# Is it Time for New Rules for SPC (Statistical Process Control)?

## Modernize the SPC Rules?

• ### No, the current rules work well enough

• Total voters
15
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#### Tim Folkerts

Super Moderator
Walter Shewhart introduced control charts 80 years ago, when computers were unheard of and all plotting and searching for out-of-control (OOC) situations had to be done by hand. He was pragmatic in his approach to statistics, creating simple, almost foolproof tests like "1 point beyond the 3 sigma limit". The rules for detecting OOC have gotten a little more sophisticated (e.g. "4 oout of 5 point more that 1 st dev from center line on one side), but they can still be done by a person looking at a paper chart.

In the end, the goal was to detect 1) changes in the mean or 2) changes in variation. Well, in this era, specific tests for these quantities (e.g. T-Tests and F-Tests) can be cranked out be computer in no time. Why not switch over to rules that are based on specific statistical tests?

PROS of the statistical approach:

* more accurately detects shifts in mean or st. dev.
* easy to adjust the sensitivity. If you wanted fewer false positives, you adjust a parameter in the program, rather that trying to create rules like "3 of 5 points more than 2 sigma from the center" to replace than the standard "2 of 3 points more than 2 sigma from the center".
* It solves the question asked recently about handling points that are on the 1,2, or 3 sigma lines. Before it made a big difference whether the point was 2.99 sigma or 3.01 sigma from the center; now it is a small change in a calculation.
* currently, many people skip many of the tests, so they miss opportunities to detect smaller shifts.

CONS:

* Requires a computer. The calculations involved would be completely impractical without specialized software (although even Excel could be set up to do the testing). On the other hand, I doubt many people calculate control limits by hand even now, so the requirement of a computer & special software is not really new.
* The rules are not easily explained to non-statisticians, so it is less intuitive. You can't draw a dot on a chart and check by eye for OOC rules.
* The system is not familiar, so it might be hard to convince customers (or even your own boss) to use something new.

To me (being mathematically inclined) the greater accuracy & flexibility of the more mathematical system outweigh the simplicity of the more intuitive system. A quick look using Excel and random data indicates that the new system is indeed better at spotting OOC conditions.

Any other thoughts??? Would it be valuable to have a system that is better at finding OOC situations, or is the current system good enough?

Tim F

#### Jim Wynne

Staff member
I voted in favor of the "old" system, which in fact includes any sort of statistical tools one might choose to use. The idea behind statistical analysis in manufacturing is the same as in any other endeavor; statistics is used to prove a point or validate a hypothesis, and that proof* or validation should abide by Occam's Razor--one should not increase, beyond what's necessary, the number of entities required to explain something. Another way of expressing the Razor is that the simplest answer is almost always the best one. If that means that Shewhart control charts are appropriate, then they should be used, and if some other method is more amenable to the desired result, no one should feel obligated to use Shewhart charts.

*"Proof" is used here in the sense of "preponderance of evidence," and not "irrefutable fact."

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Ahhh...but SPC is not about showing that two means or variances are different as would a t-test or F-test. It was established to look at "trends" in the data. SPC is more about sampling statistics than any other statistics. What Shewhart did was proposed a method to ask, does this data point come from the "population" of possible observations.

If you look at using either a z-test or t-test, your limits will be much wider than control limits.

Having said that, I do not think that all the rules for determining out of control should be implemented simultaneously. I used 3 basic rules.

1. Out of 3S limits
2. A run of 8 points above or below the center line
3. A run of eight points that are either all increasing or all decreasing.

Just my \$0.02

#### Wes Bucey

##### Prophet of Profit
I have to think about my response to the poll a little bit more, but I have an observation.

We all laugh or at least smirk when we hear the term "close enough for government work." The reason for the smirk is that we know an overwhelming majority of decisions are made on the basis of
"good enough"
versus
"as close to the perfect ideal as possible."

Similarly, the overwhelming majority of control charts are maintained to keep the system "good enough." Very few organizations have a systemic system of initiating DOE unless some crisis triggers a quest for a better way.

