运营管理第四章.pptx

Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.Beni AsllaniBeni AsllaniUniversity of Tennessee at ChattanoogaUniversity of Tennessee at ChattanoogaStatistical Process ControlOperations Management-5th EditionChapter 4Roberta Russell&Bernard W.Taylor,IIIRoberta Russell&Bernard W.Taylor,IIICopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-2 2Lecture OutlinewBasics of Statistical Process ControlBasics of Statistical Process ControlwControl ChartsControl ChartswControl Charts for AttributesControl Charts for AttributeswControl Charts for VariablesControl Charts for VariableswControl Chart PatternsControl Chart PatternswSPC with ExcelSPC with ExcelwProcess CapabilityProcess CapabilityCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-3 3Basics of Statistical Process Controlw wStatistical Process Control Statistical Process Control(SPC)(SPC)n nmonitoring production process monitoring production process to detect and prevent poor to detect and prevent poor qualityqualityw wSampleSamplen nsubset of items produced to subset of items produced to use for inspectionuse for inspectionw wControl ChartsControl Chartsn nprocess is within statistical process is within statistical control limitscontrol limitsUCLUCLLCLLCLCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-4 4VariabilitywRandomRandomn ncommon causescommon causesn ninherent in a processinherent in a processn ncan be eliminated can be eliminated only through only through improvements in the improvements in the systemsystemwNon-RandomNon-Randomn nspecial causesspecial causesn ndue to identifiable due to identifiable factorsfactorsn ncan be modified can be modified through operator or through operator or management actionmanagement actionCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-5 5SPC in TQMwSPCn ntool for identifying problems and tool for identifying problems and make improvementsmake improvementsn ncontributes to the TQM goal of contributes to the TQM goal of continuous improvementscontinuous improvementsCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-6 6Quality MeasureswAttributen na product characteristic that can be a product characteristic that can be evaluated with a discrete responseevaluated with a discrete responsen ngood bad;yes-nogood bad;yes-nowVariablen na product characteristic that is continuous a product characteristic that is continuous and can be measuredand can be measuredn nweight-lengthweight-lengthCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-7 7wNature of defect is different in serviceswService defect is a failure to meet customer requirementswMonitor times,customer satisfactionApplying SPC to ServiceCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-8 8Applying SPC to Service(cont.)w wHospitalsHospitalsn ntimeliness and quickness of care,staff responses to requests,timeliness and quickness of care,staff responses to requests,accuracy of lab tests,cleanliness,courtesy,accuracy of accuracy of lab tests,cleanliness,courtesy,accuracy of paperwork,speed of admittance and checkoutspaperwork,speed of admittance and checkoutsw wGrocery storesGrocery storesn nwaiting time to check out,frequency of out-of-stock items,waiting time to check out,frequency of out-of-stock items,quality of food items,cleanliness,customer complaints,quality of food items,cleanliness,customer complaints,checkout register errorscheckout register errorsw wAirlinesAirlinesn nflight delays,lost luggage and luggage handling,waiting time flight delays,lost luggage and luggage handling,waiting time at ticket counters and check-in,agent and flight attendant at ticket counters and check-in,agent and flight attendant courtesy,accurate flight information,passenger cabin courtesy,accurate flight information,passenger cabin cleanliness and maintenancecleanliness and maintenanceCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-9 9Applying SPC to Service(cont.)w wFast-food restaurantsFast-food restaurantsn nwaiting time for service,customer complaints,waiting time for service,customer complaints,cleanliness,food quality,order accuracy,employee cleanliness,food quality,order accuracy,employee courtesycourtesyw wCatalogue-order companiesCatalogue-order companiesn norder accuracy,operator knowledge and courtesy,order accuracy,operator knowledge and courtesy,packaging,delivery time,phone order waiting timepackaging,delivery time,phone order waiting timew wInsurance companiesInsurance companiesn nbilling accuracy,timeliness of claims processing,billing accuracy,timeliness of claims processing,agent availability and response timeagent availability and response timeCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-1010Where to Use Control Chartsw wProcess has a tendency