Question

The following data show the values of sample means and the ranges for ten samples of size 4 each. Construct the control chart for mean and range chart and determine whether the process is in control.

Sample Number	1	2	3	4	5	6	7	8	9	10
`bar"X"`	29	26	37	34	14	45	39	20	34	23
R	39	10	39	17	12	20	05	21	23	15

Answer 1

Sample Number	1	2	3	4	5	6	7	8	9	10	Total
`bar"X"`	29	26	37	34	14	45	39	20	34	23	301
R	39	10	39	17	12	20	05	21	23	15	201

Let us A₂ = 0.729, D₄ = 2.282 and D₃ = 0

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

`\overset{==}{"X"} = (sumbar"X")/"No. of samples" = 301/10` = 30.1

`bar"R" = (sum"R")/"No. of samples" = 201/10` = 20.1

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

= 30.1 +(0.73)(20.1)

= 30.1 + 14.673 = 44.773

= 44.77

CL = `\overset{==}{"X"}` = 30.1

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

= 30.1 – (0.73) (20.1)

= 30.1 – 14.673 = 15.427

= 15.43

The control limits for Range chart is 

UCL = `"D"_4 bar"R"`

= 2.28(20.1) = 45.828

= 45.83

CL = `bar"R"` = 20.1

LCL = `"D"_3 bar"R"` = 0(20.1) = 0