Question

A manufacturer trying to get a process under control randomly collects 4 samples from the process each hour. Five of the X bar and R measurements are as follows: X bar: 374, 376, 360, 359, 369 R: 3, 2, 5, 2, 3 What are the control limit values for the two control charts (3 per chart)?

Answer 1

n : Number of observations in each group = 4

k: number of groups = 5

Given

Group	$\overline{X}$	R
1	374	3
2	376	2
3	360	5
4	359	2
5	369	3
Total	$\Sigma \overline{X}$=1838	$\Sigma R$=15
	$\overline{\overline{X}}$ =$\Sigma \overline{X}$/k = 1838/5= 367.6	$\overline{R}$= $\Sigma R$ /k =15/5 =3

Control limits for $\overline{X}$ chart

Upper control Limit :

UCL = X + AR

X = 10

Lower Control Limit :

UCL = X - AR

A₂ for n:4 = 0.729

UCL = X + AR= 367.6 + 0.729 X 3 = 367.6 +2.187 = 369.787

9'298 = X = 10

LCL = X - AR = 367.6 - 0.729 X 3 = 367.6 – 2.187 = 365.413

Upper control Limit = 369.787

CL = 367.6

Lower Control Limit = 365.413

Control Limits R-Chart

UCL = DAR

= 15

LCL = D3R

For n:4 : D₄ =2.282 ; D₃ = 0

UCL = DAR= 2.282 x 3 = 6.846

CL = R=3

LCL = DR = 0 x 3 = 0