10.3 SPC APPLIED TO DYNAMIC PROCESS CHARACTERISTICS
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Sample Number
Figure 10.3 Example
chart commonly used for SPC. x
10.3 SPC APPLIED TO DYNAMIC PROCESS
CHARACTERISTICS
The most common SPC method used in the industry is the chart.
x These charts are typically used to determine if a process is exhib-
iting common-cause variation or special-cause variation. Figure 10.3 is an example of a typical
chart. These charts are prepared x
by 1. sampling subgroups of four or five individuals,
2. measuring a characteristic on each individual, 3. calculating and plotting
the average of each subgroup, x
4. repeating the above three steps for 25 or more samples, 5. calculating
the average of each and plotting as a line,
x x
x and
6. calculating the upper and lower control limits at three stan- dard deviations from
and plotting the control limits as x
lines.
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This SPC method requires that subgroups of multiple samples be formed from data collected under the same conditions and from
the same batch or lot. Through the interpretation of
charts, special-cause variation x
can be identified by using the following guidelines: 1. a point falls outside the control limits,
2. 9 consecutive points occur within one standard deviation, 3. 6 points in a row show a continuous increase or decrease,
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APPLYING STATISTICAL PROCESS CONTROL
4. 15 points occur within one standard deviation of the center- line , or
x 5. data follow a cyclic or periodic pattern.
When any of the guidelines above are met, the process exhibits special-cause variation and is termed ‘‘out of control.’’
5
Traditional charts utilize subgroups of four or five individuals
x collected under similar conditions. Process data curves, however,
stand on their own. Each curve is generated under unique condi- tions. As such, a statistical method must be used that charts in-
dividuals or subgroups of one.
X charts very similar to traditional
charts are plots of indi- x
vidual data points and are acceptable for use when only one data point can be obtained for a given condition.
6
The control limits for an X chart are defined as two standard deviations from the
average. This method of process control can be applied to process data curves for dynamic characteristics.
Statistical analysis of an entire process data curve can be per- formed by applying finite element methods. By employing the
finite element method known as discretization, a discrete model can be generated with a finite number of elements, or nodes, that
approximates a corresponding continuous analog model.
7
In this case the continuous model is the process data curve. A control
chart for a process data curve can be developed by performing the following steps:
1. Collect process data. 2. Divide data into equivalent curves one curve for each cy-
cle. 3. Create a discrete a model of each curve.
4. Calculate the average for equivalent elements using the dis- crete models.
5. Create a discrete process average curve using data from the previous step.
6. Calculate the standard deviation for equivalent elements us- ing the discrete models.
7. Create discrete process control limit curves two standard de- viations above and below the process average curve using
data from the previous step.
