TECHNOLOGY OVERVIEW
# Modified Control Charts

#### Modified Control Charts

Once a process is in control and variability well within specification limits, e.g. Cp>3, it maybe be reasonable to allow the process to drift a little within specification limits, without any noticeable effect, whilst appreciating that there is a cost in unnecessary tight control. This is actually a necessity for some high speed automatic processes where there will be some unavoidable drift in the process. For such situations a modified control chart can be used, which concerns itself only whether the process mean is located at a level where an unacceptable level of defectives is produced.

Control limits are calculated as follows

LCL= LSL +(Zbeta-Zalpha/sqrt(sub-group size)*sigma

UCL= USL -(Zbeta-Zalpha/sqrt(sub-group size)*sigma

Where:

LSL=Lower specification limit

USL=Upper specification limit

Zbeta is the Z value corresponding to an acceptable level of defectives. BIS.Net Analyst uses a value of 3 for Zbeta, which corresponds to approximately .1% of defectives.

Zalpha is the Z value corresponding to the probability of falsely concluding the process is out of control. BIS.NET Analyst uses a value of 3.

Sigma is the process standard deviation. Unless specified BIS.NET Analyst estimates process standard deviation using the xbar-sd control chart method.

**NOTE:**

Some scholars and consultants will recommend against using modified control charts as this opposes the Taguchi principle of the loss function, which concludes any deviation from the target value is a loss to society. Others will argue that Taguchi’s loss function did not include the cost of tight control when driving the loss function and that the cost of tight control cannot be justified if there is no perceivable effect caused by allowing some drift.

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