Guard Banding and SPC

I'm working as a Quality Engineer for a company that already has a well-defined SPC Methodology, handed down from way up on high by someone who probably gets paid much more than me. They also wrote the original guidelines in a different language so I get to work from a translated copy.

The math they use for control limits is the same basic concept I've seen everywhere: estimate short term standard deviation, use the sample size to estimate populationSD from sampleSD, then draw lines 3 population standards above and below target.
3 * (sigmaST/sqrt(k))
where k is the number of samples in a subgroup from a given filler

But they also throw in an interesting feature they call “Sort Limits” that appear to want to function as some sort of guardband that detects if you have a process that is at risk of being outside specification but called good by the measurement system. Makes sense to me. But then the math they use to create that guard band is
(3.05 + (1.28/sqrt(k))) * sigmaST
where k is the number of samples in a subgroup from a given filler
1.28 kinda makes sense to me if they were looking to draw a z-score type line at 5% risk; but where does the 3.05 fit in, and why is it added they way it is with the sqrt of sample size only affecting the 1.28?

Throw in the fact that when you have a multi-nozzle filler system, they make the guardband
(3.05 * SigmaST) + ((1.28/sqrt(k))*SigmaXbar)
where k is the number of samples in a subgroup from a given nozzle and SigmaXBar is the standard deviation of all the subgroup averages in the study (we use that sigma instead of sigmaST to create control limits in these cases).

This makes me think they're trying to account for two types of error, and want to accept 5% risk on one error and 0.5% on the other. But if that's the case, why mash two standard deviations together instead of squaring, adding, and taking the square root to add the variances?

Anyone have any idea what they're trying to do here? I'd hate to have to work through a translator to pester our statistician if they're doing something obvious and I just can't recognize it.

7 Replies
Trish Borzon
1397 Posts

Hi @Benjamin Cremeens - Thanks for posting. While I have NO idea how to help you…I know a few members who might.

@Duke Okes , @Grace Duffy, @Steven Prevette , @Andre Kleyner - any suggestions?

Happy Holidays!


In my opinion, is they are trying to feel good by reacting to random noise.

It sounds like there is also an issue of not understanding the role of SPC versus the targets the process is dealing with. Simply being “in control” by the SPC chart rules (and does sound like an overly complex way of estimating 3 standard deviations, but let's assume that it works) does NOT imply you have a quality product with no actions required. A process may be stable AND making unacceptable product. An example is Dr. Deming's Red Bead Experiment (well worth viewing to understand what SPC is trying to accomplish). The Six Sigma folks came up with the answer that the targets should be six standard deviations from the center line. That does not mean we set the quality targets based upon the observed standard deviation. It means that we need to IMPROVE THE PROCESS such that the output variation is reduced such that the chanxe of exceeding the quality targets is very minimal (six sigma makes claims in the ppm range).

Bottom line - rather than creating TWO different action limits, one needs to do the following as they implement SPC:

Collect initial data. Plot the center line and control limits. Now look at the requirements for the process - the targets. Do the targets fall within the SPC control limits? Well then this is Common Cause Variation and we need to change the process such that it reliably gives us product that meets the specifications / targets. Now once the process is “capable” of obtaining reliable results, then the control chart rules help us detect when a change is occurring - and we need to act PRIOR to hitting the specifications.

This is a very short overview of SPC and its interactions with specifications. Most important - a process may be STABLE but INCAPABLE, STABLE and CAPABLE, or has a TREND (SPC SIgnal) which says it is heading in an improving direction (yeah!) or the wrong direction (OOPS how do we turn this around?).

Steve Prevette

ASQ CQE, Fellow; Southern Illinois University at Carbondale

Grace Duffy
107 Posts

Steve has the right idea. It may be that we are going too deep into the science and missing the intent. I am reminded of the Taguchi method. If you have a medium or mean, go for that. Don't get tied up in the expanse. Are we concerned with how wide the range is, or where the process mean is? I agree, get beyond the noise and find the signal.

Duke Okes
239 Posts

Personally I'd ask those responsible for establishing the rules, from a learning perspective. I've used translators multiple times and never found that to be a barrier. Developing a relationship with the group responsible could be beneficial from several angles.

Thanks. I reached out to the document owner and asked them to forward my Google translated questions to their resident stat nerd. I think the stat nerd was trying to do z-score based risk on the outside edges and made the same “let’s just smash standard devs together like they aren’t scalars“ mistakes that the Gage R&R people always do, then compounded that by handing the spreadsheet off to someone who had no understanding of stats whatsoever to write the other document.

(also, hey! Carbondale! I’m in Arkansas now but grew up in Equality giving lost tourists directions to Camel Rock every weekend.)

Dilip Shah
1 Posts

Guard banding is a concept with its roots in metrology. For an explanation of how it is used in making conformance decisions, it is best to refer to ILAC:G8:02/2019 guide which can be freely downloaded from the website on their publications page. The requirement for decision rules is mentioned in clause 7.8.6 of ISO/IEC 17025 standard and ILAC G8 document provides guidelines on how to implement it. The guideline is a great document that took two years to develop from worldwide participation of metrology professionals.

I hope this helps. ASQ's Measurement Quality Division is the Body of Knowledge holder for topics related to metrology and the membership includes many subject matter experts.
Dilip Shah

It looks like we want ILAC G8:09/2019 Guidelines on Decision Rules and Statements of Conformity of which I was not aware (thank you for pointing out this resource) which discusses guard banding extensively. I have not used it in SPC, although I have pointed out that the variation reflected by the control limits will include that from the gage as well as the process. If a measurement system analysis is performed, the two standard deviations can be isolated but this will not improve the power of the SPC charts to detect process shifts.

There is meanwhile a procedure for guard banding acceptance tests to minimize the total cost of accepting borderline nonconforming work, and rejecting borderline conforming work. This requires knowledge of both the process variation and gage variation. If the gage is assumed to return a normally-distributed result whose mean is the part's true measurement, this will work even if the quality characteristic does not follow the normal distribution. The double integral across each region (e.g. parts are good and the gage returns specification results) can be reduced to a single integral with the cumulative normal distribution and can be handled by numerical integration.

With regard to the original issue of SPC, though, the standard deviation upon which the control limits are based is the square root of (process variance + gage variance). Even if we know the gage variance, this does not help with the control limits although we can isolate the process variance for calculation of the process performance indices.