Control Charts  Control chart: A time-ordered diagram that is used to determine whether observed variations are abnormal. A sample statistic that falls between the UCL and the LCL indicates that the process is exhibiting common causes of variation; a statistic that falls outside the control limits indicates that the process is exhibiting assignable causes of variation. © 2007 Pearson Education
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OTHER CHARTS AVAILABLE FROM GOOGLE CHARTS Traditional Graphs Diagrams Area Charts (Traditional and Stepped) Bubble Charts Bar Charts Box and Whisker Plots (Candlestick Charts) Column Charts Calendar Charts Combo Charts Gauge Charts Histograms Geographic Charts Intervals Organizational Charts Line Charts Tables Pie Charts Timelines Scatter Charts Tree Map Charts Time Series (Annotated) Word Trees Trend lines **User created community charts are also available**
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Control Charts for Variables Control Chart Factors Factor for UCL Factor for Factor Control - Special Metal Screw UCL for Size of Charts and LCL for LCL for Sample R-Charts R-Charts R = 0.0020 x - Charts x-Charts (n) (A2) x = 0.5025 (D3) (D4) 2 1.880 UCL = x + A x 2R 3 1.023 LCL 4 x = x - A0.729 2R 5 6 7 0.577 0.483 0.419 0 0 0 0 0 0.076 3.267 2.575 2.282 2.115 2.004 1.924
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Why do we need 2 charts? Consistent, but the average is in the wrong place UCL UCL LCL LCL X-Bar Chart R Chart The average works out ok, but way too much variability between points UCL UCL LCL LCL X-Bar Chart R Chart
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Lead Indicators of Quality Variation Variation indicates indicates poor poor quality. quality. To To measure measure variation, variation, there there are are several several tools tools that that can can be be used: used: Histograms Histograms Run Run Charts Charts Control Control Charts Charts UCL Defects 7-15 LCL Notice AArun that with process upper Notice runchart chart thatthis this with process upper and seems lower control be limits. of and seems lowerto to control beout out limits. of control controlon onFridays. Fridays.
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Control Charts for Variables Control Chart Factors Factor for UCL Factor for Factor Control - Special Metal Screw UCL for Size of Charts and LCL for LCL for Sample R-Charts R-Charts R = 0.0020 D4 = 2.2080 R - Charts x-Charts (n) (A2) (D3) (D4) 2 3 4 5 6 7 1.880 1.023 0.729 0.577 0.483 0.419 0 0 0 0 0 0.076 3.267 2.575 2.282 2.115 2.004 1.924
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Causes of Variation  Two basic categories of variation in output include common causes and assignable causes.  Common causes are the purely random, unidentifiable sources of variation that are unavoidable with the current process.  If process variability results solely from common causes of variation, a typical assumption is that the distribution is symmetric, with most observations near the center.  Assignable causes of variation are any variationcausing factors that can be identified and eliminated, such as a machine needing repair. © 2007 Pearson Education
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West Allis Industries R-chart Control Chart Factors Example 6.1 Factor Size of for Sample Charts (n) Factor for UCL Factor for and LCL for LCL for x-Charts R-Charts (A2) (D3) 2 1.880 0 3.267 3 1.023 0 R = 0.0021 2.575 4 0.729 0 D4 = 2.282 2.282 5 0.577 0 UCLR = D4R = 2.282 (0.0021) = 0.00479 in. D3 = 0 2.115 LCLR = D3R 0.483 0 (0.0021) = 0 in. 0 © 2007 Pearson Education 6 2.004 UCL R(D4)
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West Allis Industries x-chart Control Chart Factor Example 6.1 Factor Size of for Sample Charts (n) Factor for UCL Factor for and LCL for LCL for x-Charts R-Charts (A2) (D3) 2 1.880 0 3.267 3 1.023 0 R = 0.0021 A2 = 0.729 =x = 0.5027 2.575 0.729+ 0.729 (0.0021) 0= 0.5042 in. UCLx4= x= + A2R = 0.5027 2.282 = LCLx 5= x - A2R = 0.5027 0.577– 0.729 (0.0021) =0 0.5012 in. © 2007 Pearson Education 2.115 UCL R(D4)
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