Statistical-Quality-Control：统计质量控制课件.ppt

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1、,Statistical Process Control,PowerPoint presentation to accompany Heizer and Render Operations Management, Eleventh EditionPrinciples of Operations Management, Ninth EditionPowerPoint slides by Jeff Heyl,6, 2014 Pearson Education, Inc.,SUPPLEMENT,Statistical Process ControlPow,Learning Objectives,Ap

2、ply quality management tools for problem solvingIdentify the importance of data in quality management,6S2,Learning ObjectivesApply quali,Introduction,Statistical process control is a statistical technique that is widely used to ensure that the process meets standards. Acceptance sampling is used to

3、determine acceptance or rejection of material evaluated by a sample.,6S3,IntroductionStatistical Qualit,Introduction,Firing,Preparing the clay for throwing,Wedging,Throwing,Pinching pots,Painting,Pottery Making Process,6S4,IntroductionFiringPreparing th,Introduction,6S5,Introduction6S5,Statistical P

4、rocess Control Chart (SPC),Variability is inherent in every process. Natural variation can not be eliminated Assignable variation - Deviation that can be traced to a specific reason: machine vibration, tool wear, new worker.,6S6,Statistical Process Control Ch,Statistical Process Control Chart (SPC),

5、The essence of SPC is the application of statistical techniques to prevent, detect, and eliminate defective products or services by identifying assignable variation.,6S7,Statistical Process Control Ch,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,Sample number,Mean,Out ofcontrol,Natural variationdue to chan

6、ce,Abnormal variationdue to assignable sources,Abnormal variationdue to assignable sources,A control chart is a time-ordered plot obtained from an ongoing process,6S8,Statistical Process Control Chart (SPC),0123456789101112131415UCLLCLSa,Statistical Process Control Chart (SPC),Attribute Data (discre

7、te): qualitative characteristic or condition, such as pass/fail, good/bad, go/no go.,Variable Data (continuous): quantifiable conditions along a scale, such as speed, length, density, etc.,6S9,Statistical Process Control Ch,Take random samplesCalculate the upper control limit (UCL) and the lower con

8、trol limit (LCL)Plot UCL, LCL and the measured valuesIf 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.If one or more data points fall outside the control limits, then the process is as

9、sumed to be out of control and corrective actions need to be taken.,Statistical Process Control Chart (SPC),6S-10,Take random samplesStatistical,x-Charts,Lower control limit (LCL) = x - A2R,Upper control limit (UCL) = x + A2R,whereR=average range of the samplesA2=control chart factor from Table S6.1

10、(page 241) x=average of the sample means,6S11,x-Charts Lower control limit (,Range=18-13=5,Hour 1BoxWeight ofNumberOat Flakes117213316418517616715817916,x-Charts,6S12,Range=17-14=3,Hour 2BoxWeight ofNumberOat Flakes114216315414517615715814917,R=(5+3)/2 = 4,Range=18-13=5Hour 1x-Charts,x-Charts,Lower

11、control limit (LCL) = x - A2R,Upper control limit (UCL) = x + A2R,whereR=average range of the samplesA2=control chart factor from Table S6.1 (page241) x=average of the sample means,6S13,x-Charts Lower control limit (,Average=(17+13+16)/9=16.11,Hour 1BoxWeight ofNumberOat Flakes1172133164185176167158

12、17916,x-Charts,6S14,Average=(14+16+17)/9=15.22,Hour 2BoxWeight ofNumberOat Flakes114216315414517615715814917,x=(16.11+15.22)/2 = 15.665,Average=(17+13+16)/9=16.11,x-Charts,Lower control limit (LCL) = x - A2R,Upper control limit (UCL) = x + A2R,whereR=average range of the samplesA2=control chart fact

13、or from Table S6.1 (page241) x=average of the sample means,6S15,x-Charts Lower control limit (,x-Charts,6S16,x-Charts Sample Size Mean Fa,x-Charts,Lower control limit (LCL) = x - A2R,Upper control limit (UCL) = x + A2R,whereR=average range of the samplesA2=control chart factor from Table S6.1 (page2

14、41) x=average of the sample means,6S17,x-Charts Lower control limit (,x-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

15、 size = n = 7,A2 = ?,6S18,x-Charts Example S6.1: Eight s,x-Charts,6S19,x-Charts 6S19Sample Size Me,x-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

16、 any actions be taken?,A2 = 0.42,6S20,x-Charts Example S6.1: Eight s,x-Charts,Control Chart for sample of 7 tubes,6.36 = Mean,Sample number,|123456789101112,It is assumed that the central tendency of process is in control with 99.73% confidence. No actions need to be taken except to continuously mon

17、itor this process.,6S21,x-Charts Control Chart for sam,Steps in Creating Charts,Take samples from the population and compute the appropriate sample statisticUse the sample statistic to calculate control limitsPlot control limits and measured valuesDetermine the state of the process (in or out of con

18、trol)Investigate possible assignable causes and take actions,6S22,Steps in Creating ChartsTake s,R-Charts,Lower control limit (LCL) = D3R,Upper control limit (UCL) = D4R,whereR=average range of the samplesD3 and D4=control chart factors from Table S6.1 (Page 241),6S23,R-ChartsLower control limit (L,

19、R-Charts,6S24,R-Charts6S24Sample Size Mea,R-Charts,Average range R = 5.3 poundsSample size n = 5From Table S6.1 D4 = ? D3 = ?,Example S6.2,6S25,R-ChartsAverage range R = 5.3,R-Charts,6S26,R-Charts6S26Sample Size Mea,R-Charts,UCLR = D4R= (2.12)(5.3)= 11.2 pounds,LCLR = D3R= (0)(5.3)= 0 pounds,Average

