Twelve samples were collected from a production line. Each sample contains 8 units (observations). You are asked to develop an X chart to monitor the average of the 8 units based on the twelve samples. Assume the averages of the 12 samples are X11 , X22 , ...., X1212 . Each of the twelve x-bar values is obtained from averaging the measures of the 8 randomly collected units in a sample. The sum X11 + X22 + ....+ X1212 =750. The sum of the ranges from the twelve samples, R₁+R2+...+R₁₂=48. [Use Table 10.3. Since partial results are given, no detailed sample measures on the individual units are needed.]

Construct a 3 mean chart (X-bar chart) using Table 10.3 (Round all answers to three decimal places.)

(1) The quality standard is (the center line):

(2) The lower control limit is (LCL):

Construct a 3 R chart:

(3) The quality standard is (the center line):

(4) The upper control limit is (UCL):