human reliability in engineering systems

Human reliability in engineering systems

introuductionIn 1958 williams recognized that human element reliability must be included in overall system reliability.In 1960 proved that human error is the cause for %20 to %50 of all equipment failure.In 1962,a database known as DATA STORE containing time and human performance reliability estimates for human engineering design features was established.In 1973,ieee transaction on reliability published a special issue on human reliability.In 1980,a selective bibliography on human reliability was published covering the period from 1958 to 1978.The first book on human reliability entitled human reliability with human factors appeared in 1986.

Terms and definitionsHuman error:this is the failure to perform a given task that could resault in the disruption of scheduled operations or damage to property and equipment.Human performance: this is a measure of human functions subject to specified conditions.Continuous task: this is a task that involves some sort of tracking activity: for example, monitoring a changing situation.Human reliability: this is the probability of accomplishing a task successfully by the human at any required stage in system operations within a stated minimum time.

Human error occurrence examplesHuman operator accounted for over %90 of the documented air traffic control system errors.Over %50 of all technical medical equipment problems are due to operator errors.Up to %90 of accidents both generally and in medical devices are caused by human mistakes.A study of 23000 defects in the production of nuclear components revealed that approximately %82 of the defects were due to human errors.During the period from june 1,1973 to june 30,1975,401 human errors occurred in U.S commercial light water nuclear reactors.

Human error occurrence types: Design errors: these types of errors are the result of inadequate design. for example the placement of controls and displays so far apart that an operator is unable to use them in an effective manner.Operator errors :these errors are the result of operator mistakes and the conditions that lead to operator errors include lack of proper procedures ,complex tax ,poor training and operator carelessness.Assembly errors: these errors occur during product assembly due to humans.Inspection errors: these errors occur because of less than %100 accuracy of inspectors.Maintenance errors: the errors occur in the field due to oversights by the maintenance personnel.Installations errors: these errors occur due to various reasons including using the wrong installation related blueprints or instructions.Handling errors: these errors basically occur because of inadequate storage or transportation facilities.

Causes for the occurrence of human errors:Poor motivation of involved personnel.Poor training or skill of concerned personnel.Poor equipment design.Inadequate or poorly written equipment operating and maintenance procedures.Poor job environment: poor lighting ,high/low temperature ,high noise level ,crowded work space, ,etc.Inadequate work tools.Complex tasks.Poor work layout

Human error occurrence classification:decision error: occur when the wrong decision is made after considering the situation.Action error: are the result of no action ,incorrect action ,or the performance of correct action on the wrong object when required.Transmission error: occur when information that must be passed or to others is not send ,sent incorrectly ,or sent to the wrong destination.Checking error: occur when system require checks,the incorrect checks are made ,checks are omitted ,or correct checks are made on the wrong object.Diagnostic errors :are the result of misinterpreting the actual situation when an abnormal event occurs.Retrieval errors :occur when required information either from an individual,an individual memory,or from any other reference source is not received or the incorrect information is recieved.

Factors that influence on human performance:Reaction to stressTime at workFatigueGroup interaction and identificationSocial pressureRepetitive workSupervisors expectationsMoraleSocial interactionCrew efficiencyIdle time

Stress factors and operator stress characteristicsDissatisfied with the current job.Faced with serious financial problems.Working with individuals having unpredictable temperaments.Low chance of promotion from current position.facing a possible work layoff.Current job below ability and experience.Conducting tasks under extremely tight time schedules.Having health problems.Excessive demands of superior.Inadequate expertise to conduct the tasks required in the current job.Often tasks work home to meet deadlines.Having difficulties with spouse/children.

The operator stress characteristics include:short decision making timeSeveral displays difficult to discriminate.Requirement to perform steps at high speedPoor feedback for the determination of accuracy of actions taken.Requirement for prolonged monitoring.Very long sequence of steps required to perform a task.Requirement to make decisions on the basis of data obtain from various different sources.Requirement to operate at high speed more than one control simultaneously.

Human performance reliability in continuous time and mean time to human error (mtthe) measureAs humans perform time continuous tasks such as aircraft maneuvering ,scope monitoring ,and missile countdown, a general expression for human performance reliability can be developed the same way as for the development of the general classical reliability functions.

Human reliability evaluation methods

Probability tree method: this is used to perform task analysis by diagrammatically representing critical human actions and other events associated with the system.

Fault tree method: this special case has been discussed in the class.

Markov method: this is a powerful reliability engineering tool that can also be used to perform time continuous human reliability analysis.

Human reliability markov modelingReliability analysis of a system with human error: this mathematical model represent a system which can fail either due to hardware failure or to a human error.

