Interpretation & Calculations
An excerpt from Statistical Process Control Demystified (McGraw-Hill 2011) by Paul Keller.
In cases where the multiple stream effects cannot be eliminated, a modification of the X chart is recommended. A batch means chart, available in some advanced SPC software, accommodate the multiple stream process by converting the X-bar (aka averages) chart into a simple Individual-x chart (discussed in Chapter 6), where the plotted value is the subgroup average. The range chart is maintained to provide estimate of the within subgroup variation: in this case the between stream variation. Special causes disrupting the stream to stream differences would be noted as out of control on the range chart. The x chart monitors the overall average of the multiple streams, providing indication of the process location. The only difference between the batch mean and the standard X chart is the control limits, which are calculated based on the moving range between the subgroup (multiple stream) averages. This follows the general approach for n = 1 individuals data for the standard x chart (discussed in detail in Chapter 6).
Fig 5-6: SPC-PC IV Software detects irrational subgroups in X-bar /Range chart
Figure 5.7 shows the batch means chart for the data previously presented in Figure 5.6. Note the range chart is unchanged from Figure 5.6. The plotted groups on the X chart are also unchanged. The control limits on the X chart are calculated based on the short-term variation between subgroups, as is done on a standard x chart for individuals data. A change in the average output of the multiple streams is now evident on the batch means x chart, indicated by an out of control condition at group 45.
Fig 5-7: SPC-PC IV Software detects rpcess shift using Batch Means chart.
Figure 5.8 provides a revised batch means chart with a new control region beginning at group 45 to accommodate the process shift.
Fig 5-8: SPC-PC IV Software displays Batch Means chart of multi-stream process with process shift.
The process capability of the multistream process is more complicated, since a single distribution cannot be fit to the multiple streams. By definition, the multiple streams each require unique distributions, and unique estimates of process capability. The process capability for a multistream process would generally be expressed using the worst case stream.
Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).