648 0.494901733 550.0237998

51 1.382292 551.382292 0.845086409 552.0117515

52 4.79824 554.79824 4.346555045 553.239931

53 2.632285 552.632285 0.301985048 551.6112287

54 1.827704 551.827704 0.605083218 554.5840758

55 4.94303 554.94303 3.052427014 552.3185994

56 4.104815 554.104815 0.574027626 552.1146069

57 4.263581 554.263581 3.50864095 551.7066045

58 4.530906 554.530906 4.711098033 550.6901865

59 1.605564 551.605564 1.037264435 553.4485581

60 0.125759 550.125759 2.879226704 551.1929084

61 0.149838 550.149838 1.561887518 550.1139333

62 3.466795 553.466795 1.428009912 554.4250918

63 1.956183 551.956183 3.454986341 554.6955269

64 0.160969 550.160969 1.73253533 551.1440556

65 0.921059 550.921059 1.293150886 552.6932538

66 1.535383 551.535383 3.090951421 550.9714555

67 1.443713 551.443713 4.686267802 553.6740585

68 1.689031 551.689031 4.782779124 552.5015576

69 4.752872 554.752872 2.971547965 551.0888718

70 4.223678 554.223678 0.531671395 552.9805817

71 3.02954 553.02954 2.506667303 554.5307259

72 1.375357 551.375357 1.102075238 551.0306975

73 0.876679 550.876679 2.270766878 551.9306082

74 3.916922 553.916922 2.456007868 552.0416259

75 0.549906 550.549906 2.764872503 551.513507

76 4.099773 554.099773 2.452848848 551.2298288

77 0.36444 550.36444 0.715950124 554.9693951

78 0.994278 550.994278 0.568706246 551.5987408

79 0.97853 550.97853 1.417535932 552.5269439

80 3.402812 553.402812 2.829970516 554.9240057

81 0.239821 550.239821 0.599588242 552.0019476

82 3.104901 553.104901 0.192715636 553.4461236

83 0.675904 550.675904 2.582283051 550.1749302

84 0.81549 550.81549 1.663360949 551.8559318

85 0.427308 550.427308 4.206022114 550.136142

86 1.595782 551.595782 0.248308901 554.2943154

87 0.875308 550.875308 2.456086533 552.8717148

88 3.198968 553.198968 3.334657372 550.6198281

89 4.68922 554.68922 2.699569393 554.566756

90 4.421327 554.421327 1.433076115 553.727031

91 2.497841 552.497841 3.572182096 553.3091533

92 3.968873 553.968873 4.39350027 552.8976956

93 3.798593 553.798593 4.070156785 550.2712463

94 3.074151 553.074151 1.820717008 553.7003739

95 1.357998 551.357998 4.588860591 550.7437712

96 3.167427 553.167427 0.354465324 551.4441513

97 3.807784 553.807784 1.253358079 553.2399004

98 1.519649 551.519649 0.219460902 553.8477463

99 4.14298 554.14298 2.073765249 553.0252743

100 1.836327 551.836327 4.664892582 554.188263

101 1.043494 551.043494 3.478114841 553.5608944

102 2.933536 552.933536 3.535928218 553.6552939

103 3.58806 553.58806 0.858192115 550.2526586

104 3.456189 553.456189 4.759195811 552.4006221

105 2.403267 552.403267 1.901206428 552.8430918

106 3.751835 553.751835 2.379464279 554.5160084

107 0.343114 550.343114 4.778285356 554.7154656

108 2.200595 552.200595 4.887792252 553.6719714

109 0.792136 550.792136 1.812196174 552.1075005

110 4.07553 554.07553 4.21208257 553.43341

111 3.22977 553.22977 4.085180667 553.0947417

112 1.514994 551.514994 1.301063717 551.0526405

113 4.504542 554.504542 0.729002247 551.0061296

