1. EXAMPLE I
List 3, 10, 16, 1, 5, 14, 11, 6
Index i….,n : counts the elements of the original list
Median
(for sorted
list)
1
2
0,5
1
2 2
(n uneven)
(n even)
1
2
n
n n
x
X
x x
+
+
⎧
⎪⎪
= ⎨ ⎛ ⎞
+⎪ ⎜ ⎟
⎪ ⎝ ⎠⎩
Mean
(Average)
1
1 n
i
i
X x
n =
= ∑
Root Mean
Square
Deviation
2
1
n
i
i
n
x X
S
n
=
⎛ ⎞
−⎜ ⎟
⎝ ⎠=
∑
↓ 3 10 16 1 5 14 11 6
X− =
sq =
∑ =
(∑)2
=
(∑)2
/n
√ (∑)2
/n =

2. EXAMPLE II
Data Months Seq. 1 2 3 4 5 6 7 8 9 10 11 12
Performance 39 41 41 41 43 44 41 42 40 41 44 40
Histogram
0
1
2
3
4
5
6
39 40 41 42 43 44
Moving range 1 ,i > 0i i imR x x+= −
39 41 41 41 43 44 41 42 40 41 44 40ix
imR -
Control Limit x
R
CL X
CL mR
=
=
Upper
Natural
Process Limit
2.66xUNPL X mR= +
Lower
Natural
Process Limit
2.66xUNPL X mR= −
Upper
Control Limit
3.268xUNPL mR=
X-Chart
31
33
35
37
39
41
43
45
mR-Chart
0
1
2
3
4
5
6