# Control Chart – 8 points in a row in one of Average

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- This topic has 6 replies, 4 voices, and was last updated 14 years, 6 months ago by Brit.

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- July 20, 2006 at 2:54 pm #23821
Hello,

I would be grateful if you could help me in answering the following question:

How much of an issue is to have 8 points in a row in one side (lower side) of the mean of de Range chart (in a X-Bar, R Control Chart)?

Thank you

Rodders0July 20, 2006 at 7:30 pm #57033

Adam L BowdenParticipant@Adam-L-Bowden**Include @Adam-L-Bowden in your post and this person will**

be notified via email.Please refer to the following Western Electric Rules… Regards, Adam

_______________________________________________

The Western Electric Rules are general rules for detecting “out-of-control” or non-random conditions for data plotted on a run chart (plot of data as a function of time). Statistically calculated upper and lower control limits, when placed on a run chart, transform it into a control chart. The upper and lower control limits are located plus and minus 3 standard deviations respectively from the mean value or centerline of the plotted data. Locations of the data points and their trends with respect to the control limits and centerline value indicate whether or not a non-random signal in the data is present, with respect to the rules.

There are 5 basic rules with respect to how the data is situated on a control chart to indicate if it is not in statistical control (i.e. special causes of variation are present instead of random sources). These are as follows:Rule 1: Any single data point falls beyond 3 standard deviations from the centerline (i.e., any points fall outside of the upper or lower control limits);

Rule 2: Two out of three consecutive points fall beyond 2 standard deviations from the centerline, on the same side of the centerline;

Rule 3: Four out of five consecutive points fall beyond 1 standard deviation, on the same side of the centerline;

Rule 4: Eight consecutive points fall on the same side of the centerline;

Rule 5: Fifteen consecutive points fall within one standard deviation of the centerline.

If the data satisfy any of these conditions then it can be said that special cause(s) of variation in the data is present. Each of the rules has about the same probability of occurrence (approximately 3 in 1000). Another 6th rule is sometimes used, where if a trend of six consecutive points increasing or decreasing is observed then the data is also considered to exhibit non-random behavior.0July 21, 2006 at 7:21 am #57034Thanks for your reply.

I know and understand the rules you have posted. However, my original post regards the Range chart, not the “main control chart”.

Is your post saying that those rules are applied for both X-Bar and Range chart?

Thanks

Rodders0July 25, 2006 at 10:21 pm #57040yes. The values for (Rbar)D3 and (Rbar)D4 used to find the control limits in an r chart are derived from 3 times an estimated standard deviaiton, just like “main” control chart.

0July 26, 2006 at 8:37 am #57041the theory is all well and good, but you need to look at this more practically.Do you have an issue? Maybe maybe not, if all the 8 points were above the centre line then you probably would have because the variation within your subgroup would have increased. As all the data points are below the centre line things may be looking up. Have you made improvements or changes that would cause the variation within each subgroup to decrease, if yes then you should expect this change and it may be time to re-calculate your control limits. If not then are there other reasons this might have occurred, is the measuring equipment working properly and in the same way as before etc, etc.

The graphs are just telling you that something is unusual (3 in 1000 chance) it’s up to you to look at the practical problem and work out why and whether it’s an issue or not.0July 26, 2006 at 8:40 am #57042Thanks, appreciate your inputs.

the answer to my post is now “obvious” however, I do feel my brain freezes sometimes on simple (and sometimes not so simple) stats.

Thanks again

rodders0July 26, 2006 at 4:16 pm #57045Yes – good point.

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