114 0.030695 550.030695 0.139352866 551.3030282

115 1.684491 551.684491 4.418265422 550.0863857

116 2.139218 552.139218 2.081012751 551.0776881

117 0.203658 550.203658 4.733469414 550.974095

118 4.09075 554.09075 0.440596317 551.2391937

119 2.145334 552.145334 1.896835125 552.3791303

120 4.206868 554.206868 2.958079664 550.0656591

121 2.486516 552.486516 1.042478173 553.7746609

122 1.898109 551.898109 2.879882243 552.627507

123 0.216196 550.216196 3.902776859 553.5992999

124 3.499922 553.499922 1.401643656 554.0270514

125 4.769584 554.769584 0.788142384 550.4078297

126 3.861901 553.861901 2.948941177 554.1442335

127 3.143877 553.143877 3.753850281 554.3426807

128 4.518001 554.518001 0.021869154 551.3906766

129 0.107562 550.107562 4.990077025 553.2190755

130 0.188916 550.188916 3.491151221 552.3874909

131 3.614412 553.614412 2.369909543 551.7512999

132 4.575872 554.575872 3.378542438 551.9688042

133 0.24863 550.24863 4.906167324 553.3797604

134 4.229501 554.229501 3.800118677 554.8117656

135 0.374242 550.374242 4.553066852 550.5982278

136 3.054325 553.054325 0.009402526 553.5023538

137 4.353167 554.353167 3.571240641 554.719378

138 2.700441 552.700441 3.925943358 554.5294651

139 3.091169 553.091169 3.025691654 551.0156709

140 0.636657 550.636657 0.558929041 553.7636099

141 2.384824 552.384824 4.9704868 551.6893161

142 0.719679 550.719679 4.527593984 552.1356577

143 1.432291 551.432291 2.135440718 554.8757131

144 1.323017 551.323017 0.611722494 553.2445596

145 3.003773 553.003773 2.52435526 554.3404207

146 2.600281 552.600281 2.012897355 552.2985507

147 4.108908 554.108908 1.46381837 553.277485

148 3.764341 553.764341 1.369574256 552.8834748

149 0.736677 550.736677 0.184474726 551.4370144

150 4.33354 554.33354 2.213637969 554.3711553

151 2.463711 552.463711 3.908972058 552.671662

152 3.229788 553.229788 0.560175936 551.3357989

153 0.174458 550.174458 4.766119653 550.6882034

154 0.643409 550.643409 1.176175439 554.12222

155 0.015121 550.015121 0.16212473 552.5228192

156 4.271811 554.271811 3.400512559 554.8187605

157 1.239462 551.239462 3.972765568 554.9609036

158 1.309417 551.309417 1.684438497 554.9572547

159 0.43042 550.43042 2.970069602 551.4957973

160 1.851841 551.851841 1.018391689 552.0602625

161 3.84932 553.84932 1.968937472 553.5267607

162 1.530453 551.530453 4.155255068 554.5725075

163 2.557769 552.557769 1.104924219 552.8460074

164 3.249104 553.249104 1.388782267 553.0917418

165 1.400214 551.400214 4.363037322 551.3182979

166 4.238475 554.238475 4.379077436 552.4847275

167 1.924537 551.924537 1.75651333 551.4319892

168 4.717753 554.717753 4.406293572 550.1182923

169 4.77329 554.77329 2.16185333 552.4775275

170 4.510135 554.510135 3.248244271 553.4002404

171 1.928881 551.928881 0.494499682 553.3903331

172 4.933143 554.933143 1.635123076 550.7952351

173 4.052847 554.052847 2.924472577 550.1760197

174 3.136848 553.136848 1.601211906 551.1768547

175 3.438008 553.438008 4.397329101 552.9728081

176 2.708709 552.708709 4.97765406 551.9515066