20、 range R = 5.3 poundsSample size n = 5From Table S6.1 D4 = 2.12, D3 = 0,Example S6.2,6S27,R-ChartsUCLR = D4RLCLR = D3R,R-Charts,n=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 u

21、nder statistical control? Why or why not? Should any actions be taken?,D3 =? D4 = ?,6S28,R-Chartsn=7 Example S6.3: Refe,R-Charts,6S29,R-Charts6S29Sample Size Mea,R-Charts,6S30,Example S6.3: Refer to Example S6.1. Eight samples of seven tubes were taken at random intervals. Construct the R-chart with

22、 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-Charts6S30Example S6.3: Ref,R-Charts,Control Chart for sample of 7 tubes,Sample number,|123456789101112,0.17 = R,The variation of process is in control with 99.73%

23、 confidence.,6S31,R-ChartsControl Chart for samp,Mean and Range Charts,(a) The central tendency of process is in control, but its variation is not in control.,6S32,Mean and Range ChartsR-chart(R,Mean and Range Charts,(b) The variation of process is in control, but its central tendency is not in cont

24、rol.,R-chart,(R-chart does not detect changes in mean),UCL,LCL,6S33,Mean and Range Charts(b) The v,R-Chart and X-Chart,Example 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 produ

25、ction 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 = 3.0,6S34,R-Chart and X-ChartExample S6.,R-Chart and X-Chart,Control Chart for sample of 4 resistors,6.84 = UCL,0 = LCL,Sample number,|123456789101112,3.0 = R,The variatio

26、n of process is in control with 99.73% confidence.,6S35,R-Chart and X-ChartControl Cha,R-Chart and X-Chart,X= (100.5 + 101.5 + + 101.0)/7 99.79,n = 4, A2 = 0.73,R = (3 + 2 + + 4)/7 = 3.0,6S36,R-Chart and X-ChartX= (100.5 +,R-Chart and X-Charts,Control Chart,101.98 = UCL,97.6 = LCL,99.79 = Mean,Sampl

27、e number,|123456789101112,The 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.,6S37,R-Chart and X-

28、ChartsControl Ch,EX 1 in class,A 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. Calcul

29、ate the control limits, plot the control charts, and determine if the process is in control,6S38,EX 1 in classA part that conne,R-Chart and X-Chart,6S39,Example S6.5: Resistors for electronic circuits are manufactured at Omega Corporation in Denton, TX. The head of the firms Continuous Improvement D

30、ivision 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 statistic

31、al control? Why or why not?,R-Chart and X-Chart6S39Exampl,R-Chart and X-Chart,n=4,D3 =0 D4 = 2.28,6.84 = UCL,0 = LCL,Sample number,|123456789101112,3.0 = R,variation of process is in control with 99.73% confidence.,6S40,R-Chart and X-Chart# of Sample,R-Chart and X-Chart,n=4,102.0 = UCL,97.6 = LCL,Sa

32、mple number,|123456789101112,99.8 = X,central tendency of process is not in control with 99.73% confidence.,Thus, entire process is not in control.,6S41,A2 =0.73,X= (100.5 + + 101.0)/7 99.8,R-Chart and X-Chart# of Sample,EX 2 in class,A quality analyst wants to construct a sample mean chart for cont

33、rolling 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 control,6S42,EX 2 in classA quality analyst,Statistical Process Control Chart (SPC),Att

34、ribute Data (discrete): qualitative characteristic or condition, such as pass/fail, good/bad, go/no go.,Variable Data (continuous): quantifiable conditions along a scale, such as speed, length, density, etc.,6S43,Statistical Process Control Ch,Control Charts for Attribute Data,Categorical variablesG

35、ood/bad, yes/no, acceptable/unacceptableMeasurement is typically counting defectivesCharts may measurePercentage of defects (p-chart)Number of defects (c-chart),6S44,Control Charts for Attribute D,P-Charts,wherep=mean percent defective overall the samplesz=number of standard deviations = 3n=sample s

36、ize,6S45,P-Chartswherep=mean percent,P-Charts,Example 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 proc

37、ess is in control.,6S46,P-ChartsSampleNumberPercent,P-Charts,n = 100,Because we cannot have a negative percent defective,6S47,P-Chartsn = 100 Because we can,P-Charts,|2468101214161820,The process is not in control with 99.73% confidence.,6S48,P-Charts.11 Sample numberPer,C-Charts,A c-chart is used w

38、hen the quality cannot be measured as a percentage. Number of car accidents per month at a particular intersection Number of complaints the service center of a hotel receives per week Number of scratches on a nameplate Number of dimples found on a metal sheet,6S49,C-ChartsA c-chart is used when,C-Ch

39、arts,wherec=mean number defective overall the samples,UCL = c + 3 c,LCL = c - 3 c,6S50,C-Chartswherec=mean number,C-Charts,c = 54 / 9 = 6 complaints /week,Example S6.7: Over 9 weeks, Red Top Cab company received the following numbers of calls from irate passengers: 3, 0, 8, 9, 6, 7, 4, 9, 8, for a t

40、otal of 54 complaints. Determine the 3- control limits of a c-Chart.,Because we cannot have the negative number of defective records,UCL= c + 3 c= 6 + 3 6= 13.35,LCL= c - 3 c= 6 - 3 6= - 1.35 = 0,The process is in control with 99.73% confidence.,6S51,C-Chartsc = 54 / 9 = 6 complai,Effective quality management is data drivenThere are multiple tools to identify and prioritize process problemsThere are multiple tools to identify the relationships between variables,Managing Quality Summary,6S52,Effective quality management i,