Question

Create the X-bar and R-charts for the following 25 samples. What conclusions can you draw?

1 Sample Number Item Item 2 Item 3 Item 4 Item s Sample Mean Range (X-bar) 10.60 10.40 0.30 9.90 10.20 9.98 10.25 10.05 10.23 10.33 9.85 9.90 10.20 10.25 10.15 10.20 10.10 10.30 9.909.95 10.30 10.20 10.24 10.50 10.30 10.10 10.30 10.20 10.30 9.90 9.98 9.90 10.20 10.40 10.10 10.10 10.30 10.40 10.24 10.30 10.30 10.20 10.60 10.50 10.10 10 10.30 10.40 10.50 10.10 10.20 9.90 9.50 10.20 10.30 10.35 10.10 10.36 10.50 9.80 9.95 9.90 10.20 10.60 10.50 10.30 10.40 10.54 10.30 10.40 10.55 10.00 10.20 10.60 10.15 10.0010.50 10.20 10.40 10.60 10.80 10.10 9.90 9.50 9.90 10.50 10.00 10.60 10.30 10.50 9.90 9.80 10.60 10.40 10.30 10.40 10.20 9.90 9.60 10.50 10.10 10.60 10.28 0.70 10.17 0.35 10.07 0.40 10.09 0.40 1 4 10.3 0.30 10.16 0.40 10.12 0.50 10.27 0.30 10.34 0.50 10.30 0.40 10.05 0.85 10.14 0.70 10.28 0.80 12 1 13 14 15 16 17 18 19 20 10.20 10.50 10.70 10.10 10.40 0.40 10.36 0.55 10.29 0.60 10.42 0,70 9.96 1.00 10.22 0.80 10.38 0.40 10.14 10.23 0.55 ו0.20 10.20 9.50 9.60 9.80 10.30 10.30 10.60 10.30 9.90 9.80 9.90 10.30 10.60 9.90 10.10 9.95 | 10.20-ו10.50 10.301 10.20 23 24 25

Answer 1

First we calculate sample mean and range of Sample 23,24 and 25.

Sample	Item 1	Item 2	Item 3	Item 4	Item 5	Sample Mean	Range
23	10.20	9.50	9.60	9.80	10.30	9.88	0.80
24	10.30	10.60	10.30	9.90	9.80	10.18	0.80
25	9.90	10.30	10.60	9.90	10.10	10.16	0.70

Sample mean = Total of all items /5 , Range = Max observation - mIn observation

Sample	Sample Mean	Range
1	10.28	0.70
2	10.17	0.35
3	10.07	0.40
4	10.09	0.40
5	10.31	0.30
6	10.16	0.40
7	10.12	0.50
8	10.27	0.30
9	10.34	0.50
10	10.30	0.40
11	10.05	0.85
12	10.14	0.70
13	10.28	0.80
14	10.40	0.40
15	10.36	0.55
16	10.29	0.60
17	10.42	0.70
18	9.96	1.00
19	10.22	0.80
20	10.38	0.40
21	10.14	1.00
22	10.23	0.55
23	9.88	0.80
24	10.18	0.80
25	10.16	0.70
Total	255.20	14.90
Average	10.208	0.596

X-double bar = 10.208

R-bar = 0.596

For sample size =5, Control chart constants:

A2 = 0.577

D3= 0

D4 =2.114

Xbar chart formulas LCL=x-A R UCL = x + A R R-chart formulas LCL=D R UCL = D,a

Using formulas above:

UCLx = 10.208 + 0.577*0.596 = 10.55

LCLx = 10.208-0.577*0.596= 9.86

UCLr = 2.114*0.596 = 1.26

LCLr = 0

Observations:

• The process is in statistical control as all the sample mean values are within the control limits of X-chart
• The process variability is in control as all range values are within the control limits of R-chart.