Some (many?) folks faced with instant feedback of data find themselves rerunning a Funnel Experiment where they continually tinker with setups and target points because they ignore the concept of individual variation of a system and try to narrow the variation beyond the ability of the system to comply. (Try as one might, it is next to impossible to adjust a 50 year old Brown & Sharpe lathe to hold plus or minus one ten thousandth of an inch (1/10,000) tolerance consistently!)

I tend to agree with Jim (JSW) in letting the existing system muddle along while those with high powered equipment, automatic data collection and computers to analyze and adjust systems go the extra mile (in other words, let the control system fit the equipment and the need, rather than try to upgrade all control charts to "state of the art" statistical glory.)

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Statistical Steven said:
Ahhh...but SPC is not about showing that two means or variances are different as would a t-test or F-test. It was established to look at "trends" in the data.
Yes - SPC was never intended to be a hypothesis test. in fact you lose a lot of insight and accuracy of decision when using the hypothesis test approach over the traditional SPC approach.

I have founf that there is far more power in looking at the data in the trend line than can come from any statistics that might be applied to the data.

B

#### Brian Myers

Right tools int he right hands...

To me SPC is "statistics for the shop floor". In other words, give the operators, maintainence, and supervisors a tool they can use to help the overloaded QA/QC folks keep those machines in control. To be this tool, SPC is intentionally easy to explain, easy to implement, and easy to interpret.

Leave the fancy statistical stuff to the QA/QC folks.

Besides, Deming disliked Anova, t-tests, confidence intervals, and other statistical techniques because they "provide no basis for prediction and because they bury the information contained in the order of production".

I have seen this in action. The t-tests and confidence intervals showed nothing useful, but the raw data (run data) showed very clear trends and indicated the source of the issue very clearly. I learned from experience to carefully monitor how data is filtered and grouped. Anytime you distill a large amount of data down to a few "key" statistics, you run a great risk of losing valuable information.

SPC for manufacturing, Higher Statistical Methods for Design. QA/QC has to be able to "play" in both worlds equally adroitly.

Brian

#### Tim Folkerts

Super Moderator
JSW05 said:
...Occam's Razor--one should not increase, beyond what's necessary, the number of entities required to explain something. Another way of expressing the Razor is that the simplest answer is almost always the best one. If that means that Shewhart control charts are appropriate, then they should be used, and if some other method is more amenable to the desired result, no one should feel obligated to use Shewhart charts.
I hadn't thought about it from the perspective of Occam's Razor, but that is a good insight.

You suggest that we are free to choose alternative to Shewhart's rules, but I would argue that there are really no alternatives at the moment. What SPC system is there that doesn't start with "1 pt outside 3 sigma"?

Besides, are the current rules really that simple? There are 8 rules listed in Minitab and I'm sure there are others. The rules themselves seem arbitrary and the choice of which rules people actually use is often arbitrary. Lots of arbitrary rules is the antithesis of Occam's Razor.

Bev D said:
Yes - SPC was never intended to be a hypothesis test. in fact you lose a lot of insight and accuracy of decision when using the hypothesis test approach over the traditional SPC approach.
But aren't the current rules simply crude hypothesis tests anyway?
• 1 pt +/- 3 sigma
= test for a large shift in mean
• 2 of 3 pts +/- 2 sigma
= test for a moderate shift in mean, or a shift in sigma
• 8 pts all on one side
= test for small shift in mean
• 15 pts within +/- sigma
= test for decreases in sigma
• ...
And all the rules suffer from the problem that no one really knows what sort of confidence the rules provide with detecting what sort of changes.

I have found that there is far more power in looking at the data in the trend line than can come from any statistics that might be applied to the data.
But as Steve Prevette has indicated (particularly in his "Lies, ****ed Lies, and Statistics), it it easy to misinterpret data. Of course you & I would never do that , but those less knowledgeable in the ways of statistics might.

Statistical Steven said:
What Shewhart did was proposed a method to ask, does this data point come from the "population" of possible observations.
But isn't one of the simplest ways to determine if a set of points comes from the same population to perform the tests that tell you if there has been a significant change in either the mean of the standard deviation?

