Question

# The following samples have been taken from an on-going process. Use these values to create both...

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:

 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

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