Quality Money Management : Process Engineering and Best Practices for Systematic Trading and Investment

257

These values can be used as known values of  and  , and the control charts can be con-

structed. For the X bar chart, the upper and lower control limits can be written as:

UCL

CL

LCL







XAR

X

XAR

2

2

For the R control chart for range, the control limits can be calculated as:

UCL

CL

LCL





DR

R

DR

4

= 3

The factors used in construction of control charts for various values of n are shown here:

For the sample data, where n  5 and k  20, the X bar control values are

UCL

CL

LCL







..(.).

.

..(.)

0022 577 0356 0227

0022

= 0022 577 0356 ..0183

For the sample data, the R control values are

UCL

CL

LCL







2 115 0356 0753

0356

0 0356 0

.(. ).

.

= (. )

Xbar control chart

0.025

0.02

0.015

0.01

0.005

0

0.005

0.01

0.015

0.02

0.025

Xbar

UCL

CL

LCL

FIGURE 28-2

28.3. SPC CONTROL CHARTS

TABLE 28-2

Value Basic factors Factors for averages Factors for ranges

of n d 2 d 3 A A 1 A 2 D 1 D 2 D 3 D 4

2 1.128 0.853 2.121 3.760 1.880 0 3.686 0 3.267

3 1.693 0.888 1.732 2.394 1.023 0 4.358 0 2.575

4 2.059 0.880 1.500 1.880 0.729 0 4.698 0 2.282

5 2.326 0.864 1.342 1.596 0.557 0 4.918 0 2.115