a. Based on the sampling done, the control limits for 3-sigma x overbar x chart are (round all intermediate calculations to three decimal places before proceeding with further calculations):

Upper Control Limit (UCL Subscript x overbar UCLx) =

Lower Control Limit (LCL Subscript x overbar LCLx) =

Based on the x overbar x-chart, the wire cutting process has been (In control/out of control)

b. The control limits for the 3-sigma R-chart are (round all intermediate calculations to three decimal places before proceeding with further calculations):

Upper Control Limit ( UCL Subscript Upper R UCLR) =

Lower Control Limit ( LCL Subscript Upper R LCLR) =

Based on the R-chart, the wire cutting process has been (IN CONTROL/ Out of control)

Refer to Table 56.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem. Sampling 4 pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results: Hour R 0.71" 1.18 Hour 19 3.25" 3.10 3.22 Hour 7 8 9 10 11 12 1.43 3.05" 2.65 3.02 2.85 2.83 2.97 R 0.53" 1.13 0.71 1.33 1.17 0.40 Hour 13 14 15 16 17 18 3.11" 2.83 3.12 2.84 2.86 2.74 R 0.85" 1.31 1.06 0.50 1.43 1.29 R. 1.61" 1.09 1.08 0.46 3.41" 2.89 2.65 3.28 2.94 2.64 21 3.39 3.07 2.86 1.26 1.17 0.32 1.58 6 24 0.97