Non Standard X-Bar Charts

The BIS.Net Team BIS.Net Team

There are many applications where normal X-Bar Charts will not work. The X-Bar Chart as proposed by Walter Shewhart is based on within subgroup variation. It assumes variation between subgroups is due to assignable variation. By basing control limits on within subgroup variation it is argued that computed control limits are not affected by assignable causes.

This approach works for many applications and should be the preferred option. However, sometimes it does not work. For some processes control limits will be too wide, such as shown below.

Shewhart chart demonstrating the issues with spc theory

For other processes they will be too tight.

There can be many reasons for control limits being too tight. One reason is non-normality the data. Shewhart x-bar charts are not as robust to non-normality as is often believed. Common subgroup sample sizes are too small for the central limit theorem to take over. This of course depends on the degree of non-normality. Another reason for limits being too tight can be due to inherent time to time variation. Shewhart’s research was for select processes mainly in the telecommunications process. Many processes today are far more complicated consisting of inherent time to time variation, which must also be left alone. Food processes, dependent on mother nature, can come under this category. Mother nature does not practice SPC and is variable.

Control charts where limits are too wide can result when applying these to stream processes. Both situations are covered in the knowledge base.

In both instances there are procedures that can be applied to determining the correct standard deviation on which to base the control chart limits. If this is possible then this is the approach that should be used. Machine powered control charts can also be used, but these too may not work if the underlying distribution cannot be found.

When all else fails non-standard control chart s can be used to obtain limits that can be used in the interim, or permanently if it is not possible to rectify the situation. This would at least ensure that assignable causes are detected outside the norm.

Non-standard control charts are based on the standard deviation of the averages.

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