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

___________________________________________________________________________

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

Thanks for installing the Bottom of every post plugin by Corey Salzano. Contact me if you need custom WordPress plugins or website design.