Reliability analysis of a human performing a time continuous task under fluctuating environment: this mathematical method represents a human performing a time continuous task under fluctuating environment.

Human error dataHuman reliability predictions are only as effective as the body of quantitative on which they are made.

The collection and maintenance of human error data are at least as important as making various types of human reliability predictions.

Means to collecting human error dataExperimental studies.

Expert judgments.

Self made error reports.

Human data recorder.

Automatic data recorder.

Published literature.

Human error dataSpecific human error data banks and sources

Human error data for selective tasks

Brief description of selected human eror data banks

Specific human error data banks and sourcesData storeOperational performance recording and evaluation data systemNuclear plant reliability data systemAerojet general methodAviation safety reporting systemBunker ramo tablesSafety related operator action programTechnique for establishing personnel performance standards

Brief description of selected human error data banksData store: the data store was established in 1962 by american institute for research, pittsburgh and it contains estimates for time and human performance reliability.

Aviation safety reporting system: originally this databank was developed by the national aeronautics and space administration (NASA) and contains information on civil aircraft accidents.

Operational performance recording and evaluation data system: this system was developed to collect data on operational human performance by the U.S navy electronics laboratory, san diego.

Learning from other fields: PSTNFCC-collected data on outages in the US public-switched telephone networkmetric: breakdown of customer calls blocked by system outages (excluding natural disasters). Jan-June 2001

Human error accounts for 56% of all blocked calls

General Data

DateCo.Human-Co.Human-Out.NatureHard. FailSoft.FailOverldVand.TimeDur (min)#people * minutesBlocked Calls

15/28/01AT&TX6PM30671447593331415973067

26/9/01AT&TX8AM262514947474500170828292625

35/24/01AT&TX11:40PM1654488330165

41/30/01AT&TX9:31PM40349992553372152403

52/5/01AT&TX3:47PM4133211702762332957413

62/9/01AT&TX2:01PM44975719809505923449

72/22/01AT&TX4:25PM14015162420324910140

83/9/01AT&TX2:45PM2357937360101327235

94/3/01AT&TX2:35PM49077195580472625490

104/19/01AT&TX9:47AM1556140480118849155

115/3/01AT&TX2:40PM143286143

121/9/01BellSX4:52AM411395968230941

131/15/01BellSX10:40AM893276891789

144/14/01BellSX1:54AM1561535040037440156

154/20/01BellSX3:52PM28887552864224597288

166/11/01BellSX1:03PM13610807784279746136

176/26/01BellSX3:01PM3420400001121034

182/1/01BellSX1:45AM3111365476651255311

192/9/01BellSX3:45PM2092610410001984841209

202/16/01BellSX5:55PM789742200069006678

213/27/01BellSX8:10AM470?0470

224/3/01BellSX10:53AM67478467139246067

234/6/01BellSX12:29PM2102100210

244/13/01Citi.X5:43PM16?30016

251/24/01ICGX4AM4175421000207000417

262/26/01MCIX3:36PM33624107664215246336

274/13/01MCIX1:30PM37539827625318621375

281/2/01QwestX9:43PM1770265500047001770

294/21/01QwestX7:55AM31516002000130600315

305/16/01QwestX3:59PM221442000221

315/31/01QwestX6:29AM207801090066600207

326/27/01QwestX12:43PM1043541408104

DateCo.Human-Co.Human-Out.NatureHard. FailSoft.FailOverldVand.TimeDur (min)#people * minutes