If you look at using either a z-test or t-test, your limits will be much wider than control limits.
I don't think so. And anyway, control limits are rather arbitrary. Why artificially draw a lines at 1,2,3 sigma? Why not every 0.5 sigma? Or 0.67 sigma? Instead, why not "draw the lines" at some known statistical level like "look for a shift in mean or in sigma that would only occur by random 0.3% of the time"?

The rules I would propose would run something like this. Flag the result of any test that would occur less that 1/1000 times (or a similar small number) for:
• 1 point (to detect drastic changes)
• 3 pts with a new mean (to detect large changes)
• 10 pts with a new mean (to detect medium changes)
• 30 pts with a new mean (to detect small changes)
• 3 pts with a new sigma (to detect large changes)
• 10 pts with a new sigma (to detect medium changes)
• 30 pts with a new sigma (to detect small changes)
• 10 pts with a non-zero slope (to detect trends)
Granted, the exact interpretation of probabilities depends on the distribution. Still, there is at least a specific, rational choice in the tests and the interpretation.

Tim Folkerts

#### Jim Wynne

Staff member
Tim Folkerts said:
You suggest that we are free to choose alternative to Shewhart's rules, but I would argue that there are really no alternatives at the moment. What SPC system is there that doesn't start with "1 pt outside 3 sigma"?
What I was suggesting is that we are free to determine the statistical methods that best fit the case at hand, whether that be Shewhart charts and the WECO rules, or some other method. We should also feel free to suggest alternatives to customers who normally expect x-bar/r charts, although I realize that some customers would rather see a well-constructed fudged control chart than have to think about something else.

Tim Folkerts said:
Besides, are the current rules really that simple? There are 8 rules listed in Minitab and I'm sure there are others. The rules themselves seem arbitrary and the choice of which rules people actually use is often arbitrary. Lots of arbitrary rules is the antithesis of Occam's Razor.
No, the choice of rule application should be guided by the Razor. We know, for instance, that it's dangerous to apply the rules on top of one another. Far from arbitrary, the rules are based on probability of occurrence, and tell us when to suspect that something might be amiss.

#### Tim Folkerts

Super Moderator
JSW05 said:
No, the choice of rule application should be guided by the Razor. We know, for instance, that it's dangerous to apply the rules on top of one another.
I agree in principle, but is that how most people choose which rules to use? My unsystematic observations are that most people pick a few rules that "seem" right to them. I doubt many people really think about the statistical implications of using particular rules, let alone think about particular combinations.

Far from arbitrary, the rules are based on probability of occurrence, and tell us when to suspect that something might be amiss.
What I am proposing is basically to bring those probabilities out into the open, and make them more robust. A rule like "2 of 3 pts at least 2 sigma out" is an approximation for a more precise rule. Consider the following sets of three consecutive points on an I-chart or X-bar chart (measured in standard deviations from the center):
• 2.9, 1.9, 1.9
• 2.1, 1.9, 1.9
• 2.1, 2.1, 0.5
I'll bet by any statistical test (and just about everyone's intuition), these are in order of "unusualness", but by SPC rules, only the least "unusual" will trigger the alarm.

Since the computing power is now easily available, why not use a more accurate test? Why be restricted to an oversimplification of the "true" rule?

Tim F

#### Tim Folkerts

Super Moderator
Brian Myers said:
To me SPC is "statistics for the shop floor". In other words, give the operators, maintainence, and supervisors a tool they can use to help the overloaded QA/QC folks keep those machines in control. To be this tool, SPC is intentionally easy to explain, easy to implement, and easy to interpret.
To me, this is probably the biggest reason not to change. The current system can be used well enough with minimal train and minimal statistical expertise. For small operations, a fancy system may be overkill, in the same way an expensive robotic system would be overkill for a 3 person machine shop.

Besides, Deming disliked Anova, t-tests, confidence intervals, and other statistical techniques because they "provide no basis for prediction and because they bury the information contained in the order of production".
I'm trying to get the best of both worlds. By recalculating t-tests after every new point, my system maintains information about the run order. The information about unusual t-test results is immediately available, just the same way the information from an unusual "8 in a row on the same side" test is available immediately.

Tim F

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