# Basics of Statistical Process Control by nfy87895

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```									              Basics of Statistical Process Control
(SPC)
While it is beyond the scope of this section to explain the details of Statistical Process Control (SPC), a
summary of SPC concepts may help clarify the significance of the charts that TRACK 2 generates.

No matter how tightly controlled and well run a process is, variations exist in the quality of the resulting
product. It is important to evaluate these variations to determine if the resulting product characteristics
are within acceptable quality limits. For example, the steam in a boiler must be of a specified purity,
temperature, etc. The outflow of a waste treatment plant must meet discharge standards.

Some variation is inherent in the process itself. Other variation, can be attributed to "special causes" that
are outside of the process. Possible "special causes" could be improperly calibrated instruments,
insufficient training, outdated reagents, etc. As these "special causes" of variation are detected,
procedures can be developed and implemented to ensure that these do not continue.

SPC techniques use random sampling and statistical analysis, instead of continuous monitoring, to
determine with almost complete confidence, whether the variation is due to the process itself or to
special causes. When SPC techniques are used, the frequency and timing of measurement testing is
usually defined by a statistician.

X-BAR AND RANGE CHARTS
The primary SPC tools are X-Bar and Range charts. Each pair of charts is derived from the same data
set. For the SPC analysis, the randomly acquired measurements are organized in groups, the size of
which is normally defined by the statistician. The data included in the groups should cover a time period
during which all normal process variations will occur.
For each group of data, the points on the X-Bar represents its average. The Range chart displays the
difference between the highest and lowest measurement in the group.
The X-Bar points or group averages are placed on the X-Bar chart. The program calculates the average
of all the X-Bar points and the standard deviation of these points. Three horizontal lines are placed on
the X-Bar chart as follows
• X-Bar average
• Upper Control Limit (UCL) at + 3 standard deviations
• Lower Control Limit (LCL) at -3 standard deviations.
The Range chart is created in a similar manner. The Range points for each group of data are placed on
the Range chart. The program calculates the average of all the Range points and the standard deviation
of these points. Three horizontal lines are placed on the Range chart as follows
• Range average
• Upper Control Limit (UCL) at + 3 standard deviations
• Lower Control Limit (LCL) at -3 standard deviations.
Basics of SPC                                                                                          2

Any variation that falls within the Upper and Lower Control Limits are virtually certain to result from
the process itself (99.97% confidence factor). If one of the groups falls outside of these Control Limits,
there is a similar certainty (99.97%) that the cause was due to a factor other than the process itself. It
should be possible to identify the specific reason(s) why this group's measurement was outside the
Control Limit and to implement procedures to eliminate these causes. By eliminating special causes, the
range is narrowed between the Upper and Lower Control Limits. It is then possible to evaluate the
benefits of modifying the process itself to narrow these limits even more.

MEASUREMENT GROUPING
The grouping of measurements can be done many ways. The three most common measurement
groupings, sub-group size, running average, or individual readings can be used in Track 2.

Regardless of which grouping method is used, the SPC analysis produces an X-Bar and Range chart.

All Upper and Lower Control Limit calculations are based on the average and range points on the chart.

SUB-GROUP SIZE
A specific subgroup size is specified. The program goes to the first data point for the measurement and
extracts the specified number of data points (equal to the specified sub-group size) for that measurement.
The average and range of that
group of data points are
calculated and retained for
display in the chart and SPC
tables. The values of the group's
individual data points are not
used further in the SPC
calculation or in the charts. The
program proceeds to the next
data point and again extracts a
group of data points to calculate
the second group average and
range. The process repeats itself
until the last data point of the
measurement is reached.

P.O. Box 7951  Wilmington, DE 19810
Phone: (302) 479-0706  Fax: (302) 479-0790  Email: lxf@lxf.com  Web Site: www.lxf.com
Basics of SPC                                                                                           3

RUNNING AVERAGE
A group size is specified. In the running average grouping method, the program goes to the first data
point for the measurement and
extracts the specified number of
data points (equal to the group
size) for that measurement. The
average and range of that group of
data points are calculated and
retained for display in the chart
and SPC tables. This first data
point in the group is then
discarded and the next data point
in sequence is added to keep the
group size constant. The average
and range are calculated again.
This process continues until the
last data point is reached.

the X-Bar is populated by
chart is the difference between
beginning with the earliest data
point and continuing to the last
data point.

PROCESS CAPABILITY CHARTS
While the X-Bar and Range charts describe whether or not a process is in statistical control, a Process
Capability chart is used to determine whether or not the process is "capable" or, basically, does it meet
the customer's needs as defined by upper and lower specification limits.

Measurements are grouped in six ranges. Each range consists of one standard deviation from the
average, going from -3 to +3 standard deviations. The number of measurements contained in each range
defines the relative height of the bar that is displayed. This is called the "frequency distribution" of the
measurement.

Finally, a "normal" bell-shaped curve is superimposed on the bars.

P.O. Box 7951  Wilmington, DE 19810
Phone: (302) 479-0706  Fax: (302) 479-0790  Email: lxf@lxf.com  Web Site: www.lxf.com
Basics of SPC                                                                                            4

Three types of "control" limits are used in this program.

Operational Control Limits are used
to ensure that some safety or
economic factor is not being
exceeded. These limits could relate to
temperature, pressure, chemical
residuals, inventory, or other process
variables. Corrective actions are
frequently associated with these
limits. If the limits are exceeded, the
implementation of a corrective action
can bring the process back into
control.

Upper/Lower Control Limits are
calculated from SPC X-Bar and
Range values. These limits are ±3 standard deviations from the calculated average, and represent a
99.97% confidence factor that any reading which falls between these limits is a result of normal process
variations.

Specification Limits are used to describe the minimum and maximum acceptable levels of some process
characteristic. Acceptance in this case is used to describe the range of variation that would be acceptable
to a customer. These limits may or may not be related to other types of limits.

The Process Capability chart contains three elements. Vertical lines are drawn on each chart to display
the average of all measurements on the graph and the pair of upper and lower specification limits, if
entered.

CONCLUSIONS
Statistical process control is not merely a collection of analytical tools. It is, rather, a operating
philosophy where the analyses are used to improve the process and make it more efficient.

In order to fully implement SPC it is necessary to investigate the subject in much more detail than is
provided here.

P.O. Box 7951  Wilmington, DE 19810
Phone: (302) 479-0706  Fax: (302) 479-0790  Email: lxf@lxf.com  Web Site: www.lxf.com

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