1、Statistical Process ControlPowerPoint presentation to accompany Heizer and Render Operations Management,Eleventh EditionPrinciples of Operations Management,Ninth EditionPowerPoint slides by Jeff Heyl 2014 Pearson Education,Inc.Learning Objectives1.Apply quality management tools for problem solving2.
2、Identify the importance of data in quality managementIntroductionStatistical 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 de
3、termine acceptance or rejection of material evaluated by a sample.IntroductionFiringPreparing the clay for throwingWedgingThrowingPinching potsPaintingPottery Making ProcessIntroductionStatistical Process Control Chart(SPC)pVariability is inherent in every process.nNatural variation can not be elimi
4、nated nAssignable variation-Deviation that can be traced to a specific reason:machine vibration,tool wear,new worker.VariationNatural VariationAssignable VariationStatistical Process Control Chart(SPC)pThe essence of SPC is the application of statistical techniques to prevent,detect,and eliminate de
5、fective products or services by identifying assignable variation.012345678910 11 12 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
6、ongoing processStatistical Process Control Chart(SPC)Statistical Process Control Chart(SPC)Control ChartsControl Charts for Variable DataControl Charts for Attribute Data-charts(for controlling central tendency)xR-charts(for controlling variation)p-charts(for controlling percent defective)c-charts(f
7、or 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.1.Take random samples2.Calculate the upper control limit(UCL)and th
8、e 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
9、process is assumed to be out of control and corrective actions need to be taken.Statistical Process Control Chart(SPC)6S-10 x-Charts Range=18-13=5x-Charts Range=17-14=3x-Charts Average=(17+13+16)/9=16.11x-Charts Average=(14+16+17)/9=15.22x-Charts x-Charts x-Charts x-Charts Example S6.1:Eight samples
10、 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=?x-Charts x-Charts oz 29.6)17.0(42.036.62RAxLCLoz 36.6834.6.38.636.6xoz 43.6)17.0(42.036.62RAxUCLoz
11、17.0818.0.18.016.0RExample 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 x-Charts It is assumed that the central tendency of process is in
12、 control with 99.73%confidence.No actions need to be taken except to continuously monitor this process.Steps 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 value
13、s4.Determine the state of the process(in or out of control)5.Investigate possible assignable causes and take actionsR-ChartsR-ChartsR-ChartsR-ChartsR-ChartsR-Chartsoz 17.0818.0.18.016.0Rn=7 Example S6.3:Refer to Example S6.1.Eight samples of seven tubes were taken at random intervals.Construct the R
14、-chart with 3-control limits.Is the current process under statistical control?Why or why not?Should any actions be taken?D3=?D4=?R-ChartsR-Chartsoz 17.0818.0.18.016.0RExample S6.3:Refer to Example S6.1.Eight samples of seven tubes were taken at random intervals.Construct the R-chart with 3-control l
15、imits.Is the current process under statistical control?Why or why not?Should any actions be taken?oz 01.0)17.0(08.03RDLCLoz 33.0)17.0(92.14RDUCLD3=0.08,D4=1.92 R-ChartsThe variation of process is in control with 99.73%confidence.Mean and Range Charts(a)The central tendency of process is in control,b
16、ut its variation is not in control.Mean and Range Charts(b)The variation of process is in control,but its central tendency is not in control.R-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 bo
17、th 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 0)0.3(03RDLCL6.84)0.3(28.24RDUCLR-Chart and X-ChartThe variation of process is in control with 99.73%confidence.R-Chart and X-ChartX=(100.5+101.5+10
18、1.0)/7 99.79 n=4,A2=0.73 R=(3+2+4)/7=3.0 97.6)0.3(73.079.992RAxLCL101.98)0.3(73.079.992RAxUCLR-Chart and X-ChartsThe 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 tende
19、ncy is out of control although its variation is under control.EX 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 s
20、amples of size four were collected.Calculate the control limits,plot the control charts,and determine if the process is in controlNo.of SampleMeanRange14.010.0423.980.0634.000.0243.990.0554.000.0663.970.0274.020.0283.990.0493.980.05104.010.06R-Chart and X-ChartExample S6.5:Resistors for electronic c
21、ircuits 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
22、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 range3241254S
23、ample mean100.5101.5100.099.599.097.0101.03.074.23Rn=4 D3=0 D4=2.28 03RDLCL84.60.328.24RDUCLvariation of process is in control with 99.73%confidence.R-Chart and X-Chart#of Sample1234567Sample range3241254Sample mean100.5101.5100.099.599.097.0101.03.074.23Rn=4 central tendency of process is not in co
24、ntrol with 99.73%confidence.Thus,entire process is not in control.A2=0.73 X=(100.5+101.0)/7 99.8 97.6)0.3(73.08.992RAxLCL102.0)0.3(73.08.992RAxUCLEX 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 pac
25、kages 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 4Monday23222324Tuesday23211921Wednesday20192021Thursday18192019Friday18202220Statistical Process Control Chart(SPC)Control
26、 ChartsControl Charts for Variable DataControl Charts for Attribute Data-charts(for controlling central tendency)xR-charts(for controlling variation)p-charts(for controlling percent defective)c-charts(for controlling number of defects)pAttribute Data(discrete):qualitative characteristic or condition
27、,such as pass/fail,good/bad,go/no go.pVariable Data(continuous):quantifiable conditions along a scale,such as speed,length,density,etc.Control Charts for Attribute DatapCategorical variablesnGood/bad,yes/no,acceptable/unacceptablepMeasurement is typically counting defectivespCharts may measurenPerce
28、ntage of defects(p-chart)nNumber of defects(c-chart)P-ChartsnppzpzpUCLp)1(nppzpzpLCLp)1(P-ChartsExample 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 w
29、ith 3-control limits and determine if the process is in control.P-Charts040.0)20)(100(80examined records ofnumber Totalerrors ofnumber Totalp099.0100)04.01(04.0304.0)1(nppzpUCL0019.0100)04.01(04.0304.0)1(nppzpLCLn=100 Because we cannot have a negative percent defective 040.02004.0.05.006.0samples of
30、Number defectivefraction Total ,porP-Charts|Possible assignable causes presentPossible good assignable causes presentThe process is not in control with 99.73%confidence.C-ChartspA c-chart is used when the quality cannot be measured as a percentage.nNumber of car accidents per month at a particular i
31、ntersection nNumber of complaints the service center of a hotel receives per week nNumber of scratches on a nameplate nNumber of dimples found on a metal sheet C-ChartsC-Charts|1|2|3|4|5|6|7|8|94 2 Example S6.7:Over 9 weeks,Red Top Cab company received the following numbers of calls from irate passe
32、ngers:3,0,8,9,6,7,4,9,8,for a total of 54 complaints.Determine the 3-control limits of a c-Chart.Because we cannot have the negative number of defective recordsThe process is in control with 99.73%confidence.1.Effective quality management is data driven2.There are multiple tools to identify and prioritize process problems3.There are multiple tools to identify the relationships between variablesManaging Quality Summary
