Transcript Process Control Charts - Washington University in St. Louis

Process Control Charts
By: Brian Murphy
Control Charts are an on-line processmonitoring technique.
 Used to determine if a process is capable
or out of control.
 In control processes operate with only
chance causes of variation.
 Out of control processes have assignable
causes of variation and can be
restructured when identified.


Control Chart Contains
◦ A center line (usually the arithmetic mean or
the average of a collection of sample ranges)
◦ A Lower and Upper Control Limit (LCL and UCL)
◦ Points beyond the control limits indicate that
the process is out of control.

Formulas:
◦ xave = grand average of x = (x1+x2+…+xm)/m
Or R=xmax-xmin
R1, R2,…,Rm: ranges of m samples
Rave = (R1+R2+…+Rm)/m

Control Limits for R chart:
◦ UCL = D4*Rave
◦ Center Line = Rave
◦ LCL = D3*Rave

Control Limits for x chart:
◦ UCL = xave + A2*Rave
◦ Center Line = xave
◦ LCL = xave –A2*Rave
*See next slide for values of D3, D4 and A2
n
A2
D3
D4
2
1.88
0
3.267
3
1.023
0
2.574
4
0.729
0
2.282
5
0.577
0
2.114
6
0.483
0
2.004
7
0.419
0.076
1.924
8
0.373
0.136
1.864
9
0.337
0.184
1.816
10
0.308
0.223
1.777
*n denotes sample size

Rules for determining out of control
process: