100-Metodos-de-Qualidade-Total

DATA COLLECTION, ANALYSIS AND DISPLAY
233
Table 1 Data used to monilor thickness of machined parts
Lot no.
2 3 4 5
Xl X2 XJ X4 X;
Sum
X
Mean
X
Range
R
2
3
4
5
6
21.0 + 18.9 + 19.8 + 19.7 + 18.2
19.8 + 19.9 + 19.1 + 20.0 + 18.2
20.0 + 19.2 + 19.5 + 20.2 + 18.6
19.5 + 18.6 + 19.9 + 19.7 + 19.8
20.5 + 18.0 + 18.8 + 18.6 + 18.6
20.8 + 18.1 + 19.0 + 20. 1 + 19.5
97.6
97.0
97.5
97.5
94.5
97.5
19.52
19.40
19.50
19.50
18.90
19.50
2.8
1.8
1.6
1.3
2.5
2.7
29
30
18.1 + 20.2 + 20.2 + 18.4 + 18.8
20.9 + 19.2 + 18.0 + 18.4 + 18.3
95.7
94.8
19.14
18.96
2.1
2.9
Total
567.0
57.0
Mean
18.9
1.9
Benefit
It can be difficult to separate out random variation (often called common
cause or non-assignable variation) from real variation caused by changes to
the process. X-R charts are a way of doing this for the variables data with a
sample size that is greater than 1.
Example
Figures 1 and 2 show the use of an X-R chart to monitor the thickness of
machined parts using the data given in Table 1. The number of sampling
points m = 30; the size of each sample n = 5.
Reference
m = 30n = 5
'iR 57
R =
= = 1 . 9
m 30
'iX 567
X = = = 18 . 9
m 30
UCLR = D4R = 2.11 X 1.9 = 4
LCLR = D3R = 0 x 1. 9 = 0
A2R_ = 0.58 x 1.9 = 1.1
UCLx = _X+ A2R = 18.9 + 1.1 = 20
LCLx = X-A2R = 18.9 - 1.1 = 17.8
J.S. Oakland and R.F. Followell (1994) Statistical Process Control. London: Butterworth/
Heinemann.