332/23/01QwestX5:01AM9482720001030094

342/23/01QwestX8:10PM16543807500180000165

353/10/01QwestX10:09AM27810369400609400278

364/30/01QwestX2:38AM12774676002800127

374/13/01QwestX3:56PM6720502008190067

384/23/01QwestX2:30PM57119699500176500571

393/22/01RockHX8:18AM1471127945750000147

405/27/01RockHX11:10AM9599750001200095

411/4/01SBCX4:33AM103515000032677103

423/15/01SBCX1:42PM92365258412342392

433/14/01SBCX11:31AM6419507846937964

444/6/01SBCX2:02AM1074079161988107

454/11/01SBCX8:56AM3313164366596133

464/23/01SBCX10:00PM204056854802040

476/1/01SBCX10:47AM10037673551811292991003

486/6/01SBCX2:17PM45174510045345

496/9/01SBCX8:03AM6387791183238247349936387

506/9/01SBCX9:29AM6414633395219764

511/3/01SBCX4:30AM11040327336002140311040

526/15/01SBCX5:55AM1207690320192259120

536/27/01SBCX4:25AM38182324479838

541/10/01SBCX8:47PM198608909462407198

551/17/01SBCX10:39PM4219248182013742

561/26/01SBCX11:07AM1218235381134497121

571/29/01SBCX9:33AM16812352872317520168

581/31/01SBCX3:38PM89529149525755889

592/23/01SBCX3:46AM26927079154302000269

603/11/01SBCX1:20AM182102081988778182

614/8/01SBCX3:25PM76656252424159376

622/8/01SprintX2:10AM15243352800001524

634/4/01SprintX8:21PM14117546463373328141

641/28/01TUPRX12PM13200?13200

652/2/01VerizonX7:12PM1498664946310334149

665/16/01VerizonX8:46AM8222942780082

672/6/01VerizonX10:02AM238335745002383

682/10/01VerizonX5:30AM147023520001470


693/28/01VerizonX8:02PM274379547002743

704/2/01VerizonX9:14PM122262078420012226

714/27/01VerizonX12:26AM5939393713223559

725/3/01VerizonX3:30PM1700258400001700

735/14/01VerizonX10:42AM30448003424157906304

745/9/00AllTelX10:22PM31109674973941

753/16/00AmerX9:05AM4266145464

765/9/00AmerX1:24PM613050000

771/10/00AT&TX9:25AM1205846760

783/29/00AT&TX4:22AM33010423380

794/17/00AT&TX12:30PM2066618986

804/26/00AT&TX9:55AM33212038652

815/25/00AT&TX11:09AM373369220

826/13/00AT&TX2:10PM91529190330

837/11/00AT&TX1:30PM123065594670

847/18/00AT&TX5:52AM1434901182

857/31/00AT&TX12:49PM602004060

868/2/00AT&TX12:46PM22413450976

878/4/00AT&TX10AM28322930641

881/21/00AT&TX2:50PM552515205

898/15/00AT&TX10:50AM602726220

908/24/00AT&TX2:37AM63823466916

919/1/00AT&TX10:25AM84097893600

929/20/00AT&TX2:48AM432003361305600

9311/28/00AT&TX8:50AM28796185467

9412/4/00AT&TX11:55AM24013924320

9512/8/00AT&TX11:55AM75878162686

9612/28/00AT&TX1:45AM56527766925

971/26/00AT&TX9:20PM2160129306240

981/27/00AT&TX8:55AM28370973853

992/8/00AT&TX11:30AM28515015225

1002/24/00AT&TX8:40AM5118680994

1012/25/00AT&TX4:15AM1260196617960

1023/11/00AT&TX2:50AM50517256860

1033/16/00AT&TX9:02AM351721755

1041/4/00BellAX5:23AM1706222000


1055/9/00BellAX10:14AM28618361200

1065/20/00BellAX10:55PM780541538210

1075/25/00BellAX12:34AM1466263400

1086/1/00BellAX6PM12901935000

1096/18/00BellAX3:15PM36029736000

1106/18/00BellAX4:17PM793237900000

1116/23/00BellAX5:11AM1144674000

1126/25/00BellAX5:28AM9758976000

1136/28/00BellAX6:19PM3234912000

1146/28/00BellAX6:50PM37534541250

1152/20/00BellAX6:21AM449?

