Statistical Quality Control：统计质量控制.ppt
Statistical Process ControlPowerPoint presentation to accompany Heizer and Render Operations Management,Eleventh EditionPrinciples of Operations Management,Ninth EditionPowerPoint slides by Jeff Heyl6 2014 Pearson Education,Inc.SUPPLEMENTSUPPLEMENTLearning Objectives1.Apply quality management tools for problem solving2.Identify the importance of data in quality management6S6S2 2IntroductionStatistical Quality ControlStatistical Process Control(SPC)Acceptance Sampling(AS)pStatistical process control is a statistical technique that is widely used to ensure that the process meets standards.pAcceptance sampling is used to determine acceptance or rejection of material evaluated by a sample.6S6S3 3IntroductionFiringPreparing the clay for throwingWedgingThrowingPinching potsPaintingPottery Making Process6S6S4 4Introduction6S6S5 5Statistical Process Control Chart(SPC)pVariability is inherent in every process.nNatural variation can not be eliminated nAssignable variation-Deviation that can be traced to a specific reason:machine vibration,tool wear,new worker.VariationNatural VariationAssignable Variation6S6S6 6Statistical Process Control Chart(SPC)pThe essence of SPC is the application of statistical techniques to prevent,detect,and eliminate defective products or services by identifying assignable variation.6S6S7 7012345678910 1112 13 14 15UCLLCLSample numberMeanOut ofcontrolNatural variationdue to chanceAbnormal variationdue to assignable sourcesAbnormal variationdue to assignable sourcesA control chart is a time-ordered plot obtained from an ongoing process6S6S8 8Statistical Process Control Chart(SPC)Statistical Process Control Chart(SPC)Control ChartsControl Charts for Variable DataControl Charts for Attribute Data-charts(for controlling central tendency)R-charts(for controlling variation)p-charts(for controlling percent defective)c-charts(for controlling number of defects)pAttribute Data(discrete):qualitative characteristic or condition,such as pass/fail,good/bad,go/no go.pVariable Data(continuous):quantifiable conditions along a scale,such as speed,length,density,etc.6S6S9 91.Take random samples2.Calculate the upper control limit(UCL)and the lower control limit(LCL)3.Plot UCL,LCL and the measured values4.If all the measured values fall within the LCL and the UCL,then the process is assumed to be in control and no actions should be taken except continuing to monitor.5.If one or more data points fall outside the control limits,then the process is assumed to be out of control and corrective actions need to be taken.Statistical Process Control Chart(SPC)6S-10 x-Charts Lower control limit Lower control limit(LCL)(LCL)=x-A=x-A2 2R RUpper control limit Upper control limit(UCL)(UCL)=x+A=x+A2 2R RwherewhereR R=average range of the samplesaverage range of the samplesA A2 2=control chart factor from Table S6.1(page 241)control chart factor from Table S6.1(page 241)x x=average of the sample meansaverage of the sample means6S6S1111Range=18-13=5Hour 1Hour 1BoxBoxWeight ofWeight ofNumberNumberOat FlakesOat Flakes1 117172 213133 316164 418185 517176 616167 715158 817179 91616x-Charts 6S6S1212Range=17-14=3Hour 2Hour 2BoxBoxWeight ofWeight ofNumberNumberOat FlakesOat Flakes1 114142 216163 315154 414145 517176 615157 715158 814149 91717R R=(5+3)/2=4(5+3)/2=4x-Charts Lower control limit Lower control limit(LCL)(LCL)=x-A=x-A2 2R RUpper control limit Upper control limit(UCL)(UCL)=x+A=x+A2 2R RwherewhereR R=average range of the samplesaverage range of the samplesA A2 2=control chart factor from Table S6.1(page241)control chart factor from Table S6.1(page241)x x=average of the sample meansaverage of the sample means6S6S1313Average=(17+13+16)/9=16.11Hour 1Hour 1BoxBoxWeight ofWeight