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:

Answer 1

						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