Cusum plot

The reactor pressure is reduced to 0 psig to flash off any remaining water after a desired temperature is reached. Simultaneous ramp up of the heat source to a new setpoint is also carried out. The duration spent at this second setpoint is monitored using CUSUM plots to ensure the batch reaches a desired final reactor temperature within the prescribed batch time. The heat source subsequently is removed and the material is allowed to continue reacting until the final desired temperature is reached. The last stage involves the removal of the finished polymer as evidenced by the rise in the reactor pressure. Each reactor is equipped with sensors that measure the relevant temperature, pressure, and the heat source variable values. These sensors are interfaced to a distributed control system that monitors and controls the processing steps. 

A typical cusum plot showing a lack of control with a negative deviation developing after 20 observations. 

In many cases a Cusum plot will not show the expected horizontal line but rather a line with a small but constant slope owing to the value attributed to the mean of means being incorrect. The plot is still acceptable and in such cases a change in the slope will indicate a change from the expected value and the possibility of error. Some of the difficulties with the Cusum plot is that variations are most obvious retrospectively, little information can be gained from a single point and errors are only apparent from several consecutive points. Thus it is debatable whether this type of plot can be classed as true quality control. 

Figure 3 Cusum Plot for Inventory Model before and after Deleting Outputs.

In the next subsection a test for initial-condition bias based on the characteristic behavior of the cusum plot is given. 

Schruben (1982) used the characteristic behavior of the cusum plot to derive a statisticeil test for the presence of initial-condition bias. The test would typictilly be performed on an output process tifter remedial measures, such as data deletion, have been applied. The null hypothesis of the test is that there is no negative initial-condition bias (biased low) in the mean of the output process. 

The use of QC control charts and subsidiary aids like the Cusum plot is an example of facing the fact that Murphy s Law predicts that something wiU surely go wrong if we wait long enough. These tools help in catching such problems early so as to take remedial action. 

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