# 3 standard error control limits 1.5 sigma shift

Six Sigma – iSixSigma Forums Old Forums General 3 standard error control limits 1.5 sigma shift

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• #68791

denton
Participant

The Minitab Xbar and R calculation compares the change in the mean vs. local variation, as measured by subgroup range.  This is the appropriate way to do it.  The purpose of a Control Chart is to test whether your process has really changed, vs. whether the change in the subgroup mean can be attributed to random variation.  If you have a 1.5 sigma shift, you want your Control Chart to detect it.
The 1.5 sigma shift is generally connected to Process Capability, rather than Control Charts, and many of us believe that it doesn’t really belong there, either.

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#27852

Patrick
Participant

I have been using Minitab to calculate control limits for X-bar & R charts, but have noticed that it only uses short term standard deviation to calculate the 3 standard error limits. Is it more appropriate to use the long term standard deviation to calculate control limits, especially since the process will shift approx 1.5 sigma over time, or is it better to recalculate the limits as you go.
Any ideas
Patrick

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#68793

Cone
Participant

Use short term sigma for control limits and recalculate control limits only when you have evidence and root cause for a process improvement.
The alledged 1.5 sigma shift does not exist when SPC rules are followed. The shift can be controlled to less than .5 sigma and it is easy to prove that.
Gary

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#68802

Ken Myers
Participant

Patrick,
You never want to use the total or long-term standard deviations to compute the control limits on process control charts.  If you do, as the others above suggest, all plotted values will always be found within the control limits.  Since changes are observed when values exceed these limits the control charts are rendered useless in signaling process change.
Ken

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#68825

Jim Parnella
Participant

Patrick,
Denton, Gary and Ken are absolutely correct – use the short-term variability for your control chart limits.

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#68829

Schmidt
Participant

In establishing control chart limits, the practitioner should always refer back to the basic intent of control charting, that is, to detect significant, non-random changes in the etablished inherent and acceptable variations of a process.
Thus, the practitioner’s knowledge of the process and the sources of the process’s inherent variations should guide him on how to measure these inherent variations. Once the practitioner has quantified the inherent variations in terms of a particular sigma. The simple 3-sigma limits are the appropriate limits that should be applied in detecting significant and non random changes.
The 1.5 sigma shift has no place in control charting.

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#68830

TomF
Member

Hi,
I completely agree that the 1.5 “shift” needlessly adds confusion to the calculation and understanding of “sigma”–the Six Sigma metric.
I think that the word “shift” is misleading.  I think that they had intended to use the word drift.
A process may drift within +/- 1.5 standard deviations (I am defining standard deviation as the standard deviation of individual measurements) without any signals on a SPC chart.  If you use a subgroup n=5, then then Average Run Length is 4.5 subgroups.  In other words, it will take on average 4.5 subgroups to detect that a process has shifted by 1 standard deviation by having a datapoint go outside the control limits.  Of course, this does not take into account the Western Electric Rules.  However, the Average Run Length is only 1.6 subgroups to detect a shift of 1.5 standard deviations.  These numbers are higher if your subgroup size is smaller.
If your process is constantly drifting within this  +/- 1.5 standard deviations area, it is possible that you will not see any out of control subgroups.
While I view including a 1.5 sigma shift into any capability calculation as non-value added, the X bar and R control charts may allow the process to drift within a band of 1.5 standard deviations.  However, if there is a one-time shift of 0.5 standard deviations, then the control chart will eventually detect it.
Hope this clarifies where the 1.5 “shift” came from.
TomF

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#68831

Patrick
Participant

All,
thanks for helping to clear up this one
rgds,
Patrick

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#68853

Cone
Participant

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#68876

TomF
Member

The Average Run Lengths are based upon control chart theory.  There is no data in developing the Average Run Lengths.  These were not empirically derived.
The distance from the new shifted mean to the control limit is
(3- t * sqrt(n)) * sigma x bar
where t = the amount of shift in population sigma, n = subgroup size and sigma x bar = the theoretical standard deviation of the averages.
Using the calculated distance above as a Z score, the probability on detecting a shift in the first subgroup is 1 minus the probability of the above Z score.   Lets call this probability Pd.
The probability for the first subgroup detecting the shift is
Prob1 = 1- Pd.
The probability for the second subgroup detecting the shift is
Prob2 = (1 – Pd)*Pd
The probability for the third subgroup is
Prob3 = (1 – Pd)*(1 – Pd)*Pd
The Expected Value is the Average Run Length.  You can do the mathmatical manipulation, but the simplified formula is
Average Run Length = 1/Pd
Hope this helps.  It is hard to explain when you’re limited to text only.

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#68884

Cone
Participant

My statement was not about average run length calculations, I know about the calculations and accept the work done on this at least 50 years ago.
My statement is the quoting of processes shifting 1.5 sigma as a given. It simply is not true. Using SPC rules as defined by Shewhart over 70 years ago will give much less. Our friends at Toyota and Nippondenso know how to get much much less on almost everything they do without using SPC as defined by Shewhart. In fact most true implementers of SMED (yes they really do mean single digit minutes from last good part to first good part) and rational tool change policy get much less. The 1.5 sigma shift is a good tool for the sloppy way most Western companies run their processes. Their engineers and technicians are not expected to truely know their process, they are not required to have a good knowledge transfer mechanism in place. They do not train their workers. For this, putting a goal of limiting their shift to ONLY 1.5 represents tremendous improvement.
1.5 shift is not some law of nature, it is only a step in the right direction. The good process management companies do much, much better.

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#68885

TomF
Member

Hi Gary,
The 1.5 sigma shift is a worst case estimate of the drift in the mean.  I agree that improvements can be made to improve centering the process.  CUSUM charts come to mind as just one option.
I must plead ignorance.  I am not familiar with the acronym SMED.  Can you enlighten me?
Thanks.

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#68886

Cone
Participant

SMED – Single Minute Exchange of Die. Read the book by Shingo. It is generally put under the heading of Lean tools but to truely achieve a quick change over you not only have to do it quickly, you have to know how to take your tools directly to target, not measure and adjust to target.
Again, I would tell you that 1.5 sigma is not worst case, it is just better than we normally see. Doing better just requires process knowledge and trained workers.

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#68892

TomF
Member

Thanks Gary,