Part of any quality control, ISO9000,
quality assurance,
or Six Sigma plan must
use some type of SPC, (statistical
process control), to implement control
charts to control the processes. The origins of SPC, or statistical
process control, date back to the 1920’s and Dr. Shewhart. Statistical
process control was not well received by U.S. manufactures, so Dr.
Shewhart first applied his theories in Japan.
The concept is to be able to control your processes by monitoring
changes in the process, environment, or labor, using control charts.
This is achieved by collecting random
data samples from groups or subgroups of product, (see stratified
sampling), at various stages of the product's manufacturing
using inspection methods. You can then start plotting the data points on
a control chart, which is a line chart. Be aware of any sampling
bias problems that may occur.
You must also create a distribution
chart to know how your data is grouped as a whole. The following is
for data that is called variable. Variable data can be taken in sample
sizes, or subgroups of 2 to 5 pieces thus the data can have a range,
(R Bar), and an average or mean also known as XBar.
Range is important so that you can tell if the
entire process is shifting and by how much, or if the any shifting is
just during certain times. Like when the next shift starts, when
material from supplier X starts being pulled from stock, or when the
environmental variables change. (humidity or temperature and the
like)
This is the arithmetic mean
or average. Simply take the total measurements from all the samples
and divide by the number of subgroups.
An example of would be like
temperatures taken in different spots of a large stadium. If you
took 4 readings from the ...
Measurement Point 
Actual Measurement 
North 
68.5 
South 
75.5 
East 
72.3 
West 
73.4 
Your range would be 7.0, (75.5 
68.5 = 7.0)
Your average, (mean), would be 72.425
(68.5 + 75.5 + 72.3 + 73.4 = 289.7)
(289.7 / 4 = 72.425)
There are 2 type of samples that we
deal with. One we will call the observations or subgroups, and the
other we will call the sample. You must decide how many samples you need
to take to represent the population for an acceptable
result . Think of it as putting the data into a grid. We will call the
observations, or subgroups columns and the samples rows. So the
subgroup is a portion of the entire sample you choose. (see stratified
sampling and sampling
bias)
If we decide to take 30 samples, then
this could be put into ...
2 subgroups of 15 observations (2
rows and 15 columns) 2x15=30
6 subgroups of 5 observations (6 rows and 5 columns)
6x5=30
Some use 30, which is a number that
was acquired from the 1930's and based on how many widgets can be
produced in one hour now vs. then, it is not very accurate for today's
industries. Motorola at one time used 75 and Juran says to use 125.
However many you use, it must be able to be divided by the observations.
So if you used 30 as a sample, you could 2 columns of observations and
15 rows of samples, or 2 x 15 = 30. You could also use 5 columns of
observations and 6 rows of samples, or 5 x 6 = 30.
Note: try to do
this so that you do not need to change the observations. There are
advantages and disadvantages to using both 2 and 5, which are the most
popular to use. The observation is important because it is the basis for
the factor table you use to establish control limits. I just find that
if you don't keep changing this, you get better results over the long
run.
When Motorola used 75, they wanted it
as 5 columns of observations and 15 rows of samples, or 5 x 15 = 75.
If our widget is a gear, there could
several parameters that we need to chart, but we are only going to look
at diameter for simplicity.
We only take the large sample size
once to establish control limits. After that we add 1 sample of how ever
many observations we choose, typically 25, to the grid and
calculate the mean and range. So for t he example, we will take 15
samples using 3 observations. Our grid would look like this...
Part
Number: 54T54 
Parameter:
 Diameter 
Blue
Print Location: A2 
Specification
Minimum  .195 
Specification
Maximum  .208 
Specification
Nominal  .201 







n 
Date/Time 
x1 
x2 
x3 
XBar 
Range 
1 
4/7/1997
22:54 
0.206 
0.194 
0.203 
0.201 
0.012 
2 
4/7/1997
23:55 
0.196 
0.192 
0.223 
0.204 
0.031 
3 
4/7/1997
24:55 
0.215 
0.220 
0.238 
0.224 
0.023 
4 
4/7/1997
25:55 
0.230 
0.234 
0.229 
0.231 
0.005 
5 
4/7/1997
26:55 
0.223 
0.230 
0.227 
0.227 
0.007 











Totals 
1.087 
0.078 




Avg. 
0.217 
0.016 
Nominal is what the process typically
runs at. If you have an upper and lower specification limits, then
the nominal is usually the middle of that number, (Max Spec  Min Spec)
/ 2 + Min Spec or in this case...
(.208  .195 = 0.013 / 2 = 0.0065 + .109 = 0.2015)
The totals of the Average at the
bottom of 0.0217 and 0..16 are also known as Double XBar and Double
RBar.
When doing X Bar and Range charts,
one needs to establish upper
control limits and lower
control limits. These limits are +/ 3 sigma from the Double XBar.
The X Bar control chart should have
sigma zones applied to them in order to look at trends. WECO,
(Western Electric Company), rules,
are used for trending with the zones. For more information on zones and WECO
rules as they apply to Xbar and R bar control charts, please
see XBar and Range Control Charts.
Distribution
Charts
Distribution
charts MUST be used with XBar and Range charts. Not using these 3
types of charts together can and does lead to a misinterpretation of the
data. A distribution chart shows how the data is distributed over the
entire range.
The center of the distribution is the
mean, (XBar or average), of the data being evaluated. The data
is stacked in cells around the mean. A typical normal distribution will
have stacks that look similar to a bell, called a bell shape curve. See
Below.
Using ZeroRejects,
you can easily see where your data is in relation to your specification
and design margin.
For addition information...
Process
or Product Monitoring and Control
^{*} Reference
Quality Planning and Analysis  Juran/Gryan