177 4.027053 554.027053 3.789754507 551.9404828

178 4.917845 554.917845 3.968722946 550.2749243

179 0.265314 550.265314 2.058849117 554.4632176

180 0.035247 550.035247 1.882638949 550.5827528

181 3.814501 553.814501 4.975322816 553.7973523

182 2.041519 552.041519 1.203132148 553.3343435

183 3.262145 553.262145 4.779655848 550.6705908

184 0.88297 550.88297 3.927503639 551.1189237

185 1.132966 551.132966 4.877476789 550.8350439

186 2.665335 552.665335 2.078987186 551.1297712

187 3.956636 553.956636 1.192241552 551.110347

188 3.764129 553.764129 1.658735397 553.7288611

189 2.108187 552.108187 0.919692705 554.6115466

190 3.622199 553.622199 4.875575833 553.4131103

191 1.137125 551.137125 2.607878256 550.6537281

192 3.490444 553.490444 2.734163066 552.9556763

193 4.259335 554.259335 2.876025996 550.4033068

194 3.626934 553.626934 3.751467713 550.3982517

195 2.316213 552.316213 3.88164643 551.6170222

196 3.162111 553.162111 4.933452513 550.8711029

197 1.162832 551.162832 1.6454459 554.2731705

198 1.447283 551.447283 2.793135619 550.1000699

199 1.370114 551.370114 0.177408022 552.1155553

200 4.261027 554.261027 2.667793319 551.9808474

201 1.068809 551.068809 0.429084859 550.7976395

202 4.105895 554.105895 1.558565469 550.7881766

203 0.691012 550.691012 1.489393826 552.7671446

204 2.221004 552.221004 3.369949377 554.3369065

205 1.539851 551.539851 2.950486367 550.3863703

206 3.906018 553.906018 1.254869623 552.4636393

207 0.401867 550.401867 2.793018145 554.2085832

208 3.448113 553.448113 3.635511576 550.6595056

209 1.081074 551.081074 0.233630421 554.1452398

210 2.807398 552.807398 3.61765305 552.8858373

211 0.768578 550.768578 0.622130731 550.170382

212 1.439309 551.439309 4.602246411 552.8197314

213 0.436312 550.436312 0.5808309 552.4469774

214 2.577749 552.577749 1.299991062 550.5991169

215 3.747025 553.747025 4.697670528 551.6103037

216 3.128865 553.128865 2.899925007 551.6239186

217 2.674783 552.674783 0.238211211 552.2656878

218 2.103359 552.103359 4.938833491 553.1505884

219 1.771785 551.771785 4.635343154 552.4324268

220 2.642696 552.642696 3.758158953 552.6068399

221 0.238005 550.238005 2.703494411 553.9045025

222 0.75485 550.75485 3.592398871 553.367637

223 0.984955 550.984955 4.499262391 552.2177251

224 1.970364 551.970364 4.489489563 554.6626789

225 2.133281 552.133281 2.5423093 551.2803648

226 4.258704 554.258704 0.829580596 550.3850782

227 3.487989 553.487989 1.658572869 551.9715045

228 0.380666 550.380666 4.381089191 551.6254893

229 4.546509 554.546509 1.444866476 552.755748

230 3.171285 553.171285 1.002326732 551.4540333

231 0.969251 550.969251 0.172963378 553.2859722

232 0.630212 550.630212 1.299667779 554.94614

233 4.300552 554.300552 3.340112452 550.3045935

234 2.452901 552.452901 4.638867123 552.1974906

235 2.307935 552.307935 2.070654647 553.1695103

236 2.74486 552.74486 3.630384318 553.4855428

237 3.171108 553.171108 2.474712903 550.597234

238 4.893449 554.893449 1.753192465 554.1063231

239 3.326054 553.326054 0.363132036 551.9282614