to go out of controlProcess has a tendency to go out of controlw wProcess is particularly harmful and costly if it Process is particularly harmful and costly if it goes out of controlgoes out of controlw wExamplesExamplesn nat the beginning of a process because it is a waste of at the beginning of a process because it is a waste of time and money to begin production process with bad time and money to begin production process with bad suppliessuppliesn nbefore a costly or irreversible point,after which before a costly or irreversible point,after which product is difficult to rework or correctproduct is difficult to rework or correctn nbefore and after assembly or painting operations that before and after assembly or painting operations that might cover defectsmight cover defectsn nbefore the outgoing final product or service is before the outgoing final product or service is delivereddeliveredCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-1111Control Chartsw wA graph that establishes A graph that establishes control limits of a control limits of a processprocessw wControl limitsControl limitsn nupper and lower bands of upper and lower bands of a control charta control chartwTypes of chartsn nAttributesAttributesl lp-chartp-chartl lc-chartc-chartn nVariablesVariablesl lrange(R-chart)range(R-chart)l lmean(x bar chart)mean(x bar chart)Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-1212Process Control Chart1 12 23 34 45 56 67 78 89 91010Sample numberSample numberUpperUppercontrolcontrollimitlimitProcessProcessaverageaverageLowerLowercontrolcontrollimitlimitOut of controlOut of controlCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-1313Normal Distribution =0=01 1 2 2 3 3 -1-1 -2-2 -3-3 95%99.74%Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-1414A Process Is in Control If 1.no sample points outside limits2.most points near process average3.about equal number of points above and below centerline4.points appear randomly distributedCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-1515Control Charts for Attributesp-chartsuses portion defective in a samplec-chartsuses number of defects in an itemCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-1616p-ChartUCL=p+z pLCL=p-z pz=number of standard deviations from process averagep=sample proportion defective;an estimate of process average p=standard deviation of sample proportion p p=p p(1-(1-p p)n nCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-1717p-Chart Example20 samples of 100 pairs of jeans20 samples of 100 pairs of jeansNUMBER OFNUMBER OFPROPORTIONPROPORTIONSAMPLESAMPLEDEFECTIVESDEFECTIVESDEFECTIVEDEFECTIVE1 16 6.06.062 20 0.00.003 34 4.04.04:20201818.18.18200200Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-1818p-Chart Example(cont.)UCL=p+z =0.10+3p(1-p)n0.10(1-0.10)100UCL=0.190LCL=0.010LCL=p-z =0.10-3p(1-p)n0.10(1-0.10)100=200/20(100)=0.10total defectivestotal sample observationsp=Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-19190.020.020.040.040.060.060.080.080.100.100.120.120.140.140.160.160.180.180.200.20Proportion defectiveProportion defectiveSample numberSample number2 24 46 68 8101012121414161618182020UCL=0.190LCL=0.010p=0.10p-Chart Example(cont.)Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-2020c-ChartUCL=UCL=c c+z z c cLCL=LCL=c c-z z c cwherec=number of defects per sample c c=c cCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-2121c-Chart(cont.)Number of defects in 15 sample roomsNumber of defects in 15 sample rooms1 121 122 82 83 163 16:15 1515 15 190 190SAMPLESAMPLEc c=12.67=12.671901901515UCLUCL=c c+z z c c=12.67+3 12.67=12.67+3 12.67=23.35=23.35LCLLCL=c c+z z c c=12.67-3 12.67=12.67-3 12.67=1.99=1.99NUMBER OF DEFECTSCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-22223 36 69 912121515181821212424Number of defectsNumber of defectsSample numberSample number2 24 46 68 81010121214141616UCL=23.35LCL=1.99c=12.67c-Chart(cont.)Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-2323Control Charts for VariablesMean chart(x-Chart)uses average of a sampleRange chart(R-Chart)uses amount of dispersion in a sampleCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-2424x-bar Chartx x=x x1 1+x x2 2+.+.x xk kk k=UCL=UCL=x x+A A2 2R RLCL=LCL=x x-A A2 2R R=wherewherex x=average of sample means=average of sample means=Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-2525x-bar Chart ExampleExample 15.4Example 15.4OBSERVATIONS(SLIP-RING DIAMETER,CM)SAMPLE k 12345xR15.025.014.944.994.964.980.0825.015.035.074.954.965.000.1234.995.004.934.924.994.970.0845.034.915.014.984.894.960.1454.954.925.035.055.014.990.1364.975.065.064.965.035.010.1075.055.015.104.964.995.020.1485.095.105.004.995.085.050.1195.145.104.995.085.095.080.15105.014.985.085.074.995.030.1050.091.15Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-2626UCL=x+A2R=5.01+(0.58)(0.115)=5.08LCL=x-A2R=5.01-(0.58)(0.115)=4.94=x=5.01 cm=xk50.0910 x-bar Chart Example(cont.)Retrieve Factor Value A2Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-2727x-bar x-bar Chart Chart Example Example(cont.)(cont.)UCL=5.08LCL=4.94MeanSample number|1|2|3|4|5|6|7|8|9|105.10 5.08 5.06 5.04 5.02 5.00 4.98 4.96 4.94 4.92 x=5.01=Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-2828R-ChartUCL=D4RLCL=D3RR=RkwherewhereR R=range of each sample=range of each samplek k=number of samples=number of samplesCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-2929R-Chart ExampleOBSERVATIONS(SLIP-RING DIAMETER,CM)OBSERVATIONS(SLIP-RING DIAMETER,CM)SAMPLE SAMPLE k k 1 12 23 34 45 5x xR R1 15.025.025.015.014.944.944.994.994.964.964.984.980.080.082 25.015.015.035.035.075.074.954.954.964.965.005.000.120.123 34.994.995.005.004.934.934.924.924.994.994.974.970.080.084 45.035.034.914.915.015.014.984.984.894.894.964.960.140.145 54.954.954.924.925.035.035.055.055.015.014.994.990.130.136 64.974.975.065.065.065.064.964.965.035.035.015.010.100.107 75.055.055.015.015.105.104.964.964.994.995.025.020.140.148 85.095.095.105.105.005.004.994.995.085.085.055.050.110.119 95.145.145.105.104.994.995.085.085.095.095.085.080.150.1510105.015.014.984.985.085.085.075.074.994.995.035.030.100.1050.0950.091.151.15Example 15.3Example 15.3Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-3030R-Chart Example(cont.)Example 15.3Example 15.3RkR=0.115 1.1510UCL=D4R=2.11(0.115)=0.243LCL=D3R=0(0.115)=0Retrieve Factor Values DRetrieve Factor Values D3 3 and D and D4 4Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-3131R-Chart Example(cont.)UCL=0.243LCL=0RangeSample numberR=0.115|1|2|3|4|5|6|7|8|9|100.28 0.24 0.20 0.16 0.12 0.08 0.04 0 Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-3232Using x-bar and R-Charts TogetherProcess average and process variability must be in controlIt is possible for samples to have very narrow ranges,but their averages is beyond control limitsIt is possible for sample averages to be in control,but ranges might be very largeCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-3333Control Chart PatternsUCLUCLLCLLCLSample observationsSample observationsconsistently above theconsistently above thecenter linecenter lineLCLLCLUCLUCLSample observationsSample observationsconsistently below theconsistently below thecenter linecenter lineCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-3434Control Chart Patterns(cont.)LCLLCLUCLUCLSample observationsSample observationsconsistently increasingconsistently increasingUCLUCLLCLLCLSample observationsSample observationsconsistently decreasingconsistently decreasingCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-3535Zones for Pattern TestsUCLLCLZone AZone BZone CZone CZone BZone AProcess average3 sigma=x+A2R=3 sigma=x-A2R=2 sigma=x+(A2R)=232 sigma=x-(A2R)=231 sigma=x+(A2R)=131 sigma=x-(A2R)=13x=Sample number|1|2|3|4|5|6|7|8|9|10|11|12|13Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-3636Control Chart Patterns8 consecutive points on one side of the center line8 consecutive points up or down across zones14 points alternating up or down2 out of 3 consecutive points in zone A but still inside the control limits4 out of 5 consecutive points in zone A or BCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-3737Performing a Pattern Test1 14.984.98B BB B2 25.005.00B BU UC C3 34.954.95B BD DA A4 44.964.96B BD DA A5 54.994.99B BU UC C6 65.015.01U UC C7 75.025.02A AU UC C8 85.055.05A AU UB B9 95.085.08A AU UA A10105.035.03A AD DB BSAMPLESAMPLEx xABOVE/BELOWABOVE/BELOWUP/DOWNUP/DOWNZONEZONECopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-3838Sample SizeAttribute charts require larger sample sizes50 to 100 parts in a sampleVariable charts require smaller samples2 to 10 parts in a sampleCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-3939SPC with ExcelUCL=0.19LCL=0.01Copyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-4040SPC with Excel:FormulasCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-4141Process CapabilitywTolerancesn ndesign specifications reflecting product design specifications reflecting product requirementsrequirementswProcess capabilityn nrange of natural variability in a process what range of natural variability in a process what we measure with control chartswe measure with control chartsCopyright 2006 John Wiley&Sons,Inc.Copyright 2006 John Wiley&Sons,Inc.4-4-4242Process Capability(b)Design specifications(b)Design specifications and natural variation the and natural variation the same;process is capable same;process is capable of meeting specifications