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Chapter 16: Quality Control MethodsSupplementary ExercisesΣx i, x = 422. 31 , Σs i= 402 , s = 15. 4615 , Σ i= 1074r = 41.307739. n = 6, k = 26, = 10, 980( ) ( )3 15.4615 1−.952S chart: 15.4615 ±= 15.4615 ± 14.9141 ≈ .55,30.37.9523 (.848)( 41.31)R chart: 41 .31 ± = 41.31 ± 41.44 , so LCL = 0, UCL = 82.752.5363X( 15.4615)chart based on s : 422 .31 ± = 402.42,442.20.952 63( 41.3077)X chart based on r : 422 .31±= 402.36,442.262.536 62r ,40. A c chart is appropriate here. Σx i= 92 so 92 x = = 3. 833 , and24x ± 3 x = 3.833 ± 5.874 , giving LCL = 0 and UCL = 9.7. Because x 22 = 10 > UCL, theprocess appears to have been out of control at the time that the 22 nd plate was obtained.480

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