Quản trị kinh doanh - Chapter 3: Statistical process control

Statistical Process Control1Chapter 3Lecture OutlineBasics of Statistical Process ControlControl ChartsControl Charts for AttributesControl Charts for VariablesControl Chart PatternsSPC with Excel and OM ToolsProcess CapabilityCopyright 2011 John Wiley & Sons, Inc.3-2Statistical Process Control (SPC)Statistical Process Controlmonitoring production process to detect and prevent poor qualitySamplesubset of items produced to use for inspectionControl Chartsprocess is within statistical control limitsCopyright 2011 John Wiley & Sons, Inc.3-3UCLLCLProcess VariabilityRandominherent in a processdepends on equipment and machinery, engineering, operator, and system of measurementnatural occurrencesNon-Randomspecial causesidentifiable and correctableinclude equipment out of adjustment, defective materials, changes in parts or materials, broken machinery or equipment, operator fatigue or poor work methods, or errors due to lack of training Copyright 2011 John Wiley & Sons, Inc.3-4SPC in Quality ManagementSPC usesIs the process in control?Identify problems in order to make improvementsContribute to the TQM goal of continuous improvementCopyright 2011 John Wiley & Sons, Inc.3-5Quality Measures:Attributes and VariablesAttributeA characteristic which is evaluated with a discrete responsegood/bad; yes/no; correct/incorrectVariable measureA characteristic that is continuous and can be measuredWeight, length, voltage, volumeCopyright 2011 John Wiley & Sons, Inc.3-6SPC Applied to ServicesNature of defects is different in servicesService defect is a failure to meet customer requirementsMonitor time and customer satisfactionCopyright 2011 John Wiley & Sons, Inc.3-7SPC Applied to ServicesHospitalstimeliness & quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance & checkoutsGrocery storeswaiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errorsAirlinesflight delays, lost luggage & luggage handling, waiting time at ticket counters & check-in, agent & flight attendant courtesy, accurate flight information, cabin cleanliness & maintenanceCopyright 2011 John Wiley & Sons, Inc.3-8SPC Applied to ServicesFast-food restaurantswaiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesyCatalogue-order companiesorder accuracy, operator knowledge & courtesy, packaging, delivery time, phone order waiting timeInsurance companiesbilling accuracy, timeliness of claims processing, agent availability & response timeCopyright 2011 John Wiley & Sons, Inc.3-9Where to Use Control ChartsProcess Has a tendency to go out of controlIs particularly harmful and costly if it goes out of controlExamplesAt beginning of process because of waste to begin production process with bad suppliesBefore a costly or irreversible point, after which product is difficult to rework or correctBefore and after assembly or painting operations that might cover defectsBefore the outgoing final product or service is deliveredCopyright 2011 John Wiley & Sons, Inc.3-10Control ChartsA graph that monitors process qualityControl limitsupper and lower bands of a control chartAttributes chartp-chartc-chartVariables chartmean (x bar – chart)range (R-chart)Copyright 2011 John Wiley & Sons, Inc.3-11Process Control ChartCopyright 2011 John Wiley & Sons, Inc.3-1212345678910Sample numberUppercontrollimitProcessaverageLowercontrollimitOut of controlNormal DistributionProbabilities for Z= 2.00 and Z = 3.00Copyright 2011 John Wiley & Sons, Inc.3-13=0123-1-2-395%99.74%A Process Is in Control If Copyright 2011 John Wiley & Sons, Inc.3-14 no sample points outside limits most points near process average about equal number of points above and below centerline points appear randomly distributedControl Charts for Attributesp-chartuses portion defective in a samplec-chartuses number of defects (non-conformities) in a sampleCopyright 2011 John Wiley & Sons, Inc.3-15p-ChartCopyright 2011 John Wiley & Sons, Inc.3-16UCL = p + zpLCL = p - zpz = number of standard deviations from process averagep = sample proportion defective; estimates process meanp = standard deviation of sample proportionp = p(1 - p)nConstruction of p-ChartCopyright 2011 John Wiley & Sons, Inc.3-1720 samples of 100 