TECHNOLOGY OVERVIEW
# Modified Control Charts for Individuals Charts for Six Sigma Processes

#### Modified Control Charts for Individual Charts for Six Sigma Processes

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.

A six sigma process that is centered at target has a Cp and Cpk index of 2.0. A six sigma process assumes that a shift in process average as high as 1.5 standard deviations from target will not cause perceivable problems. Control limits are set to detect the process wandering outside the 1.5 Sd limit.

Modified Control Charts are normally used for data with subgroup size greater than 1, say 5. However there are many instances where rational subgroups are not appropriate, such as for high speed automatic filling processes where single measurements are recorded. For these instances the x-bar chart is replaced with an exponential control chart.

LCL = Target - 1.5 * ProcessSd - 3 * ProcessSd * Sqrt((1 - (1 - alpha) ^ (2 * R)) * alpha / (2 - alpha))

UCL = Target + 1.5 * ProcessSd + 3 * ProcessSd * Sqrt((1 - (1 - alpha) ^ (2 * R)) * alpha / (2 - alpha))

Where:

Target is the aim value midway between the specification limits

Unless specified BIS.NET Analyst estimates process standard deviation using the moving range method.

Alpha is the smoothing constant.

**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. For highspeed filling processes where some drift is unavoidable this is the only option.

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