ofNumberNumberOat FlakesOat Flakes1 117172 213133 316164 418185 517176 616167 715158 817179 91616x-Charts 6S6S1414Average=(14+16+17)/9=15.22Hour 2Hour 2BoxBoxWeight ofWeight ofNumberNumberOat FlakesOat Flakes1 114142 216163 315154 414145 517176 615157 715158 814149 91717x x=(16.11+15.22)/2=15.665(16.11+15.22)/2=15.665x-Charts Lower control limit Lower control limit(LCL)(LCL)=x-A=x-A2 2R RUpper control limit Upper control limit(UCL)(UCL)=x+A=x+A2 2R RwherewhereR R=average range of the samplesaverage range of the samplesA A2 2=control chart factor from Table S6.1(page241)control chart factor from Table S6.1(page241)x x=average of the sample meansaverage of the sample means6S6S1515x-Charts Sample Size Sample Size Mean Factor Mean Factor Upper Range Upper Range Lower RangeLower Range n n A A2 2 D D4 4 D D3 32 21.881.883.273.270 03 31.021.022.582.580 04 4.73.732.282.280 05 5.58.582.122.120 06 6.48.482.002.000 07 7.42.421.921.920.080.088 8.37.371.861.860.140.149 9.34.341.821.820.180.181010.31.311.781.780.220.221111.29.291.741.740.260.266S6S1616x-Charts Lower control limit Lower control limit(LCL)(LCL)=x-A=x-A2 2R RUpper control limit Upper control limit(UCL)(UCL)=x+A=x+A2 2R RwherewhereR R=average range of the samplesaverage range of the samplesA A2 2=control chart factor from Table S6.1(page241)control chart factor from Table S6.1(page241)x x=average of the sample meansaverage of the sample means6S6S1717x-Charts Example S6.1:Eight samples of seven tubes were taken at random intervals.Construct the x-chart with 3-control limit.Is the current process under statistical control?Why or why not?Should any actions be taken?Sample size=n=7A2=?6S6S1818x-Charts 6S6S1919Sample Size Sample Size Mean Factor Mean Factor Upper Range Upper Range Lower RangeLower Range n n A A2 2 D D4 4 D D3 32 21.881.883.273.270 03 31.021.022.582.580 04 4.73.732.282.280 05 5.58.582.122.120 06 6.48.482.002.000 07 7.42.421.921.920.080.088 8.37.371.861.860.140.149 9.34.341.821.820.180.181010.31.311.781.780.220.221111.29.291.741.740.260.26x-Charts Example S6.1:Eight samples of seven tubes were taken at random intervals.Construct the x-chart with 3-control limit.Is the current process under statistical control?Why or why not?Should any actions be taken?A2=0.42 6S6S2020 x-Charts Control Chart Control Chart for sample of for sample of 7 tubes7 tubes6.43=UCL6.43=UCL6.29=LCL6.29=LCL6.36=Mean6.36=MeanSample numberSample number|1 12 23 34 45 56 67 78 89 9 1010 1111 1212It is assumed that the central tendency of process is in control with 99.73%confidence.No actions need to be taken except to continuously monitor this process.6S6S2121Steps in Creating Charts1.Take samples from the population and compute the appropriate sample statistic2.Use the sample statistic to calculate control limits3.Plot control limits and measured values4.Determine the state of the process(in or out of control)5.Investigate possible assignable causes and take actions6S6S2222R-ChartsLower control limit Lower control limit(LCL)(LCL)=D=D3 3R RUpper control limit Upper control limit(UCL)(UCL)=D=D4 4R RwherewhereR R=average range of the samplesaverage range of the samplesD D3 3 and D and D4 4=control chart factors from Table S6.1 control chart factors from Table S6.1(Page 241)(Page 241)6S6S2323R-Charts6S6S2424Sample Size Sample Size Mean Factor Mean Factor Upper Range Upper Range Lower RangeLower Range n n A A2 2 D D4 4 D D3 32 21.881.883.273.270 03 31.021.022.582.580 04 4.73.732.282.280 05 5.58.582.122.120 06 6.48.482.002.000 07 7.42.421.921.920.080.088 8.37.371.861.860.140.149 9.34.341.821.820.180.181010.31.311.781.780.220.221111.29.291.741.740.260.26R-ChartsAverage range R Average range R=5.3=5.3 poundspoundsSample size n Sample size n=5=5From From Table S6.1Table S6.1 D D4 4 =?