# X-Bar/Range Chart

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• #31336

Murray
Participant

How do you detect a shift in sigma using SPC rule #1 only within a 1 sample subgroup after the shift has occurred? Any help would be appreciated.

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#82494

Gabriel
Participant

Short:
Ussually, you don’t.
Long:
I don’t know which is #1 for you. Imagine the rule “7 points in a row above the average”. If you are sampling every hour, you will assume that the process become unstable before the first point of the row then you have at least 7 hours of lead time until you become aware. But anyway, SPC in general (and Xbar-R in particular) is intended to demonstrate unstability, and not stability. If an OOC signal shows, then it is very unlikely that it was only by chance, then you assume that a special cause is pressent. If no OOC signal shows, then you can say that you don’t have enough evidence to state, with the desired confidence, that a special cause is pressent.
Lets take the case of a process where the average has a shift upwards, and let’s consider the “1 point above the UCL” rule in an Xbar chart. Regardless of the subgroup size, that OOC signal will happen by chance only in 0.135% of the points. That’s a very low probability, so if you find it you assume that there something more than chance: a special cause, unstability. But let’s ask the question in the other way: Given that tha process average has actually shifted upwards, what is the probility of getting 1 point above the UCL in the first m points after the shift? That will deppend on the subgroup size (n), the magnitude of the shift (compared with the stable process variation, i.e. k times sigma) and m.
For exampe, with a shift of 0.5 sigmas (k=0.5) and subgroups of 3 parts (n=3) you have less than 2% of chance of finding the first point (m=1) above UCL, and even after m=20 points your chances of having found at least 1 point above the UCL are less than 30%. Even if your subgroup size is n=10 you have less than 8% of chance of finding the OOC signal in the first point after the shift, and after 20 points there is still a 20% of chance that you didn’t find even one piont above the UCL.
Now, if the shift goes to 1.5 sigmas (k=1.5), with subgroups of 3 you have a 34% of chance of getting the first point above the UCL and by the 15th point your chances are better than 99%. And if using subgroups of 10, you already have better than 99% of chance of geting at least one point above the UCL in the first 2 points, with better than 95% for the first point.
It is interesting to note that for a 0 sigmas shift (no shift, the process remains stable) you still have a chance of 0.13% of finding the first point above the UCL just because of random variation, and this chance goes to 2.7% for at least one point above the UCL in the first 20 points, or 5.3% if you include both “above UCL” abd “below LCL”. This is risk of a false alarm for the “1 point beyound cintrol limits” rule only and in the Xbar chart only. If you include all the 6 clasical rules and both the Xbar and the R charts the probabilities of a false alarm go way up. For example, if you used SPC sheets with 30 points and the process never went unstable, you would find about 1 out of 3 sheets showing 1 or more “false alarm” OOC signals either in the Xbar or R charts.

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#82499

Chip Hewette
Participant

Could you clarify what you mean by “shift in sigma?”  I’m unaware of a sigma value on the X-Bar/Range Chart.
If you are asking “how do I determine if what I did made a difference?” you may need to use another tool.  Charts are often slow to respond to experimentation.
If you have a long run chart showing X-bar and R-bar, from which you gather that the process sigma is estimated by R-bar / D2, this information can be used to see if you have effected a meaningful change.  However, experiments are best used with replication within the experiment to determine control limits for the effects.
If you are asking “how do I know if moving the control knob on my process made a difference using a control chart?” one has to make judgments.  Are the parts within external customer specification?  Are the parts in conformance with contractual requirements?  Can the machine (process) run safely at the new setting?  If so, one can practice an evolutionary approach by slowing changing the process knob.  Do a search on EVOP to learn more about this technique.  You won’t be able to prove a difference occurred within one subgroup, but you will over time.

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#82504

Gabriel
Participant

Chip: Typical SPC for variable data includes 2 charts. 1 for position (Xbar, median or individuals) and 1 for spread (R, s or mooving R). So a shift in sigma can be observed in the chart for spread, i.e. the R chart in an Xbar/R chart. As you said, however, the chart might take long until it displays an OOC signal because of that shift in sigma.

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#82508

Chip Hewette
Participant

I was just seeking to clarify the original question with my statement that a value for sigma is not on the X-Bar / Range chart.  It is not calculated from a single subgroup on this type of chart.  I am aware of the two graphs on X-Bar and Range charts.

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#82513

Hemanth
Participant

Hi
Supporting what Gabriel explained. You can actually see this work with the help of this SPC simulator..
http://www.symphonytech.com/quincunx.htm

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#82516

Sean Stephan
Member

If you have one subgroup you should not be using a x-bar /r chart. Use Individual moving range because it is meant for individual measurements with one subgroup.
I agree with Chip that if you want to see if you have improved a process you should use another tool such as T-test or Anova or a capability histogram of before process improvement and after process improvement. In mintab, it gives you the Z-score short term & long term, % defective to the Spec limits, the mean , sigma of the process, etc. This analysis can give you great information to see if you made a difference.

Sean Stephan, BB

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