Statistical Process Control | Chart for Means (x-bar chart)

Thank you very much. I scanned my textbook for hours trying to figure out these calculations and the way you explained was much more clear and allowed me to move forward. Looks like other commenters have experienced the same.

You are to construct an x-bar chart such that the control limits would include 97% of the sample means, where the random samples would be of size 5; this it say that type I error would occur with 3% probability. The process standard deviation is known to be 3.2. The following data is used to construct the control chart.

You are to calculate the UCL only. Round your answer to TWO places of decimal.


Sample # obs 1 obs 2 obs 3 obs 4 obs 5
1 17 16 17 10 17
2 16 17 15 10 20
3 13 20 11 12 20
4 18 18 12 20 18
5 17 15 15 10 15

can you please solve this?

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Sorry pls I'm not still clear with how you get the Control constant

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Hello. It takes some time, sampling and processing to get to those UCL, LCL and mean value. So when you come to this situation like data point 5 is out of control then normally one cannot go on just like that but must consider what to do with this outlier and what to do with the limits...
When (condition) and how (procedure of recalculation) to reset the new upper&lower control limits. Is there a video or clear procedure for available ?

Brilliant.

Great work, but I am not a Maths genius , how did yuo arrive at the figure of UCL = 23.1??? I am getting a figure of 497.80+ 0.577 = 498. 37 multiplied by 23.10 = 11,512.50 ---Can some one please explain ???? How did he arrive at 511.10 for UCL???? Thanks and kind regards...

Awesome explanation, still valid and simplified.. thank you.

why did we use A2 and not A3? how to determine?

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Why you took value on n as 5 from table

You should take value of A2 from N=10 not from N=5

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Excellent and crisp explanation

What if sample size is uneven.