Page 78 - DMGT206_PRODUCTION_AND_OPERATIONS_MANAGEMENT

Unit 4: Quality Control

(iii) The value of A . From tables the values are given. Notes
2
For n = 5, A = 0.577, D = 0 and D = 2115.
2 3 4
OUT OF
CONTROL

110
UCLR = 106.02
100
90
80
70 CLx = 71.6
60

50
40 LCL = 37.17
30
20 OUT OF
CONTROL
10
0
2 4 6 8 10 12

The upper control limit (UCL) and the lower control limit (LCL) are calculated as follows:

UCLX = + A = 71.6 + 0.577 (59.66) = 106.024
2
LCLX = – A = 71.6 – 0.577 (59.66) = 37.176.
2
The control chart for this example is shown above.

Since the sample mean points corresponding to sample numbers 8 and 10 lie outside the control
limits, the X-chart indicates lack of control in process average. This suggests the presence of
some assignable causes of variations which must be detected and corrected.
Eliminating these points from X -chart only.

Revised = [859.2 – (33.4 + 112.4)]/ (12–2) = 71.34

New UCL = 71.34 + A = 71.34 + 34.6 = 105.94
2
New LCL = 71.34 + R = 71.34 – 34.6 = 36.74.
2
Control limits for R-chart. The 3-s control limits are given by:

UCLR = D4R = 2.115  59.66 = 126.1809
LCLR = D3R = 0

CLR = R = 59.66

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