1163/1/00BellAX9:20AM754372500

1173/2/00BellAX2:19AM29617256800

1183/20/00BellAX12:19AM1319170000

1193/24/00BellAX11:28PM4321500000

1205/8/00BellAX2:13AM491999200

1217/21/00VerizonX2:18PM22819935180

1228/2/00VerizonX10:23AM898010000

1238/2/00VerizonX6:36AM1155108223500

1248/2/00VerizonX8:45AM1014332900

12511/13/00VerizonX2:16AM228438352800

12610/31/00VerizonX12:22AM422368800

127

128

129

FCC data: 2000, 2001

Human Error-Co

DateCo.TimeDur (min)#people * minutes

12/22/01AT&T4:25PM14015162420

25/24/01AT&T11:40PM1654488330

31/15/01BellS10:40AM893276891

44/14/01BellS1:54AM15615350400

51/31/01SBC3:38PM895291495

66/27/01SBC4:25AM38182324

71/4/01SBC4:33AM1035150000

84/20/01BellS3:52PM28887552864

94/3/01AT&T2:35PM49077195580

104/6/01BellS12:29PM210210

112/8/01Sprint2:10AM1524335280000

122/23/01Qwest5:01AM948272000

134/13/01MCI1:30PM37539827625

144/23/01Qwest2:30PM57119699500

154/3/01BellS10:53AM674784671

165/31/01Qwest6:29AM2078010900

173/15/01SBC1:42PM923652584

186/9/01SBC9:29AM64146333952

191/17/01SBC10:39PM421924818

204/8/01SBC3:25PM766562524

212/2/01Verizon7:12PM1498664946

225/16/01Verizon8:46AM82229427800

235/14/01Verizon10:42AM30448003424

245/9/00Amer1:24PM613050000

256/13/00AT&T2:10PM91529190330

267/18/00AT&T5:52AM1434901182

265/9/00BellA10:14AM28618361200

275/25/00BellA12:34AM1466263400

286/18/00BellA4:17PM793237900000

293/2/00BellA2:19AM29617256800

303/20/00BellA12:19AM1319170000

315/8/00BellA2:13AM491999200

328/2/00Verizon10:23AM898010000

338/2/00Verizon6:36AM1155108223500

348/2/00Verizon8:45AM1014332900

People*min

114015162420

21654488330

3893276891

415615350400

5895291495

638182324

71035150000

828887552864

949077195580

10210210

111524335280000

12948272000

1337539827625

1457119699500

15674784671

162078010900

17923652584

1864146333952

19421924818

20766562524

211498664946

2282229427800

2330448003424

Total Min=5415Total min=1054444508

Human Error-Out.

Human Error: Out.

DateCo.TimeDur (min)#people * minutesPeople*min

12/5/01AT&T3:47PM413321170276413321170276

22/9/01AT&T2:01PM4497571980944975719809

33/9/01AT&T2:45PM23579373602357937360

44/19/01AT&T9:47AM15561404801556140480

56/11/01BellS1:03PM1361080778413610807784

63/27/01BellS8:10AM470?470

74/3/01BellS10:53AM674784671674784671

81/26/01SBC11:07AM12182353811218235381

91/29/01SBC9:33AM1681235287216812352872

104/17/00AT&T12:30PM2066618986

114/26/00AT&T9:55AM33212038652

127/11/00AT&T1:30PM123065594670

138/2/00AT&T12:46PM22413450976

148/24/00AT&T2:37AM63823466916Total min:2214Total min=447148633

159/1/00AT&T10:25AM84097893600

1611/28/00AT&T8:50AM28796185467

1712/4/00AT&T11:55AM24013924320

1812/8/00AT&T11:55AM75878162686

191/27/00AT&T8:55AM28370973853

202/8/00AT&T11:30AM28515015225

212/25/00AT&T4:15AM1260196617960

221/4/00BellA5:23AM1706222000

236/18/00BellA3:15PM36029736000

246/23/00BellA5:11AM1144674000

256/28/00BellA6:19PM3234912000

266/28/00BellA6:50PM37534541250

273/1/00BellA9:20AM754372500

287/21/00Verizon2:18PM22819935180

Overload

Overload


12/9/01BellS3:45PM209261041000

22/16/01BellS5:55PM7897422000

People *min

209261041000

7897422000

Total Min:287Total min=358463000

Vandalism

Vandalism


11/2/01Qwest9:43PM17702655000

24/23/01SBC10:00PM20405685480

33/28/01Verizon8:02PM27437954700

45/3/01Verizon3:30PM17002584000

People*min

17702655000

20405685480

27437954700

17002584000

Total min:8253Total Min=18879180

Nature

Act of Nature


16/9/01AT&T8AM262514947474500

21/30/01AT&T9:31PM40349992553

35/16/01Qwest3:59PM221442000

44/6/01SBC2:02AM1074079161

56/1/01SBC10:47AM100376735518

66/9/01SBC8:03AM6387791183238

71/3/01SBC4:30AM1104032733600

81/10/01SBC8:47PM1986089094

91/28/01TUPR12PM13200

102/6/01Verizon10:02AM23833574500

112/10/01Verizon5:30AM14702352000

124/2/01Verizon9:14PM1222620784200

131/26/00AT&T9:20PM2160129306240

145/20/00BellA10:55PM780541538210

156/1/00BellA6PM12901935000

People*min:

262514947474500

40349992553

221442000

1074079161

100376735518

6387791183238

1104032733600

1986089094

13200

23833574500

14702352000

1222620784200

Total min:51263Total min:15935440364

Software

Software Failure


16/26/01BellS3:01PM342040000

24/13/01Citi.5:43PM16

32/26/01MCI3:36PM33624107664

44/21/01Qwest7:55AM31516002000

52/23/01SBC3:46AM26927079154

65/9/00AllTel10:22PM311096749

78/4/00AT&T10AM28322930641

89/20/00AT&T2:48AM432003361305600

93/11/00AT&T2:50AM50517256860

People*min

342040000

16

33624107664

31516002000

26927079154

Total min:970Total min=69228818

Hardware

Hardware Failure

DateCo.TimeDur (min)#people * minutesPeople*min

15/28/01AT&T6PM30671447593333067144759333

25/3/01AT&T2:40PM143286143286

31/9/01BellS4:52AM411395968411395968

42/1/01BellS1:45AM3111365476631113654766

51/24/01ICG4AM41754210004175421000

62/23/01Qwest8:10PM1654380750016543807500

73/10/01Qwest10:09AM2781036940027810369400

84/30/01Qwest2:38AM12774676001277467600

94/13/01Qwest3:56PM672050200672050200

103/22/01RockH8:18AM1471127945714711279457

115/27/01RockH11:10AM959975000959975000

123/14/01SBC11:31AM641950784641950784

134/11/01SBC8:56AM331316436331316436

146/6/01SBC2:17PM451745100451745100

156/15/01SBC5:55AM12076903201207690320

163/11/01SBC1:20AM1821020819818210208198

174/4/01Sprint8:21PM1411754646314117546463

184/27/01Verizon12:26AM593939371593939371

193/16/00Amer9:05AM4266145464Total min:5502Total min=294577182

201/10/00AT&T9:25AM1205846760

213/29/00AT&T4:22AM33010423380

225/25/00AT&T11:09AM373369220

237/31/00AT&T12:49PM602004060

241/21/00AT&T2:50PM552515205

258/15/00AT&T10:50AM602726220

2612/28/00AT&T1:45AM56527766925

272/24/00AT&T8:40AM5118680994

283/16/00AT&T9:02AM351721755

296/25/00BellA5:28AM9758976000

302/20/00BellA6:21AM449?

313/24/00BellA11:28PM4321500000

3211/13/00Verizon2:16AM228438352800

3310/31/00Verizon12:22AM422368800

Outage #

31.5068493151

12.3287671233

24.6575342466

16.4383561644

6.8493150685

2.7397260274

5.4794520548

&LPatricia Enriquez&CNumber of Outages (Percentages)&RFCC Data: 2001 (January-June)

Dr. Richard Kuhn(1997)

%

Number of Outages (Percentages)

Outage #-No Nature

37.7049180328

14.7540983607

29.5081967213

8.1967213115

3.2786885246

6.5573770492

Number of Outages (Nature Factored Out)

Outage #- Kuhn

25

24

19

11

14

6

1

%

Number of Outages: Kuhn (1992-1994)

Magnitude-Min

7.3270729595

2.995778307

7.4447932453

69.3643104568

1.3125135311

0.3883416324

11.1671898679

&LPatricia Enriquez&CMagnitude of Failure&RFCC Data:2001 (January-June)

Dr. Richard Kuhn(1997)

%

Magnitude of Failure (minutes)

Magnitude-No Nature

7.3841713981

7.7166786913

9.5893848615

6.0855108379

4.5013959033

64.7212898773

%

Magnitude of Failures: minutes (Nature Factored out)

Magnitude-Kuhn

14

14

7

18

2

44

1

%

Magnitude of Failure (Customer minutes)

Magnitude-Kuhn-NoNature

6.3083224254149.4

15.2049993666360.1

6.7474559811159.8

5.0373685766119.3

47.44753620741123.7

19.2543174429456

%

minutes

Magnitude: 1992-1994 (Nature factored out)

Duration

5415

2214

5502

51263

970

287

8253

&LPatricia Enriquez&CDuration of Outage&RFCC data: 2001 (January-June)

Dr. Richard Kuhn (1997)

minutes:

Duration of Outage (minutes)

People-Minutes

5.8006049575

2.4598094614

1.6204986126

87.6624551352

0.3808346687

1.9719409026

0.103856262

&LPatricia Enriquez&CPeople * Minutes&RFCC data: 2001 (January-June)

%

Number of People * Minutes

People-Minutes-No Nature

46.9041351408

19.8902073567

13.1034756681

3.079458246

16.1829339141

0.8397896744

Number of People * Minutes: 2001(Nature Factored out)

Magnitude-no overload

7.8626540633

8.2167073049

10.2107618825

6.4798423461

68.9167974882

Magnitude of Failure:2001 (outage minutes)

Magnitude-Kuhn-no overload

12.0038566608

28.932990519

12.8394664953

9.5854089667

36.6382773582

Magnitude of Failure: 1992-1994 (Average outage minutes)

