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1、Tools for ManagersStatistical Process ControlProfessor Stephen R.LawrenceProfessor Stephen R.LawrenceCollege of Business and AdministrationCollege of Business and AdministrationGraduate School of Business AdministrationGraduate School of Business AdministrationUniversity of ColoradoUniversity of Col
2、oradoDenver,ColoradoDenver,ColoradoCauses of VariationNatural CausesAssignable CausesWhat prevents perfection?Process variation.qqInherent to processInherent to processqqRandomRandomqqCannot be controlledCannot be controlledqqCannot be preventedCannot be preventedqqExamplesExamples weatherweather ac
3、curacy of measurementsaccuracy of measurements capability of machinecapability of machineCauses of VariationNatural CausesAssignable CausesWhat prevents perfection?Process variation.n nExogenous to processExogenous to processn nNot randomNot randomn nControllableControllablen nPreventablePreventable
4、n nExamplesExamples tool weartool wear“Monday”effect“Monday”effect poor maintenancepoor maintenanceqInherent to processqRandomqCannot be controlledqCannot be preventedqExamplesweatheraccuracy of measurementscapability of machineProduct Specificationand Process Variationn nProduct specificationProduc
5、t specification desired range of product attributedesired range of product attribute part of product designpart of product design length,weight,thickness,color,.length,weight,thickness,color,.nominal specificationnominal specification upper and lower specification limitsupper and lower specification
6、 limitsn nProcess variabilityProcess variability inherent variation in processesinherent variation in processes limits what can actually be achievedlimits what can actually be achieved defines and limits process defines and limits process capabilitycapabilityn nProcess may not be capable of meeting
7、Process may not be capable of meeting specification!specification!Process CapabilityLSLUSLSpecn nCapableCapable process processn nVery Very capablecapable process processn nProcess Process notnot capable capableProcess variationProcess Capability Index In nMeasure of capability of process to meet(fa
8、ll Measure of capability of process to meet(fall within)specification limitswithin)specification limitsProcess Capability Index In nMeasure of capability of process to meet(fall Measure of capability of process to meet(fall within)specification limitswithin)specification limitsn nTake“width”of proce
9、ss variation as 6Take“width”of process variation as 6 LSLUSLSpec6 3 Process Capability Index In nMeasure of capability of process to meet(fall Measure of capability of process to meet(fall within)specification limitswithin)specification limitsn nTake“width”of process variation as 6Take“width”of proc
10、ess variation as 6 LSLUSLSpec6 3 99.7%Process Capability Index In nMeasure of capability of process to meet(fall Measure of capability of process to meet(fall within)specification limitswithin)specification limitsn nTake“width”of process variation as 6Take“width”of process variation as 6 n nIf If 6
11、6 (USL-LSL)1.0,process is.capablen nIf Cp 1.0,process is.not capableProcess Capability-ExampleA manufacturer of granola bars has a weight specification2 ounces plus or minus 0.05 ounces.If the standard deviationof the bar-making machine is 0.02 ounces,is the process capable?Process Capability-Exampl
12、eA manufacturer of granola bars has a weight specification2 ounces plus or minus 0.05 ounces.If the standard deviationof the bar-making machine is 0.02 ounces,is the process capable?USL =2+0.05 =2.05 ouncesProcess Capability-ExampleA manufacturer of granola bars has a weight specification2 ounces pl
13、us or minus 0.05 ounces.If the standard deviationof the bar-making machine is 0.02 ounces,is the process capable?USL =2+0.05 =2.05 ouncesLSL =2-0.05 =1.95 ouncesProcess Capability-ExampleA manufacturer of granola bars has a weight specification2 ounces plus or minus 0.05 ounces.If the standard devia
14、tionof the bar-making machine is 0.02 ounces,is the process capable?USL =2+0.05 =2.05 ouncesLSL =2-0.05 =1.95 ouncesCp =(USL-LSL)/6 =(2.05-1.95)/6(0.02)=0.1/0.12=0.85Process Capability-ExampleA manufacturer of granola bars has a weight specification2 ounces plus or minus 0.05 ounces.If the standard
15、deviationof the bar-making machine is 0.02 ounces,is the process capable?USL =2+0.05 =2.05 ouncesLSL =2-0.05 =1.95 ouncesCp =(USL-LSL)/6 =(2.05-1.95)/6(0.02)=0.1/0.12=0.85Therefore,the process is not capable!Process CenteringLSLUSLSpecn nCapable and centeredn nCapable but not centeredn nCapable but
16、not centeredProcess Centering-ExampleFor the granola bar manufacturer,if the process is incorrectly centered at 2.05 instead of 2.00 ounces,whatfraction of bars will be out of specification?Process Centering-ExampleFor the granola bar manufacturer,if the process is incorrectly centered at 2.05 inste