pairs of jeans NUMBER OF PROPORTIONSAMPLE # DEFECTIVES DEFECTIVE 1 6 .06 2 0 .00 3 4 .04 : : : : : : 20 18 .18 200Construction of p-ChartCopyright 2011 John Wiley & Sons, Inc.3-18UCL = 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 =Construction of p-ChartCopyright 2011 John Wiley & Sons, Inc.3-190.020.040.060.080.100.120.140.160.180.20Proportion defectiveSample number2468101214161820UCL = 0.190LCL = 0.010p = 0.10p-Chart in ExcelCopyright 2011 John Wiley & Sons, Inc.3-20Click on “Insert” then “Charts” to construct control chartI4 + 3*SQRT(I4*(1-I4)/100)I4 - 3*SQRT(I4*(1-I4)/100)Column values copiedfrom I5 and I6c-ChartCopyright 2011 John Wiley & Sons, Inc.3-21UCL = c + zcLCL = c - zcwhere c = number of defects per samplec = cc-ChartCopyright 2011 John Wiley & Sons, Inc.3-22Number of defects in 15 sample rooms 1 12 2 8 3 16 : : : : 15 15 190SAMPLE c = = 12.6719015UCL = c + zc = 12.67 + 3 12.67 = 23.35LCL = c - zc = 12.67 - 3 12.67 = 1.99NUMBER OF DEFECTSc-ChartCopyright 2011 John Wiley & Sons, Inc.3-233691215182124Number of defectsSample number246810121416UCL = 23.35LCL = 1.99c = 12.67Control Charts for VariablesCopyright 2011 John Wiley & Sons, Inc.3-24Range chart ( R-Chart )Plot sample range (variability)Mean chart ( x -Chart )Plot sample averages3-25x-bar Chart:  KnownUCL = x + z x LCL = x - z x--==Where = process standard deviationx = standard deviation of sample means =/k = number of samples (subgroups)n = sample size (number of observations) x1 + x2 + ... + xkkX = =---nCopyright 2011 John Wiley & Sons, Inc.Observations(Slip-Ring Diameter, cm) nSample k 1 2 3 4 5-x-bar Chart Example:  KnownCopyright 2011 John Wiley & Sons, Inc.3-26xWe know σ = .08x-bar Chart Example:  KnownCopyright 2011 John Wiley & Sons, Inc.3-27= 5.01 - 3(.08 / )10= 4.93_____1050.09= 5.01X = =LCL = x - z x =-UCL = x + z x =-= 5.01 + 3(.08 / )10= 5.09x-bar Chart Example:  UnknownCopyright 2011 John Wiley & Sons, Inc.3-28_UCL = x + A2R LCL = x - A2R==_wherex = average of the sample meansR = average range value=_Copyright 2011 John Wiley & Sons, Inc.3-29Control Chart Factors n A2 D3 D42 1.880 0.000 3.2673 1.023 0.000 2.5754 0.729 0.000 2.2825 0.577 0.000 2.1146 0.483 0.000 2.0047 0.419 0.076 1.9248 0.373 0.136 1.8649 0.337 0.184 1.81610 0.308 0.223 1.77711 0.285 0.256 1.74412 0.266 0.283 1.71713 0.249 0.307 1.69314 0.235 0.328 1.67215 0.223 0.347 1.65316 0.212 0.363 1.63717 0.203 0.378 1.62218 0.194 0.391 1.60919 0.187 0.404 1.59620 0.180 0.415 1.58521 0.173 0.425 1.57522 0.167 0.435 1.56523 0.162 0.443 1.55724 0.157 0.452 1.54825 0.153 0.459 1.541Factors for R-chartSample SizeFactor for X-chartx-bar Chart Example:  UnknownCopyright 2011 John Wiley & Sons, Inc.3-30 OBSERVATIONS (SLIP- RING DIAMETER, CM) SAMPLE k 1 2 3 4 5 x R 1 5.02 5.01 4.94 4.99 4.96 4.98 0.08 2 5.01 5.03 5.07 4.95 4.96 5.00 0.12 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 4 5.03 4.91 5.01 4.98 4.89 4.96 0.14 5 4.95 4.92 5.03 5.05 5.01 4.99 0.13 6 4.97 5.06 5.06 4.96 5.03 5.01 0.10 7 5.05 5.01 5.10 4.96 4.99 5.02 0.14 8 5.09 5.10 5.00 4.99 5.08 5.05 0.11 9 5.14 5.10 4.99 5.08 5.09 5.08 0.15 10 5.01 4.98 5.08 5.07 4.99 5.03 0.10 50.09 1.15Totalsx-bar Chart Example:  UnknownCopyright 2011 John Wiley & Sons, Inc.3-31∑ Rk1.1510R = = = 0.115__________UCL = x + A2R ==50.0910_____x = = = 5.01 cmxk___= 5.01 + (0.58)(0.115) = 5.08_LCL = x - A2R == 5.01 - (0.58)(0.115) = 4.94x- bar Chart ExampleCopyright 2011 John Wiley & Sons, Inc.3-32UCL = 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=R- ChartCopyright 2011 John Wiley & Sons, Inc.3-33UCL = D4R LCL = D3RR = RkWhere R = range of each sample k = number of samples (sub groups) R-Chart ExampleCopyright 2011 John Wiley & Sons, Inc.3-34 OBSERVATIONS (SLIP- RING DIAMETER, CM) SAMPLE k 1 2 3 4 5 x R 1 5.02 5.01 4.94 4.99 4.96 4.98 0.08 2 5.01 5.03 5.07 4.95 4.96 5.00 0.12 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 4 5.03 4.91 5.01 4.98 4.89 4.96 0.14 5 4.95 4.92 5.03 5.05 5.01 4.99 0.13 6 4.97 5.06 5.06 4.96 5.03 5.01 0.10 7 5.05 5.01 5.10 4.96 4.99 5.02 0.14 8 5.09 5.10 5.00 4.99 5.08 5.05 0.11 9 5.14 5.10 4.99 5.08 5.09 5.08 0.15 10 5.01 4.98 5.08 5.07 4.99 5.03 0.10 50.09 1.15TotalsR-Chart ExampleCopyright 2011 John Wiley & Sons, Inc.3-35Retrieve