=?D D3 3=?=?Example S6.2Example S6.26S6S2525R-Charts6S6S2626Sample Size Sample Size Mean Factor Mean Factor Upper Range Upper Range Lower RangeLower Range n n A A2 2 D D4 4 D D3 32 21.881.883.273.270 03 31.021.022.582.580 04 4.73.732.282.280 05 5.58.582.122.120 06 6.48.482.002.000 07 7.42.421.921.920.080.088 8.37.371.861.860.140.149 9.34.341.821.820.180.181010.31.311.781.780.220.221111.29.291.741.740.260.26R-ChartsUCLUCLR R =D=D4 4R R=(2.12)(5.3)=(2.12)(5.3)=11.2=11.2 poundspoundsLCLLCLR R =D=D3 3R R=(0)(5.3)=(0)(5.3)=0=0 poundspoundsAverage range R Average range R=5.3=5.3 poundspoundsSample size n Sample size n=5=5From From Table S6.1Table S6.1 D D4 4 =2.12,=2.12,D D3 3=0=0UCL=11.2UCL=11.2Mean=5.3Mean=5.3LCL=0LCL=0Example S6.2Example S6.26S6S2727R-Chartsn=7 Example S6.3:Refer to Example S6.1.Eight samples of seven tubes were taken at random intervals.Construct the R-chart with 3-control limits.Is the current process under statistical control?Why or why not?Should any actions be taken?D3=?D4=?6S6S2828R-Charts6S6S2929Sample Size Sample Size Mean Factor Mean Factor Upper Range Upper Range Lower RangeLower Range n n A A2 2 D D4 4 D D3 32 21.881.883.273.270 03 31.021.022.582.580 04 4.73.732.282.280 05 5.58.582.122.120 06 6.48.482.002.000 07 7.42.421.921.920.080.088 8.37.371.861.860.140.149 9.34.341.821.820.180.181010.31.311.781.780.220.221111.29.291.741.740.260.26R-Charts6S6S3030Example S6.3:Refer to Example S6.1.Eight samples of seven tubes were taken at random intervals.Construct the R-chart with 3-control limits.Is the current process under statistical control?Why or why not?Should any actions be taken?D3=0.08,D4=1.92 R-ChartsControl Chart Control Chart for sample of for sample of 7 tubes7 tubes0.33=UCL0.33=UCL0.01=LCL0.01=LCLSample numberSample number|1 12 23 34 45 56 67 78 89 9 1010 1111 12120.17=R0.17=RThe variation of process is in control with 99.73%confidence.6S6S3131Mean and Range ChartsR-chartR-chart(R-chart detects(R-chart detects increase in increase in dispersion)dispersion)UCLUCLLCLLCL(a)The central tendency of process is in control,but its variation is not in control.x-chartx-chart(x-chart does not(x-chart does not detect dispersion)detect dispersion)UCLUCLLCLLCL6S6S3232Mean and Range Charts(b)The variation of process is in control,but its central tendency is not in control.R-chartR-chart(R-chart does not(R-chart does not detect changes in detect changes in mean)mean)UCLUCLLCLLCLx-chartx-chart(x-chart detects(x-chart detects shift in central shift in central tendency)tendency)UCLUCLLCLLCL6S6S3333R-Chart and X-ChartExample S6.4:Seven random samples of four resistors each are taken to establish the quality standards.Develop the R-chart and the x-chart both with 3-control limits for the production process.Is the entire process under statistical control?Why or why not?D3=0,and D4=2.28 n=4 R=(3+2+4)/7=3.0 6S6S3434R-Chart and X-ChartControl Chart Control Chart for sample of for sample of 4 resistors4 resistors6.84=UCL6.84=UCL0=LCL0=LCLSample numberSample number|1 12 23 34 45 56 67 78 89 9 1010 1111 12123.0=R3.0=RThe variation of process is in control with 99.73%confidence.6S6S3535R-Chart and X-ChartX=(100.5+101.5+101.0)/7 99.79 n=4,A2=0.73 R=(3+2+4)/7=3.0 6S6S3636R-Chart and X-ChartsControl ChartControl Chart101.98=UCL101.98=UCL97.6=LCL97.6=LCL99.79=Mean99.79=MeanSample numberSample number|1 12 23 34 45 56 67 78 89 9 1010 1111 1212The central tendency of process is not in control with 99.73%confidence.In conclusion,with 99.7%confidence,the entire resistor production process is not in control since its central tendency is out of control although its variation is under control.6S6S3737EX 1 in classA part that connects two levels should have a distance between the two holes of 4”.It has been determined that x-bar chart and R-chart should be set up to determine if the process is in statistical control.The following ten samples of size four were collected.Calculate the control limits,plot the control charts,and determine if the process is in controlNo.of SampleMeanRange14.010.0423.980.0634.000.0243.990.0554.000.0663.970.0274.020.0283.990.0493.980.05104.010.066S6S3838R-Chart and X-Chart6S6S3939Example S6.5:Resistors for electronic circuits are manufactured at Omega Corporation in Denton,TX.The head of the firms Continuous Improvement Division is concerned about the product quality and sets up production line checks.She takes seven random samples of four resistors each to establish the quality standards.Develop the R-chart and the chart both with 3-control limits for the production process.Is the entire process under statistical control?Why or why not?#of sampleReadings of Resistance(ohms)1991001021012101103101101398102101994991009910059999981006951009796710199101103R-Chart and X-Chart#of Sample1234567Sample range3241254Sample mean100.5101.5100.099.599.097.0101.0n=4 D3=0 D4=2.28 6.84=UCL6.84=UCL0=LCL0=LCLSample numberSample number|1 12 23 34 45 56 67 78 89 9 1010 1111 12123.0=R3.0=Rvariation of process is in control with 99.73%confidence.6S6S4040R-Chart and X-Chart#of Sample1234567Sample range3241254Sample mean100.5101.5100.099.599.097.0101.0n=4 102.0=UCL102.0=UCL97.6=LCL97.6=LCLSample numberSample number|1 12 23 34 45 56 67 78 89 9 1010 1111 121299.8=X99.8=Xcentral tendency of process is not in control with 99.73%confidence.Thus,entire process is not in control.6S6S4141A2=0.73 X=(100.5+101.0)/7 99.8 EX 2 in classA quality analyst wants to construct a sample mean chart for controlling a packaging process.Each day last week,he randomly selected four packages and weighed each.The data from that activity appears below.Set up control charts to determine if the process is in statistical controlDayPackage 1Package 2Package 3Package 4Monday23222324Tuesday23211921Wednesday20192021Thursday18192019Friday182022206S6S4242Statistical Process Control Chart(SPC)Control ChartsControl Charts for Variable DataControl Charts for Attribute Data-charts(for controlling central tendency)R-charts(for controlling variation)p-charts(for controlling percent defective)c-charts(for controlling number of defects)pAttribute Data(discrete):qualitative characteristic or condition,such as pass/fail,good/bad,go/no go.pVariable Data(continuous):quantifiable conditions along a scale,such as speed,length,density,etc.6S6S4343Control Charts for Attribute DatapCategorical variablesnGood/bad,yes/no,acceptable/unacceptablepMeasurement is typically counting defectivespCharts may measurenPercentage of defects(p-chart)nNumber of defects(c-chart)6S6S4444P-Chartswherewherep p=mean percent defective overall the samplesmean percent defective overall the samplesz z=number of standard deviations=3number of standard deviations=3n n=sample sizesample size6S6S4545P-ChartsSampleSampleNumberNumberPercentPercentSampleSampleNumberNumberPercentPercentNumberNumberof Errorsof ErrorsDefectiveDefectiveNumberNumberof Errorsof ErrorsDefectiveDefective1 16 6.06.0611116 6.06.062 25 5.05.0512121 1.01.013 30 0.00.0013138 8.08.084 41 1.01.0114147 7.07.075 54 4.04.0415155 5.05.056 62 2.02.0216164 4.04.047 75 5.05.0517171111.11.118 83 3.03.0318183 3.03.039 93 3.03.0319190 0.00.0010102 2.02.0220204 4.04.04Total Total=80=80Example S6.6:Data-entry clerks at ARCO key in thousands of insurance records each day.One hundred records entered by each clerk were carefully examined and the number of errors counted.Develop a p-chart with 3-control limits and determine if the process is in control.6S6S4646P-Chartsn=100 Because we cannot have a negat
