Answer and Explanation:
As per the data given in the question,
Sum of the all mean value = 151
Average of the mean value = 151 ÷ 15 = 10.067
Similarly, Sum of the all given range = 151
Average of given range value = 151÷ 15 = 10.067
Control charts for the mean and the range, using the original 15 samples :
Upper control limit(UCL) - Lower control limit(LCL) for X bar is
= 10.067 + A2 × R bar
= 10.067 + (0.223 × 10.067)
= 12.31
LCL - UCL for X bar is
= 10.067 - A2 × R bar
= 10.067 -(0.223 × 10.067)
= 7.82
Set up the R-chart by specifying the center line and three-sigma control limits below :
UCLr = D4 × r
= 1.653 × 10.07
= 16.65
r = 10.067
= 10.07
LCLr = D3 × r
= 0.347 ×10.07
= 3.49
