chapter 1

Chapter 16: Quality Control Methods6. The limits are( 3)( .6)13 .00 = 13.00 ± .805± , from which LCL = 12.20 and UCL = 13.80.Every one of the 22 x values is well within these limits, so the process appears to be incontrol with respect to location.7. x = 12. 95 and s = . 526 , so with a = . 5940.52612 .95 3 = 12.95 ± .75 = 12.20,13.70.940 5, the control limits are± . Again, every point ( )these limits, so there is no evidence of an out-of-control process.x is between8. r =1. 336 and b = 2. 5325 , yielding the control limits1.33612 .95± 3 = 12.95 ± .77 = 12.18,13.72 . All points are between these limits,2.325 5so the process again appears to be in control with respect to location.2317.07x , s = 1. 264 , and695224a = . , giving the control limits1.26496 .54 ± 3 = 96.54 ± 1.63 = 94.91,98.17 . The value of x on the 22 nd day lies.952 69. = = 96. 54above the UCL, so the process appears to be out of control at that time.2317.07 − 98.3430.34 −1.60x and s == 1. 25023231.25096 .47 ± 3 = 96.47 ± 1.61=94.86,98.08 . All 23 remaining x values are.952 610. Now == 96. 47between these limits, so no further out-of-control signals are generated., giving the limits11.⎛ 2.81σ2.81σ⎞a. P ⎜µ 0− < X < µ0+ whenµ= µ0⎟ ⎝ nn⎠= P ( − 2 .81 < Z < 2.81) = . 9951is .005 and ARL = = 200 ..005, so the probability that a point falls outside the limits470