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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

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

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.

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