Question

In a certain bottling industry the quality control inspector recorded the weight of each of the 5 bottles selected at random during each hour of four hours in the morning.

Time	Weight in ml
8:00 AM	43	41	42	43	41
9:00 AM	40	39	40	39	44
10:00 AM	42	42	43	38	40
11:00 AM	39	43	40	39	42

Answer 1

Time	Weight in ml					`bar"X"`	R
8:00 AM	43	41	42	43	41	42	2
9:00 AM	40	39	40	39	44	40.4	5
10:00 AM	42	42	43	38	40	41	5
11:00 AM	39	43	40	39	42	40.6	4
Total						164	16

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

`\overset{==}{"X"} = (sumbar"X")/"Number of samples" = 164/4` = 41

`bar"R" = 16/4` = 4

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

= 41 + (0.58)(4)

41 + 2.32 = 43.32

CL = `\overset{==}{"X"}` = 41

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

= 41 – (0.58)(4)

= 41 – 2.32

= 38.68

The control limits for range chart is

UCL = `"D"_4 bar"R"` = 2.115(4)

= 8.46

CL = `bar"R"` = 4

LCL = `"D"_2 bar"R"` = 0(4) = 0

Conclusion: Since all the points of sample mean and Range are within the control limits, the process is in control.