Blocked calls

Blocked Calls

Total=

55787190


15/28/01AT&TX6PM3067144759333141597

26/9/01AT&TX8AM26251494747450017082829

31/30/01AT&TX9:31PM40349992553372152

42/5/01AT&TX3:47PM4133211702762332957

52/9/01AT&TX2:01PM44975719809505923

62/22/01AT&TX4:25PM14015162420324910

73/9/01AT&TX2:45PM2357937360101327

84/3/01AT&TX2:35PM49077195580472625

94/19/01AT&TX9:47AM1556140480118849

101/9/01BellSX4:52AM4113959682309

111/15/01BellSX10:40AM8932768917

124/14/01BellSX1:54AM1561535040037440

134/20/01BellSX3:52PM28887552864224597

146/11/01BellSX1:03PM13610807784279746

156/26/01BellSX3:01PM34204000011210

162/1/01BellSX1:45AM3111365476651255

172/9/01BellSX3:45PM2092610410001984841

182/16/01BellSX5:55PM7897422000690066

193/27/01BellSX8:10AM470?0

204/3/01BellSX10:53AM674784671392460

214/6/01BellSX12:29PM2102100

224/13/01Citi.X5:43PM16?300

231/24/01ICGX4AM4175421000207000

242/26/01MCIX3:36PM33624107664215246

254/13/01MCIX1:30PM37539827625318621

261/2/01QwestX9:43PM177026550004700

274/21/01QwestX7:55AM31516002000130600

285/31/01QwestX6:29AM207801090066600

282/23/01QwestX5:01AM94827200010300

292/23/01QwestX8:10PM16543807500180000

303/10/01QwestX10:09AM27810369400609400

314/30/01QwestX2:38AM12774676002800

324/13/01QwestX3:56PM67205020081900

334/23/01QwestX2:30PM57119699500176500

343/22/01RockHX8:18AM1471127945750000

355/27/01RockHX11:10AM95997500012000

361/4/01SBCX4:33AM103515000032677

373/15/01SBCX1:42PM923652584123423

383/14/01SBCX11:31AM64195078469379

394/6/01SBCX2:02AM1074079161988

404/11/01SBCX8:56AM33131643665961

416/1/01SBCX10:47AM1003767355181129299

426/6/01SBCX2:17PM451745100453

436/9/01SBCX8:03AM638779118323824734993

446/9/01SBCX9:29AM64146333952197

451/3/01SBCX4:30AM110403273360021403

466/15/01SBCX5:55AM1207690320192259

476/27/01SBCX4:25AM381823244798

481/10/01SBCX8:47PM198608909462407

491/17/01SBCX10:39PM42192481820137

501/26/01SBCX11:07AM1218235381134497

511/29/01SBCX9:33AM16812352872317520

521/31/01SBCX3:38PM895291495257558

532/23/01SBCX3:46AM26927079154302000

543/11/01SBCX1:20AM182102081988778

554/8/01SBCX3:25PM766562524241593

564/4/01SprintX8:21PM14117546463373328

572/2/01VerizonX7:12PM1498664946310334

584/27/01VerizonX12:26AM59393937132235

595/3/01VerizonX3:30PM170025840000

605/14/01VerizonX10:42AM30448003424157906

Totals=55787190

Blocked Calls-Human out

Blocked Calls

Total=

55787190


12/5/01AT&TX3:47PM4133211702762332957

22/9/01AT&TX2:01PM44975719809505923

33/9/01AT&TX2:45PM2357937360101327

44/3/01AT&TX2:35PM49077195580472625

54/19/01AT&TX9:47AM1556140480118849

64/14/01BellSX1:54AM1561535040037440

74/20/01BellSX3:52PM28887552864224597

86/11/01BellSX1:03PM13610807784279746

93/27/01BellSX8:10AM4700

104/3/01BellSX10:53AM674784671392460

114/13/01MCIX1:30PM37539827625318621

125/31/01QwestX6:29AM207801090066600

131/4/01SBCX4:33AM103515000032677

146/27/01SBCX4:25AM381823244798

151/26/01SBCX11:07AM1218235381134497

161/29/01SBCX9:33AM16812352872317520

171/31/01SBCX3:38PM895291495257558

182/2/01VerizonX7:12PM1498664946310334

Total min=41096943747675908529

Blocked Calls-Human co

Blocked Calls

Total=

55787190


12/22/01AT&TX4:25PM14015162420324910

21/15/01BellSX10:40AM8932768917

34/6/01BellSX12:29PM2102100

42/23/01QwestX5:01AM94827200010300

54/23/01QwestX2:30PM57119699500176500

63/15/01SBCX1:42PM923652584123423

76/9/01SBCX9:29AM64146333952197

81/17/01SBCX10:39PM42192481820137

94/8/01SBCX3:25PM766562524241593

105/14/01VerizonX10:42AM30448003424157906

Total min=16822528883231054973

Blocked Calls- Nature

Blocked Calls

Total=

55787190


16/9/01AT&TX8AM26251494747450017082829

21/30/01AT&TX9:31PM40349992553372152

34/6/01SBCX2:02AM1074079161988

46/1/01SBCX10:47AM1003767355181129299

56/9/01SBCX8:03AM638779118323824734993

61/3/01SBCX4:30AM110403273360021403

71/10/01SBCX8:47PM198608909462407

Total Min=217631590828766443404071

Blocked Calls-Vandalism

Blocked Calls

Total=

55787190


11/2/01QwestX9:43PM177026550004700

25/3/01VerizonX3:30PM170025840000

Total Min=347052390004700

Blocked Calls-Overload

Blocked Calls

Total=

55787190


12/9/01BellSX3:45PM2092610410001984841

22/16/01BellSX5:55PM7897422000690066

Total Min=2873584630002674907

Blocked Calls-Software

Blocked Calls

Total=

55787190


16/26/01BellSX3:01PM34204000011210

24/13/01Citi.X5:43PM16300

32/26/01MCIX3:36PM33624107664215246

44/21/01QwestX7:55AM31516002000130600

52/23/01SBCX3:46AM26927079154302000

Total Min=97069228818659356

Blocked Calls-Hardware

Blocked Calls

Total=

55787190


15/28/01AT&TX6PM3067144759333141597

21/9/01BellSX4:52AM4113959682309

32/1/01BellSX1:45AM3111365476651255

41/24/01ICGX4AM4175421000207000

52/23/01QwestX8:10PM16543807500180000

63/10/01QwestX10:09AM27810369400609400

74/30/01QwestX2:38AM12774676002800

84/13/01QwestX3:56PM67205020081900

93/22/01RockHX8:18AM1471127945750000

105/27/01RockHX11:10AM95997500012000

113/14/01SBCX11:31AM64195078469379

124/11/01SBCX8:56AM33131643665961

136/6/01SBCX2:17PM451745100453

146/15/01SBCX5:55AM1207690320192259

153/11/01SBCX1:20AM182102081988778

164/4/01SprintX8:21PM14117546463373328

174/27/01VerizonX12:26AM59393937132235

Time Min=53592945768962080654

People-Minutes-Kuhn

36.469054161

37.5013582949

18.7956969217

5.5185581894

1.715332433

People * minutes (no nature or overload)

Blocked Calls Chart

8.5194448991

47.714384397

16.8023419625

5.3246359015

21.6012379434

0.0379548965

Source Data

Number of Outages: 2001 (percent)%# of outagesTotal # of outages=73Number of Outages: Kuhn (1992-4)%

Human-co.31.506849315123Human-co.25

Human-ext.12.32876712339Human-ext.24

Hardware Failure24.657534246618Hardware Failure19

Act of Nature16.438356164412Act of Nature11

Software Failure6.84931506855Software Failure14

Overload2.73972602742Overload6

Vandalism5.47945205484Vandalism1

Number of Outages: 2001 (no nature)%# of outagesTotal # of outages=61

Human-co.37.704918032823

Human-ext.14.75409836079NO NATURE:

Hardware Failure29.508196721318Magnitude of Outages:Kuhn (1992-4)%Magnitude of Outages: 2001 (percent)%minutesTotal Minutes=3187.9Magnitude of Outages:Kuhn (1992-4)%minutesTotal minutes=2368.3

Software Failure8.19672131155Human-co.14Human-co.7.3841713981235.4Human-co.6.3083224254149.4

Overload3.27868852462Human-ext.14Human-ext.7.7166786913246Human-ext.15.2049993666360.1

Vandalism6.55737704924Hardware Failure7Hardware Failure9.5893848615305.7Hardware Failure6.7474559811159.8

Act of Nature18Software Failure6.0855108379194Software Failure5.0373685766119.3

Software Failure2Overload4.5013959033143.5Overload47.44753620741123.7

Overload44Vandalism64.72128987732063.25Vandalism19.2543174429456

Magnitude of Outages: 2001 (percent)%minutesVandalism1

Human-co.7.32707295955415Total Minutes=73904NO NATURE/OVERLOAD:

