If = 2.0144, = .0972,and there are 25 subgroups of size 5,find the UCL and the LCL for the chart.
A)[1.999,2.029]
B)[1.958,2.071]
C)[1.917,2.112]
D)[1.437,2.591]

Question

If  = 2.0144,  = .0972,and there are 25 subgroups of size 5,find the UCL and the LCL for the  chart.
A)[1.999,2.029] 
B)[1.958,2.071] 
C)[1.917,2.112] 
D)[1.437,2.591]

Quizplus · Accepted Answer

- The average of the subgroups is the value of 11eb06d7_5567_e6ae_8177_951d186e78b4_TB1736_11, which is 2.0144.
- The standard deviation of the subgroups is the square root of the average of the subgroup ranges, which is calculated as follows:
   - subgroup range = 11eb06d7_5567_e6af_8177_cbd472397e56_TB1736_11 - 11eb06d7_5567_e6ae_8177_951d186e78b4_TB1736_11 = -1.9172
   - average subgroup range = -1.9172/5 = -0.38344
   - standard deviation of subgroups = sqrt(25 * (-0.38344)^2 / 24) = 0.2166
- The control limits are calculated as follows:
   - UCL = average + 2.575*standard deviation = 2.0144 + 2.575*0.2166 = 2.0677
   - LCL = average - 2.575*standard deviation = 2.0144 - 2.575*0.2166 = 1.9613
Therefore, the answer is B, [1.958,2.071].

If = 20144, =