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Figure 4. Example of Process Control Chart Showing Oven Temperature Data

147

148

149

150

151

152

153

154

UCL = 152.8

= 150.4

LCL = 148.0

UCL = 7.3

= 3.2

LCL = 0

Where D4, D3 and A2 are constants varying by sample

size,with values for sample sizes from 2 to 10 shown in the

following partial table:

789

D4 3.27 2.57 2.28 2.11 2.00 1.92 1.86 1.82 1.78

0.08

0.14

0.18

0.22

A2 1.88 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31

* For sample sizes below 7, the LCLR would technically be

a negative number; in those cases there is no lower control

limit; this means that for a subgroup size 6, six “identical”

measurements would not be unreasonable.

Control charts are used to monitor the variability of critical

process parameters. The R chart shows basic problems with

piece to piece variability related to the process. The X chart

can often identify changes in people, machines, methods,

etc. The source of the variability can be difficult to find and

may require experimental design techniques to identify

assignable causes.

Some general rules have been established to help deter-

mine when a process is OUT-OF-CONTROL. Figure 5 shows

a control chart subdivided into zones A, B, and C corre-

sponding to 3 sigma, 2 sigma, and 1 sigma limits respectively.

In Figure 6 through Figure 9 four of the tests that can be used

to identify excessive variability and the presence of assignable

causes are shown. As familiarity with a given process

increases, more subtle tests may be employed successfully.

Once the variability is identified, the cause of the variability

must be determined. Normally, only a few factors have a signif-

icant impact on the total variability of the process. The impor-

tance of correctly identifying these factors is stressed in the

following example. Suppose a process variability depends on

the variance of five factors A, B, C, D and E. Each has a vari-

ance of 5, 3, 2, 1 and 0.4 respectively.

Since:

s tot + sA2 ) s B2 ) s C2 ) s D2 ) s E2

s tot + 52 ) 32 ) 22 ) 12 ) (0.4)

2 + 6.3

Now if only D is identified and eliminated then;

s tot + 52 ) 32 ) 22 ) (0.4)

2 + 6.2

This results in less than 2% total variability improvement.

If B, C and D were eliminated, then;

s tot + 52 ) (0.4)

2 + 5.02

This gives a considerably better improvement of 23%. If

only A is identified and reduced from 5 to 2, then;

s tot + 22 ) 32 ) 22 ) 12 ) (0.4)

2 + 4.3

Identifying and improving the variability from 5 to 2 gives

us a total variability improvement of nearly 40%.

Most techniques may be employed to identify the primary

assignable cause(s). Out-of-control conditions may be

correlated to documented process changes. The product

may be analyzed in detail using best versus worst part

comparisons or Product Analysis Lab equipment. Multi-vari-

ance analysis can be used to determine the family of varia-

tion (positional, critical or temporal). Lastly, experiments may

be run to test theoretical or factorial analysis. Whatever

method is used, assignable causes must be identified and

eliminated in the most expeditious manner possible.

After assignable causes have been eliminated, new

control limits are calculated to provide a more challenging

variability criteria for the process. As yields and variability

improve, it may become more difficult to detect improve-

ments because they become much smaller. When all

assignable causes have been eliminated and the points

remain within control limits for 25 groups, the process is said

to be in a state of control.

Freescale Semiconductor, Inc.

For More Information On This Product,

Go to: www.freescale.com

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