a) Grand mean bar{bar{X}} = ( 5.2 + 5.6 + 5.1 + 5.7 + 5.6 + 5.4 ) div 6
Grand mean bar{bar{X}} = 5.53
bar{R} = ( 0.6 + 1.0 + 1.1 + 1.0 + 0.7 + 0.8 ) div 6
bar{R} = 0.866
3-sigma Xbar-chart control limits
UCL= bar{bar{X}} + A_{2}bar{R}
The value of A2 from the table for a sample size of four equals 0.729
A2 = 0.729
UCL = 5.53 + 0.729 * 0.866
UCL = 6.16
LCL = 5.53 – 0.729 * 0.866
LCL = 4.90
3-sigma R – chart control limits
UCL= bar{R}D_{4}
UCL = 0.866 * 2.282
UCL = 1.98
LCL= 0
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b) Mean weight = ( 5.7 + 6 + 6.2 + 5.5 ) div 4
Mean weight = 5.85
The process is under control because the mean weight is less than the UCL i.e. 6.16