Question

Construct `bar"X"` and R charts for the following data:

Sample Number	Observations
1	32	36	42
2	28	32	40
3	39	52	28
4	50	42	31
5	42	45	34
6	50	29	21
7	44	52	35
8	22	35	44

(Given for n = 3, A₂ = 1.023, D₃ = 0 and D₄ = 2.574)

Answer 1

We first find the sample mean and range for each of the 8 given samples.

Sample Number	Observations			`bar"X"`	R
1	32	36	42	36.67	10
2	28	32	40	33.33	12
3	39	52	28	39.67	24
4	50	42	31	41	19
5	42	45	34	40.33	11
6	50	29	21	33.33	29
7	44	52	35	43.67	17
8	22	35	44	33.67	22
Total				301.67	144

The control limits for `bar"X"` chart is

`\overset{==}{"X"} = (sumbar"X")/"Number of samples" = 301.67/8` = 37.71

`bar"R" = 144/8` = 18

UCL = `\overset{==}{"X"} + "A"_2 bar"R"`

= 37.71 + (0.58)(18)

= 37.71 + 10.44

= 48.15

CL = `\overset{==}{"X"}` = 37.71

LCL = `\overset{==}{"X"} - "A"_2 bar"R"`

= 37.71 – (0.58)(18)

= 37.71 – 10.44

= 27.27

The control limits for Range chart is

UCL = `"D"_4 bar"R"` = 2.115(18) = 38.07

CL = `bar"R"` = 18

LCL = `"D"_3 bar"R"` = 0(18) = 0