Question

A quality control inspector has taken ten samples of size four packets each from a potato chips company. The contents of the sample are given below, Calculate the control limits for mean and range chart.

Sample Number	Observations
	1	2	3	4
1	12.5	12.3	12.6	12.7
2	12.8	12.4	12.4	12.8
3	12.1	12.6	12.5	12.4
4	12.2	12.6	12.5	12.3
5	12.4	12.5	12.5	12.5
6	12.3	12.4	12.6	12.6
7	12.6	12.7	12.5	12.8
8	12.4	12.3	12.6	12.5
9	12.6	12.5	12.3	12.6
10	12.1	12.7	12.5	12.8

(Given for n = 5, A₂ = 0.58, D₃ = 0 and D₄ = 2.115)

Answer 1

Sample Number	Observations
	1	2	3	4	`bar"X"`	R
1	12.5	12.3	12.6	12.7	12.53	0.4
2	12.8	12.4	12.4	12.8	12.6	0.4
3	12.1	12.6	12.5	12.4	12.4	0.5
4	12.2	12.6	12.5	12.3	12.4	0.4
5	12.4	12.5	12.5	12.5	12.48	0.1
6	12.3	12.4	12.6	12.6	12.48	0.3
7	12.6	12.7	12.5	12.8	12.65	0.3
8	12.4	12.3	12.6	12.5	12.45	0.3
9	12.6	12.5	12.3	12.6	12.5	0.3
10	12.1	12.7	12.5	12.8	12.53	0.7
Total					125.02	3.7

`\overset{==}{"X"} = (sumbar"X")/10 = 125.02/10` = 12.5

`bar"R" = (sum"R")/10 = 3.7/10` = 0.37

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

= 12.5 + (0.58)(0.37)

= 12.5 + 0.2146 = 12.7146

= 12.71

CL = `\overset{==}{"X"}` = 12.5

LCL = `\overset{==}{"X"} - "A"_2 bar"R"` = 12.5 - (0.58)(0.37)

= 12.5 – 0.2146 = 12.2854

= 12.29

The control limits for Range chart is 

UCL = `"D"_4 bar"R"` = (2.115)(0.37) = 0.78255

= 0.78 

CL = `bar"R"` = 0.37

LCL = `"D"_3 bar"R"` = (0)(0.37) = 0