Human-ext.2.9957783072214Magnitude of Outages: 2001 (percent)%minutesTotal Minutes=2993.9Magnitude of Outages:Kuhn (1992-4)%minutesTotal minutes=1244.6

Hardware Failure7.44479324535502Human-co.7.8626540633235.4Human-co.12.0038566608149.4

Act of Nature69.364310456851263Human-ext.8.2167073049246Human-ext.28.932990519360.1

Software Failure1.3125135311970Hardware Failure10.2107618825305.7Hardware Failure12.8394664953159.8

Overload0.3883416324287Software Failure6.4798423461194Software Failure9.5854089667119.3

Vandalism11.16718986798253Vandalism68.91679748822063.3Vandalism36.6382773582456

Duration (minutes):minutes:

Human-co.5415

Human-ext.2214

Hardware Failure5502People * Minutes: 2001 (No nature)%People*minTotal min=2248084321Blocked Calls (2001)%minutesTotal minutes=12383119

Act of Nature51263Human-co.46.90413514081054444508Human-co.8.51944489911054973

Software Failure970Human-ext.19.8902073567447148633Human-ext.47.7143843975908529

Overload287Hardware Failure13.1034756681294577182Hardware Failure16.80234196252080654

Vandalism8253Software Failure3.07945824669228818Software Failure5.3246359015659356

Overload16.1829339141363806000Overload21.60123794342674907

Vandalism0.839789674418879180Vandalism0.03795489654700

People * Minutes: 2001%People*min

Human-co.5.80060495751054444508Total min=18178181685People * Minutes: 2001 (No nature/overld): Kuhn%People*minTotal min=6441900000

Human-ext.2.4598094614447148633Human-co.36.4690541612349300000

Hardware Failure1.6204986126294577182Human-ext.37.50135829492415800000

Act of Nature87.662455135215935440364Hardware Failure18.79569692171210800000

Software Failure0.380834668769228818Software Failure5.5185581894355500000

Overload1.9719409026358463000Vandalism1.715332433110500000

Vandalism0.10385626218879180

Learning from other fields: PSTNPSTN trends: 1992-1994 vs. 2001

Minutes (millions of customer minutes/month)

CauseTrend1992-942001Human error: company98176Human error: external10075Hardware4949Software1512Overload31460Vandalism53

MARKOV METHODAssumptions:The probability of a transition occurrence from one state to another in finite time t is t .The parameter in our case is the constant human error rate. The probability of two or more transitional occurrence in t is negligible.All occurrences are independent of each other.

MARKOV METHODSystem has two states.The she state 0 represent human performing the time continuous task normally and state 1 denotes human committed error.

By using the MARKOV METHOD we can obtain the probabilites of the system being in state 1 or 0 at time t for known human error rate.P0(t+ t)=P0 (t)(1- t)

P1(t+ t)=P1 (t)( t)+P1(t)

MARKOV METHODRearranging and taking limits:

dp0(t)/d(t)=- p0(t)

dp1(t)/d(t)= p0(t) At time t=0: p0(0)=1 and p1(0)=0 so: p0(t)=exp(- t) p1(t)=1- exp(- t) Thus the human reliability R(t) is given by: R(t)=p0(t)=exp(- t)

MARKOV METHODBy integration over the time interval [0,]:

MTTHE=R(t) dt= 1/

HUMAN RELIABILITY MARKOV MODELING:This mathematical model represents a system which can be failed due to a hardware failure or a human error.Both failure rates are constant.We have the following symbols:

h:the constant human error ratenh:the constant nonhuman error ratePi(t): the probability that system is in state i at time ti=0 system operating normallyi=1 system failed due to nonhuman errori=2 system failed due to human error

HUMAN RELIABILITY MARKOV MODELING:By applying the Markov method:dp0(t)/d(t)+ (h+ nh)p0(t)=0dp1(t)/d(t)- nh p0(t)=0dp2(t)/d(t)- h p0(t)=0 Solving the above equations we have:

P0(t)=exp(-(h+nh)t)P1(t)= nh/(nh + h)[1-exp(-(h+ nh)t)] P2(t)= h/(nh + h)[1-exp(-(h+ nh)t)] The system reliability R(t) with human error is: R(t)=p0(t)=exp(-(h+nh)t)

HUMAN RELIABILITY MARKOV MODELINGBy integrating over the time interval [0,]:

MTTF= R(t)dt=1/h

Refrences:Dhillon,B.S,design reliability,fundamentals and applications,CRC press,1999

J. Reason, Human Error, Cambridge, 1990

www.eliminatemistakes.com

Human error in medicine,marc green ,2003

Thanks for your attention

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human reliability in engineering systems

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