The following samples have been taken from an on-going process. Use these values
ID: 2945756 • Letter: T
Question
The following samples have been taken from an on-going process. Use these values to create both an X bar and an R chart, and then answer the questions below. Please show work.
Sample 1: 56 48 53 58 52
Sample 2: 50 59 57 56 54
Sample 3: 61 59 56 55 58
Sample 4: 57 51 49 57 50
Sample 5: 50 49 57 55 56
Sample 6: 56 55 60 58 57
A) What is the value of the centerline for an X bar chart?
B) The upper control limit for the X bar chart is:
C) The lower control limit for the X bar chart is:
D) The upper control limit for the R chart is:
E) The lower control limit for the R chart is:
Explanation / Answer
a) value of the centerline for an X bar chart =54.967
b)
for sample size n=5 ; critical value of A2 =0.577
hence upper control limit for the X bar chart is =Xbar+A2*Rbar=54.967+0.577*7.667=59.391
c) lower control limit for the X bar chart ==Xbar-A2*Rbar=54.967-0.577*7.667=50.543
d)
for n=5 ; constant D3=0 and D4 =2.115
upper control limit for the R chart=D4*Rbar=2.115*7.667=16.215
e) lower control limit for the R chart =D3*Rbar=0*7.667=0
mean range sample 1 56 48 53 58 52 53.4 10 sample 2 50 59 57 56 54 55.2 9 sample 3 61 59 56 55 58 57.8 6 sample 4 57 51 49 57 50 52.8 8 sample 5 50 49 57 55 56 53.4 8 sample 6 56 55 60 58 57 57.2 5 total 329.8 46 average 54.967 7.667