17、ad of 2.00 ounces,whatfraction of bars will be out of specification?2.0LSL=1.95USL=2.05Process Centering-ExampleFor the granola bar manufacturer,if the process is incorrectly centered at 2.05 instead of 2.00 ounces,whatfraction of bars will be out of specification?2.0LSL=1.95USL=2.05Process Centerin
18、g-ExampleFor the granola bar manufacturer,if the process is incorrectly centered at 2.05 instead of 2.00 ounces,whatfraction of bars will be out of specification?2.0LSL=1.95USL=2.05Out of spec!Process Centering-ExampleFor the granola bar manufacturer,if the process is incorrectly centered at 2.05 in
19、stead of 2.00 ounces,whatfraction of bars will be out of specification?2.0LSL=1.95USL=2.0550%of production will be out of specification!Out of spec!Example:Process CapabilityProcess Control Chartsn nEstablishEstablish capability capability of process under of process under normalnormal conditions co
20、nditionsn nUse normal process as benchmark to Use normal process as benchmark to statistically identify statistically identify abnormalabnormal process process behaviorbehaviorn nCorrect process when signs of abnormal Correct process when signs of abnormal performance performance first begin to appe
21、arfirst begin to appearn nControl the process rather than inspect the Control the process rather than inspect the product!product!Statistical technique for tracking a process anddetermining if it is going“out to control”Process Control ChartsTheory IUpper Spec LimitLower Spec LimitTarget SpecProcess
22、 Control ChartsTheory IUpper Spec LimitLower Spec Limit6 3 Target SpecProcess Control ChartsTheory IUpper Spec LimitLower Spec LimitUpper Control LimitLower Control Limit6 3 Target SpecProcess Control Charts Theory IIUpper Control Limit(UCL)Lower Control Limit(LCL)6 3 NaturalVariationProcess Control
23、 ChartsProcess Control ChartsPracticeUCLTargetLCLTimeSamplesProcess Control Charts:PracticeUCLTargetLCLSamplesTimeNatural variationProcess Control Charts:PracticeUCLTargetLCLSamplesTimeIn controlNatural variationProcess Control Charts:PracticeUCLTargetLCLSamplesTimeIn controlNatural variationProcess
24、 Control Charts:PracticeUCLTargetLCLSamplesTimeIn controlOut of control!Natural variationProcess Control Charts:PracticeUCLTargetLCLSamplesTimeIn controlOut of control!Natural variation Look forassignable cause!Process Control Charts:PracticeUCLTargetLCLSamplesTimeIn controlOut of control!Natural va
25、riation Look forassignable cause!Problem correctedProcess Control Charts Types of Control Chartsn nVariable control chartsmonitors continuous variablesmonitors continuous variables x-bar x-bar and and R R chartschartsn nAttribute control chartsmonitors frequency(proportion)of defectivesmonitors freq
26、uency(proportion)of defectives p-p-chartschartsn nDefects control chartsmonitors number(count)of defects per unitmonitors number(count)of defects per unit c-c-chartschartsExample:Process Control ChartsProcess Control ChartsError Trade-offsn nSetting control limits too tight(e.g.,Setting control limi
27、ts too tight(e.g.,2 2)means that normal variation will often be means that normal variation will often be mistaken as an out-of-control condition mistaken as an out-of-control condition(Type I(Type I error).error).n nSetting control limits too loose(e.g.,Setting control limits too loose(e.g.,4 4)mea
28、ns that an out-of-control condition will be means that an out-of-control condition will be mistaken as normal variation mistaken as normal variation(Type II error)(Type II error).n nUsing Using control limits works well to balance Type I control limits works well to balance Type I and Type II errors
29、 in many circumstances.and Type II errors in many circumstances.n n3 3 is not sacred-use judgement.is not sacred-use judgement.Process Control ChartsWhen to Take Actionn nA single point goes beyond control limits A single point goes beyond control limits(above or below)(above or below)n nTwo consecu
30、tive points are near the same Two consecutive points are near the same limit(above or below)limit(above or below)n nA run of 5 points above or below the A run of 5 points above or below the process meanprocess meann nFive or more points trending toward either Five or more points trending toward eith
31、er limitlimitn nA sharp change in levelA sharp change in leveln nOther erratic behaviorOther erratic behaviorTools for ManagersStatistical Process ControlProfessor Stephen R.LawrenceProfessor Stephen R.LawrenceCollege of Business and AdministrationCollege of Business and AdministrationGraduate School of Business AdministrationGraduate School of Business AdministrationUniversity of ColoradoUniversity of ColoradoDenver,ColoradoDenver,Colorado