chapter 1

Chapter 16: Quality Control Methods−122. The suggested transformation is Y h(X)= sin ( n )X1sin ( p )− and approximate variance1 ( ) ( ) . −sin1 x 1 −1= sin .050 .4n= 2255nxiradians), and the values of yi= sin ( n )−1 for i = 1, 2, 3, …, 30 are= , with approximate mean value0.2255 0.2367 0.2774 0.39770.3047 0.3537 0.3381 0.28680.3537 0.3906 0.2475 0.23670.2958 0.2774 0.3218 0.32180.4446 0.2868 0.2958 0.26780.3133 0.3300 0.3047 0.38350.1882 0.3047 0.24750.3614 0.2958 0.3537(inThese give = 9. 2437yΣ iy and y = . 3081± 34n800. The control limits are1 1= .3081±3 = .3081±.1091= .2020,.4142. In contrast ot the result ofexercise 20, there I snow one point below the LCL (.1882 < .2020) as well as one point abovethe UCL.23. = 102x , = 4. 08Σ iUCL = 10.1. Because nox , and x ± 3 x = 4.08 ± 6.06 ≈ ( − 2.0,10.1)xiexceeds 10.1, the process is judged to be in control.. Thus LCL = 0 andx is equivalent to x < 3, i.e. < 924. − 3 x < 0x .25. Withxiui= , the sgiu i' are 3.75, 3.33, 3.75, 2.50, 5.00, 5.00, 12.50, 12.00, 6.67, 3.33, 1.67,3.75, 6.25, 4.00, 6.00, 12.00, 3.75, 5.00, 8.33, and 1.67 for I = 1, …, 20, giving u = 5. 5125 .ug , u ± 3 = 5.5125±9. 0933 , LCL = 0, UCL = 14.6. For = . 8For = . 6ig iuu ± 3 = 5.5125 ± 7.857 , LCL = 0, UCL = 13.4. For =1. 0g ig ,ig ,uu ± 3 = 5.5125 ± 7.0436 , LCL = 0, UCL = 12.6. Several u i' s are close to theg icorresponding UCL’s but none exceed them, so the process is judged to be in control.i474