240 3.894477 553.894477 1.998856583 550.8287358

241 2.711764 552.711764 4.268226982 552.7914902

242 2.031406 552.031406 3.883886069 551.1584441

243 4.616581 554.616581 2.926108484 554.0275685

244 1.670107 551.670107 0.891575627 551.1271585

245 3.106023 553.106023 3.70749866 551.7924247

246 0.83331 550.83331 2.704354418 554.5704573

247 3.919408 553.919408 1.327751564 554.302609

248 0.838238 550.838238 0.234094027 551.8972528

249 4.959502 554.959502 1.790337044 551.8409776

250 2.259874 552.259874 3.043672191 554.6790884

Intervale Frecvente absolute

Frecvente relative

mx x

550 100 0,4 552,448 2,9942

552,5 92 0,368

3,2289

555 58 0,232

4,3172

4,5950

250 1

0,0045

0,7097

1,8221

2,3831

5,4937

0,0711

5,5325

0,0087

0,2199

3,5232

2,8058

2,5316

5,8314

0,0524

1,5758

5,2149

2,7704

1,3522

0,0597

0,3017

3,1320

4,8733

0,9618

5,8964

0,0088

0,2963

3,3892

5,8652

6,3883

0,3743

0,7768

4,9306

2,3328

0,1932

1,0455

0,3583

3,8033

3,2382

5,4315

0,1553

1,6561

4,0805

4,4592

0,0057

0,0561

5,8783

0,1906

0,6266

0,7007

4,5614

0,0168

0,1114

0,5502

3,0911

1,0005

1,5761

5,4494

3,9076

5,0499

1,7011

0,0600

2,1812

1,5024

0,0028

1,8481

0,2833

4,3364

2,0097

0,2680

0,1654

0,8739

1,4847

6,3558

0,7218

0,0062

6,1290

0,1993

0,9956

5,1683

0,3509

5,3462

3,4077

0,1793

3,3434

4,4877

1,6351

0,7410

0,2019

4,7397

1,5676

2,9055

1,0084

0,6266

1,9584

0,3329

3,0274

1,2378

1,4568

4,8210

0,0023

0,1558

4,2753

5,1399

1,4973

0,1162

0,9704

0,4179

1,9479

2,0799

1,3117

5,5788

1,8787

2,1734

1,4620

0,0048

5,6771

1,7592

0,0321

1,3247

2,4924

4,1636

2,8761

3,5886

1,1186

0,5941

0,0037

0,4858

0,2299

0,8676

5,5858

3,4229

1,1110

5,1577

4,3311

2,0525

1,7300

0,5761

0,0978

5,8922

0,6340

3,5800

0,0224

0,6875

0,1894

1,0228

3,6973

0,0499

1,2377

3,0980

2,8019

0,0055

5,6189

6,3130

6,2947

0,9073

0,1506

1,1630

4,5121

0,1581

0,4140

1,2770

0,0013

1,0329

5,4291

0,0009

0,9061

0,8874

2,7327

5,1634

1,6166

0,2751

0,2468

0,2579

4,7237

4,0598

3,4804

1,8199

0,7850

3,1604

1,7673

2,6027

1,7386

1,7902

1,6398

4,6795

0,9308

3,2206

0,2574

4,1821

4,2028

0,6911

2,4876

3,3300

5,5143

0,1107

0,2185

2,7248

2,7561

0,1016

3,5667

4,2517

0,0002

3,0985

3,1999

2,8795

0,1914

5,1890

0,1379

0,0000

3,4196

0,7023

0,6797

0,0334

0,4932

0,0003

0,0251

2,1204

0,8451

0,0532

4,9033

1,3641

4,2570

0,2274

0,6771

0,0945

0,9886

0,7016

6,2391

4,5956

0,0629

0,5201

1,0758

3,4266

2,7489

0,2705

2,6231

0,1178

1,6638

2,4940

1,7455

0,4302

4,5034

3,4384

0,3037

0,3689

4,9763

528,7360

x Vx mlnx lnx Probabilitate

a Factoru

l K xp

normal xplog

2,114944

0,003828

6,314353

0,003828

0,001 -3,09 545,913

2 545,947

7

0,00135 -3

546,1035

546,1358

0,01 -2,326 547,529

547,5468

0,05 -1,645

548,9692

548,9762

0,1 -1,281

549,7391

549,7417

0,5 0

552,4483

552,4443

Bin Frequency Cumulative

%

550 0 0,00%

552,5 131 52,40%

555 119 100,00%

More 0 100,00%