A First Course in Quality Engineering, 2nd Edition

Quality in Production—Process Control II 317

formulas are good for the case when σ is given� The CL of R is the E(R) in

terms of the given standard deviation σ

0

, and D

2

and D

1

give the 3-sigma lim-

its for R in terms of σ

0

� In fact, D

2

 = (d

2

+

3d

3

), and D

1

 = (d

2

− 3d

3

)� To obtain the

limits for X we use A, which is simply equal to

3 n

because

σ σ

X

n

=

( )

0

�

Example 5.5

Prepare X- and R-charts for the data in Table 5.5 if the process is to be controlled

at a target T = 10. No standard value for σ is given.

Solution

The limit calculations for the case when μ is given but the value of σ is not are

shown below. From Table 5.5, the value of R is obtaine ...