chart factors D3 and D4UCL = D4R = 2.11(0.115) = 0.243LCL = D3R = 0(0.115) = 0__R-Chart ExampleCopyright 2011 John Wiley & Sons, Inc.3-36UCL = 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 –X-bar and R charts – Excel & OM ToolsCopyright 2011 John Wiley & Sons, Inc.3-37Using x- bar and R-Charts TogetherProcess average and process variability must be in controlSamples can have very narrow ranges, but sample averages might be beyond control limitsOr, sample averages may be in control, but ranges might be out of controlAn R-chart might show a distinct downward trend, suggesting some nonrandom cause is reducing variationCopyright 2011 John Wiley & Sons, Inc.3-38Control Chart PatternsRunsequence of sample values that display same characteristicPattern testdetermines if observations within limits of a control chart display a nonrandom patternCopyright 2011 John Wiley & Sons, Inc.3-39Control Chart PatternsTo identify a pattern look for:8 consecutive points on one side of the center line8 consecutive points up or down14 points alternating up or down2 out of 3 consecutive points in zone A (on one side of center line)4 out of 5 consecutive points in zone A or B (on one side of center line)Copyright 2011 John Wiley & Sons, Inc.3-40Control Chart PatternsCopyright 2011 John Wiley & Sons, Inc.3-41UCLLCLSample observationsconsistently above thecenter lineLCLUCLSample observationsconsistently below thecenter lineControl Chart PatternsCopyright 2011 John Wiley & Sons, Inc.3-42LCLUCLSample observationsconsistently increasingUCLLCLSample observationsconsistently decreasingZones for Pattern Tests3-43UCLLCLZone 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 2011 John Wiley & Sons, Inc.Performing a Pattern TestCopyright 2011 John Wiley & Sons, Inc.3-44 1 4.98 B — B 2 5.00 B U C 3 4.95 B D A 4 4.96 B D A 5 4.99 B U C 6 5.01 — U C 7 5.02 A U C 8 5.05 A U B 9 5.08 A U A 10 5.03 A D B SAMPLE x ABOVE/BELOW UP/DOWN ZONESample Size DeterminationAttribute charts require larger sample sizes50 to 100 parts in a sampleVariable charts require smaller samples2 to 10 parts in a sampleCopyright 2011 John Wiley & Sons, Inc.3-45Process CapabilityCompare natural variability to design variability Natural variabilityWhat we measure with control chartsProcess mean = 8.80 oz, Std dev. = 0.12 ozTolerancesDesign specifications reflecting product requirementsNet weight = 9.0 oz  0.5 oz Tolerances are  0.5 ozCopyright 2011 John Wiley & Sons, Inc.3-46Process CapabilityCopyright 2011 John Wiley & Sons, Inc.3-47(b) Design specifications and natural variation the same; process is capable of meeting specifications most of the time.Design SpecificationsProcess(a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time.Design SpecificationsProcessProcess CapabilityCopyright 2011 John Wiley & Sons, Inc.3-48(c) Design specifications greater than natural variation; process is capable of always conforming to specifications.Design SpecificationsProcess(d) Specifications greater than natural variation, but process off center; capable but some output will not meet upper specification.Design SpecificationsProcessProcess Capability RatioCopyright 2011 John Wiley & Sons, Inc.3-49Cp =tolerance rangeprocess rangeupper spec limit - lower spec limit 6 =Computing CpCopyright 2011 John Wiley & Sons, Inc.3-50Net weight specification = 9.0 oz  0.5 ozProcess mean = 8.80 ozProcess standard deviation = 0.12 ozCp = = = 1.39upper specification limit - lower specification limit 69.5 - 8.56(0.12)Process Capability IndexCopyright 2011 John Wiley & Sons, Inc.3-51Cpk = minimumx - lower specification limit3=upper specification limit - x3=,Computing CpkCopyright 2011 John Wiley & Sons, Inc.3-52Net weight specification = 9.0 oz  0.5 ozProcess mean = 8.80 ozProcess standard deviation = 0.12 ozCpk = minimum = minimum , = 0.83x - lower specification limit3=upper specification limit - x3=,8.80 - 8.503(0.12)9.50 - 8.803(0.12)Process Capability With ExcelCopyright 2011 John Wiley & Sons, Inc.3-53=(D6-D7)/(6*D8)See formula barProcess Capability With OM ToolsCopyright 2011 John Wiley & Sons, Inc.3-54Copyright 2011 John Wiley & Sons, Inc.3-55Copyright 2011 John Wiley & Sons, Inc.All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein.