Question

The following are the sample means and I ranges for 10 samples, each of size 5. Calculate; the control limits for the mean chart and range chart and state whether the process is in control or not.

Sample Number	1	2	3	4	5	6	7	8	9	10
Mean	5.10	4.98	5.02	4.96	4.96	5.04	4.94	4.92	4.92	4.98
Range	0.3	0.4	0.2	0.4	0.1	0.1	0.8	0.5	0.3	0.5

Answer 1

Sample Number	1	2	3	4	5	6	7	8	9	10	Total
Mean	5.10	4.98	5.02	4.96	4.96	5.04	4.94	4.92	4.92	4.98	49.82
Range	0.3	0.4	0.2	0.4	0.1	0.1	0.8	0.5	0.3	0.5	3.6

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

`\overset{==}{"X"} = (sumbar"X")/"Number of samples" = 49.82/10` = 4.982

`bar"R" = (sum"R")/"n" = 3.6/10` = 0.6

UCL = `\overset{==}{"X"} + "A"_2bar"R"`

= 4.982 + 0.577(0.36)

= 4.982 + 0.20772

= 5.18972

= 5.19

CL = `\overset{==}{"X"}` = 4.982

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

= 4.982 – 0.577(0.36)

= 4.982 – 0.20772

= 4.77428

= 4.774

The control limits for range chart is

UCL = `"D"_2bar"R"` = 2.115(3.6)

= 7.614

CL = `bar"R"` = 3.6

LCL = `"D"_3bar"R"`

= 0(0.36)

= 0