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X-Bar Charts

Consider the two Xbar charts shown below for two processes.

[see attachment]

* The charts may OR may not have instances of special cause variation.
* Identify ALL violation(s) (if any) of the eight tests where statistical signals show that special cause variation is indeed occurring.
* State which test is violated (by number OR explanation) AND circle on the charts the sample involved in the violation.
* If the chart does not show signs of special cause, state that the process is good statistical control.

Please see the attached file for the fully formatted problems.


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X-bar charts are used to see if variations are caused by normal variability ("common causes") or by a larger "special cause" that needs to be fixed. Different people have different rules or tests (and will list them in different orders) to determine if there seems to be a special cause. Here are the rules that I'm using. Check to see if they match with the ones you are using in your class.

Rule 1: Any point falls beyond 3σ from the centerline (this is represented by the upper and lower control limits).
Rule 2: Two out of three consecutive points fall beyond 2σ on the same side of the centerline.
Rule 3: Four out of five consecutive points fall beyond 1σ on the same side of the centerline.
Rule 4: Eight or more consecutive points fall on the same side of the centerline.
Rule 5: Six or more consecutive points all increasing or all decreasing, or 14 points in a row alternating up and down.
Rule 6: Eight consecutive points that fall beyond 2σ on either side of the centerline.
Rule 7: Fifteen consecutive points within 1σ on either side of the centerline.
Rule 8: There is periodicity (there is a pattern ...