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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.
10.4 DIE SURFACE TEMPERATURE CASE STUDY
151
Molten Metal Enters Solidification
Die Open Die Spray
Time sec T
emper ature
Figure 10.4 Process data curve for die surface temperature over one cycle.
Once these steps are completed, a chart can be plotted of the discrete process average model and the discrete control limit mod-
els. Process data curves can be plotted with the control limit curves. If any portion of a process data curve falls outside the
control limit curves, special-cause variation has occurred during the cycle. Once variation is distinguished as common-cause or
special-cause, improvement efforts can be focused at the process to eliminate the assignable special-causes or reduce common-
causes.
10.4 DIE SURFACE TEMPERATURE CASE STUDY
To facilitate discussion, the method presented will be applied to a specific example related to high integrity die casting processes.
Die surface temperature is a dynamic process characteristic and can be used to illustrate the statistical method presented in this
chapter. An example of a process data curve for die surface tem- perature over one cycle can be found in Figure 10.4. Time 0.0 is
defined as when metal enters the die. The metal in the die quickly begins to cool along with the die surface. When the metal solid-
ifies, the heat of fusion liberated slows the cooling of the die surface.
8
The now solid metal and the surface of the die continue to cool. When the die is opened and the solid component is
ejected, the die surface will continue to cool until an equilibrium
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APPLYING STATISTICAL PROCESS CONTROL
Figure 10.5 Thirty discrete process data curves for die surface temperature
over one cycle equal number of elements for each cycle.
temperature is reached with the bulk mass of the die. Typically, lubricants are sprayed onto the surface of the die between metal
injections. Although this may cool the surface of the die quickly, once the spray stops, the surface temperature will rise back to the
temperature of the bulk die mass. All the events described above can be associated with features illustrated in the process data
curve.
Often die surface temperature, if measured at all, is controlled by monitoring the maximum die temperature for each cycle. Al-
though this information may prove useful, it offers little under- standing of the process in comparison to the entire process data
curve. Through the examination of die temperature as a function of time, the understanding of the process is increased.
Data for die surface temperature can be obtained by instru- menting a die with a thermocouple. During processing, analog
data from the thermocouple can be recorded using a computerized data acquisition system. Such systems store the data in a digital
format. Storing the data in this manner in reality creates a discrete model of the original continuous signal from the thermocouple.
The time of each cycle will not be identical. To apply the finite element method, each process curve should be described with an
equal number of elements. Thirty process data curves for die sur- face temperature as shown in Figure 10.5. After collecting the
data, the average cycle time was calculated to be 20 s. To help correlate the elements to time, each process data curve has been
