Question

Consider the following data.

Sample1	55	74	67	47	68	67	54
Sample2	44	34	54	66	50	67	54
Sample3	67	77	74	41	66	69	77
Sample4	64	64	68	44	69	74	74
Sample5	54	64	34	64	58	56	64
Sample6	64	76	44	75	68	65	44
Sample7	84	94	64	106	78	86	86

For a range-chart for the above data, find the following:

(a) The center line: R¯=

(b) The upper control limit: UCL =  

(c) The lower control limit: LCL=

Answer 1

Solution:
Ranges for samples can be calculated as
Range = Largest Value - Smallest Value

Sample	Set1	Set2	Set3	Set4	Set5	Set6	Set7	Range
1	55	74	67	47	68	67	54	27
2	44	34	54	66	50	67	54	33
3	67	77	74	41	66	69	77	36
4	64	64	68	44	69	74	74	30
5	54	64	34	64	58	56	64	30
6	64	76	44	75	68	65	44	32
7	84	94	64	106	78	86	86	42

Solution(a)
Center Line Rbar = Range/n = (27+33+36+30+30+32+42)/7 = 230/7 = 32.86
Solution(b)
Upper control limit UCL Can be calculated as
UCL = D4*Rbar
At n= 7, D4 = 1.924
UCL = 1.924*32.86 = 63.22
Solution(c)

Lower control limit LCL Can be calculated as
LCL = D3*Rbar
At n = 7, D3 = 0.076
LCL = 0.076*32.86 = 2.5